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Universality in the emergence of oscillatory instabilities in turbulent flows

2020-02-24
Induja Pavithran , Vishnu R. Unni , Alan John Varghese +4 more
Spontaneous emergence of periodic oscillations due to self-organization is ubiquitous in turbulent flows. The emergence of such oscillatory instabilities in turbulent fluid mechanical systems is often studied in different system-specific … Spontaneous emergence of periodic oscillations due to self-organization is ubiquitous in turbulent flows. The emergence of such oscillatory instabilities in turbulent fluid mechanical systems is often studied in different system-specific frameworks. We uncover the existence of a universal scaling behaviour during self-organization in turbulent flows leading to oscillatory instability. Our experiments show that the spectral amplitude of the dominant mode of oscillations scales inversely with the Hurst exponent of a fluctuating state variable following an inverse power law relation. Interestingly, we observe the same power law behaviour with a constant exponent near -2 across various turbulent systems such as aeroacoustic, thermoacoustic and aeroelastic systems.
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Universality in spectral condensation

2020-10-15
Induja Pavithran , Vishnu R. Unni , Alan John Varghese +6 more
Abstract Self-organization is the spontaneous formation of spatial, temporal, or spatiotemporal patterns in complex systems far from equilibrium. During such self-organization, energy distributed in a broadband of frequencies gets condensed … Abstract Self-organization is the spontaneous formation of spatial, temporal, or spatiotemporal patterns in complex systems far from equilibrium. During such self-organization, energy distributed in a broadband of frequencies gets condensed into a dominant mode, analogous to a condensation phenomenon. We call this phenomenon spectral condensation and study its occurrence in fluid mechanical, optical and electronic systems. We define a set of spectral measures to quantify this condensation spanning several dynamical systems. Further, we uncover an inverse power law behaviour of spectral measures with the power corresponding to the dominant peak in the power spectrum in all the aforementioned systems.
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Abrupt transitions in turbulent thermoacoustic systems

2022-11-30
Ramesh S. Bhavi , Induja Pavithran , Amitesh Roy +1 more
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Effect of rate of change of parameter on early warning signals for critical transitions

2021-01-01
Induja Pavithran , R. I. Sujith
Many dynamical systems exhibit abrupt transitions or tipping as the control parameter is varied. In scenarios where the parameter is varied continuously, the rate of change of the control parameter … Many dynamical systems exhibit abrupt transitions or tipping as the control parameter is varied. In scenarios where the parameter is varied continuously, the rate of change of the control parameter greatly affects the performance of early warning signals (EWS) for such critical transitions. We study the impact of variation of the control parameter with a finite rate on the performance of EWS for critical transitions in a thermoacoustic system (a horizontal Rijke tube) exhibiting subcritical Hopf bifurcation. There is a growing interest in developing early warning signals for tipping in real systems. First, we explore the efficacy of early warning signals based on critical slowing down and fractal characteristics. From this study, lag-1 autocorrelation (AC) and Hurst exponent (H) are found to be good measures to predict the transition well before the tipping point. The warning time, obtained using AC and H, reduces with an increase in the rate of change of the control parameter following an inverse power law relation. Hence, for very fast rates, the warning time may be too short to perform any control action. Furthermore, we report the observation of a hyperexponential scaling relation between the AC and the variance of fluctuations during such a dynamic Hopf bifurcation. We construct a theoretical model for noisy Hopf bifurcation wherein the control parameter is continuously varied at different rates to study the effect of rate of change of the parameter on EWS. Similar results, including the hyperexponential scaling, are observed in the model as well.
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Extreme COVID-19 waves reveal hyperexponential growth and finite-time singularity

2022-04-01
Induja Pavithran , R. I. Sujith
Coronavirus disease 2019 (COVID-19) has rapidly spread throughout our planet, bringing human lives to a standstill. Understanding the early transmission dynamics of a wave helps plan intervention strategies such as … Coronavirus disease 2019 (COVID-19) has rapidly spread throughout our planet, bringing human lives to a standstill. Understanding the early transmission dynamics of a wave helps plan intervention strategies such as lockdowns that mitigate further spread, minimizing the adverse impact on humanity and the economy. Exponential growth of infections was thought to be the defining feature of an epidemic in its initial growth phase. Here we show that, contrary to common belief, early stages of extreme COVID-19 waves have an unbounded growth and finite-time singularity accompanying a hyperexponential power-law. The faster than exponential growth phase is hazardous and would entail stricter regulations to minimize further spread. Such a power-law description allows us to characterize COVID-19 waves better using single power-law exponents, rather than using piecewise exponentials. Furthermore, we identify the presence of log-periodic patterns decorating the power-law growth. These log-periodic oscillations may enable better prediction of the finite-time singularity. We anticipate that our findings of hyperexponential growth and log-periodicity will enable accurate modeling of outbreaks of COVID-19 or similar future outbreaks of other emergent epidemics.
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Emergence of order from chaos through a continuous phase transition in a turbulent reactive flow system

2024-06-20
Sivakumar Sudarsanan , Amitesh Roy , Induja Pavithran +2 more
As the Reynolds number is increased, a laminar fluid flow becomes turbulent, and the range of time and length scales associated with the flow increases. Yet, in a turbulent reactive … As the Reynolds number is increased, a laminar fluid flow becomes turbulent, and the range of time and length scales associated with the flow increases. Yet, in a turbulent reactive flow system, as we increase the Reynolds number, we observe the emergence of a single dominant timescale in the acoustic pressure fluctuations, as indicated by its loss of multifractality. Such emergence of order from chaos is intriguing. We perform experiments in a turbulent reactive flow system consisting of flame, acoustic, and hydrodynamic subsystems interacting nonlinearly. We study the evolution of short-time correlated dynamics between the acoustic field and the flame in the spatiotemporal domain of the system. The order parameter, defined as the fraction of the correlated dynamics, increases gradually from zero to one. We find that the susceptibility of the order parameter, correlation length, and correlation time diverge at a critical point between chaos and order. Our results show that the observed emergence of order from chaos is a continuous phase transition. Moreover, we provide experimental evidence that the critical exponents characterizing this transition fall in the universality class of directed percolation. Our paper demonstrates how a real-world complex, nonequilibrium turbulent reactive flow system exhibits universal behavior near a critical point.
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Tipping in complex systems under fast variations of parameters

2023-08-01
Induja Pavithran , P. R. Midhun , R. I. Sujith
Abrupt changes in the state of a system are often undesirable in natural and human-made systems. Such transitions occurring due to fast variations of system parameters are called rate-induced tipping … Abrupt changes in the state of a system are often undesirable in natural and human-made systems. Such transitions occurring due to fast variations of system parameters are called rate-induced tipping (R-tipping). While a quasi-steady or sufficiently slow variation of a parameter does not result in tipping, a continuous variation of the parameter at a rate greater than a critical rate results in tipping. Such R-tipping would be catastrophic in real-world systems. We experimentally demonstrate R-tipping in a real-world complex system and decipher its mechanism. There is a critical rate of change of parameter above which the system undergoes tipping. We discover that there is another system variable varying simultaneously at a timescale different from that of the driver (control parameter). The competition between the effects of processes at these two timescales determines if and when tipping occurs. Motivated by the experiments, we use a nonlinear oscillator model, exhibiting Hopf bifurcation, to generalize such type of tipping to complex systems where multiple comparable timescales compete to determine the dynamics. We also explain the advanced onset of tipping, which reveals that the safe operating space of the system reduces with the increase in the rate of variations of parameters.
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Explosive synchronization in a turbulent reactive flow system

2024-02-01
Amal Joseph , Induja Pavithran , R. I. Sujith
The occurrence of abrupt dynamical transitions in the macroscopic state of a system has received growing attention. We present experimental evidence for abrupt transition via explosive synchronization in a real-world … The occurrence of abrupt dynamical transitions in the macroscopic state of a system has received growing attention. We present experimental evidence for abrupt transition via explosive synchronization in a real-world complex system, namely, a turbulent reactive flow system. In contrast to the paradigmatic continuous transition to a synchronized state from an initially desynchronized state, the system exhibits a discontinuous synchronization transition with a hysteresis. We consider the fluctuating heat release rate from the turbulent flames at each spatial location as locally coupled oscillators that are coupled to the global acoustic field in the confined system. We analyze the synchronization between these two subsystems during the transition to a state of oscillatory instability and discover that explosive synchronization occurs at the onset of oscillatory instability. Further, we explore the underlying mechanism of interaction between the subsystems and construct a mathematical model of the same.
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Early warnings of tipping in a non-autonomous turbulent reactive flow system: Efficacy, reliability, and warning times

2024-01-01
Ankan Banerjee , Induja Pavithran , R. I. Sujith
Real-world complex systems such as the earth's climate, ecosystems, stock markets, and combustion engines are prone to dynamical transitions from one state to another, with catastrophic consequences. State variables of … Real-world complex systems such as the earth's climate, ecosystems, stock markets, and combustion engines are prone to dynamical transitions from one state to another, with catastrophic consequences. State variables of such systems often exhibit aperiodic fluctuations, either chaotic or stochastic in nature. Often, the parameters describing a system vary with time, showing time dependency. Constrained by these effects, it becomes difficult to be warned of an impending critical transition, as such effects contaminate the precursory signals of the transition. Therefore, a need for efficient and reliable early-warning signals (EWSs) in such complex systems is in pressing demand. Motivated by this fact, in the present work, we analyze various EWSs in the context of a non-autonomous turbulent thermoacoustic system. In particular, we investigate the efficacy of different EWS in forecasting the onset of thermoacoustic instability (TAI) and their reliability with respect to the rate of change of the control parameter. This is the first experimental study of tipping points in a non-autonomous turbulent thermoacoustic system. We consider the Reynolds number (Re) as the control parameter, which is varied linearly with time at finite rates. The considered EWSs are derived from critical slowing down, spectral properties, and fractal characteristics of the system variables. The state of TAI is associated with large amplitude acoustic pressure oscillations that could lead thermoacoustic systems to break down. We consider acoustic pressure fluctuations as a potential system variable to perform the analysis. Our analysis shows that irrespective of the rate of variation of the control parameter, the Hurst exponent and variance of autocorrelation coefficients warn of an impending transition well in advance and are more reliable than other EWS measures. Additionally, we show the variation in the warning time to an impending TAI with rates of change of the control parameter. We also investigate the variation in amplitudes of the most significant modes of acoustic pressure oscillations with the Hurst exponent. Such variations lead to scaling laws that could be significant in prediction and devising control actions to mitigate TAI.
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Imprints of log-periodicity in thermoacoustic systems close to lean blowout

2023-02-28
Ankan Banerjee , Induja Pavithran , R. I. Sujith
In the context of statistical physics, critical phenomena are accompanied by power laws having a singularity at the critical point where a sudden change in the state of the system … In the context of statistical physics, critical phenomena are accompanied by power laws having a singularity at the critical point where a sudden change in the state of the system occurs. In this work we show that lean blowout (LBO) in a turbulent thermoacoustic system is accompanied by a power law leading to finite-time singularity. As a crucial discovery of the system dynamics approaching LBO, we unravel the existence of the discrete scale invariance (DSI). In this context, we identify the presence of log-periodic oscillations in the temporal evolution of the amplitude of the dominant mode of low-frequency oscillations (A_{f}) existing in pressure fluctuations preceding LBO. The presence of DSI indicates the recursive development of blowout. Additionally, we find that A_{f} shows a faster-than-exponential growth and becomes singular when blowout occurs. We then present a model that depicts the evolution of A_{f} based on log-periodic corrections to the power law associated with its growth. Using the model, we find that blowouts can be predicted even several seconds earlier. The predicted time of LBO is in good agreement with the actual time of occurrence of LBO obtained from the experiment.
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Extreme COVID-19 waves reveal hyperexponential growth and finite-time singularity

2021-10-20
Induja Pavithran , R. I. Sujith
Abstract Coronavirus disease 2019 (COVID-19) has rapidly spread throughout our planet, bringing human lives to a standstill. Understanding the early transmission dynamics helps plan intervention strategies such as lockdowns that … Abstract Coronavirus disease 2019 (COVID-19) has rapidly spread throughout our planet, bringing human lives to a standstill. Understanding the early transmission dynamics helps plan intervention strategies such as lockdowns that mitigate further spread, minimizing the adverse impact on humanity and the economy 1–3 . Exponential growth of infections was thought to be the defining feature of an epidemic in its initial growth phase 4–7 ; any variation from an exponential growth was described by adjusting the parameters of the exponential model 7,8 . Here, we show that, contrary to common belief, early stages of extreme COVID-19 waves display an unbounded growth and finite-time singularity accompanying a hyperexponential power-law. The faster than exponential growth phase is hazardous and would entail stricter regulations. Such a power-law description allows us to characterize COVID-19 waves with single power-law exponents, better than piece-wise exponentials. Furthermore, we identify the presence of log-periodic patterns decorating the power-law growth. These log-periodic oscillations may enable better prediction of the finite-time singularity. We anticipate that our findings of hyperexponential growth and log-periodicity will help model the COVID-19 transmission more accurately.
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Imprints of log-periodicity in thermoacoustic systems close to lean blowout

2022-01-01
Ankan Banerjee , Induja Pavithran , R. I. Sujith
In the context of statistical physics, critical phenomena are accompanied by power laws having a singularity at the critical point where a sudden change in the state of the system … In the context of statistical physics, critical phenomena are accompanied by power laws having a singularity at the critical point where a sudden change in the state of the system occurs. In this work, we show that lean blowout (LBO) in a turbulent thermoacoustic system can be viewed as a critical phenomenon. As a crucial discovery of the system dynamics approaching LBO, we unravel the existence of the discrete scale invariance (DSI). In this context, we identify the presence of log-periodic oscillations in the temporal evolution of the amplitude of dominant mode of low-frequency oscillations $(A_f)$ exist in pressure fluctuations preceding LBO. The presence of DSI indicates the recursive development of blowout. Additionally, we find that $A_f$ shows a faster than exponential growth and becomes singular when blowout occurs. We then present a model that depicts the evolution of $A_f$ based on log-periodic corrections to the power law associated with its growth. Using the model, we find that blowout can be predicted even several seconds earlier. The predicted time of LBO in good agreement with the actual time of occurrence of LBO obtained from the experiment.
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Tipping in complex systems under fast variations of parameters

2022-01-01
Induja Pavithran , P. R. Midhun , R. I. Sujith
Sudden transitions in the state of a system are often undesirable in natural and human-made systems. Such transitions under fast variation of system parameters are called rate-induced tipping. We experimentally … Sudden transitions in the state of a system are often undesirable in natural and human-made systems. Such transitions under fast variation of system parameters are called rate-induced tipping. We experimentally demonstrate rate-induced tipping in a real-world complex system and decipher its mechanism. There is a critical rate of change of parameter above which the system undergoes tipping. We show that another system parameter, not under our control, changes simultaneously at a different rate, and the competition between the effects of that parameter and the control parameter determines if and when tipping occurs. Motivated by the experiments, we use a nonlinear oscillator model exhibiting Hopf bifurcation to generalize this tipping to complex systems in which slow and fast parameters compete to determine the system dynamics.
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Early warnings of tipping in a non-autonomous turbulent reactive flow system: efficacy, reliability, and warning times

2023-01-01
Ankan Banerjee , Induja Pavithran , R. I. Sujith
Real-world complex systems such as the climate, ecosystems, stock markets, and combustion engines are prone to dynamical transitions from one state to another, with catastrophic consequences. State variables of such … Real-world complex systems such as the climate, ecosystems, stock markets, and combustion engines are prone to dynamical transitions from one state to another, with catastrophic consequences. State variables of such systems often exhibit aperiodic fluctuations, either chaotic or stochastic in nature. Often, the parameters describing a system vary with time, showing time dependency. Constrained by these effects, it becomes difficult to be warned of an impending critical transition, as such effects contaminate the precursory signals of the transition. Therefore, a need for efficient and reliable early-warning signals (EWS) in such complex systems is in pressing demand. Motivated by this fact, in the present work, we analyze various EWS in the context of a non-autonomous turbulent thermoacoustic system. In particular, we investigate the efficacy of different EWS in forecasting the onset of thermoacoustic instability (TAI) and their reliability with respect to the rate of change of the control parameter. We consider the Reynolds number (Re) as the control parameter, which is varied linearly with time at finite rates. The considered EWS are derived from critical slowing down, spectral properties, and fractal characteristics of the system variables. The state of TAI is associated with large amplitude acoustic pressure oscillations that could lead thermoacoustic systems to break down. Our analysis shows that irrespective of the rate of variation of the control parameter, the Hurst exponent and variance of autocorrelation coefficients warn of an impending transition well in advance and are more reliable than other EWS measures. We also investigate the variation of amplitudes of the most significant modes of acoustic pressure oscillations with the Hurst exponent. Such variations lead to scaling laws which could be significant in prediction and devising control actions to mitigate TAI.
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Frequency shifts during whistling occurs as transition between two phase synchronised limit cycles via a state of intermittency or abruptly

2023-01-01
Ramesh S. Bhavi , Induja Pavithran , R. I. Sujith
Self-sustained oscillations arising from the interactions between the hydrodynamic and the acoustic field are disastrous in engineering systems such as segmented solid rocket motors and large gas pipelines. These self-sustained … Self-sustained oscillations arising from the interactions between the hydrodynamic and the acoustic field are disastrous in engineering systems such as segmented solid rocket motors and large gas pipelines. These self-sustained oscillations (limit cycle oscillations) are also referred to as aeroacoustic instabilities, which can be heard as a whistle. Understanding the change in dynamical state by altering the control parameter in an aeroacoustic system is critical in designing control strategies for aeroacoustic instabilities. In this study, as the control parameter Reynolds number ($Re$) is varied, we hear a change in the whistling frequency. We show that this change in frequency occurs via the state of intermittency, which has bursts of periodic fluctuations amidst the regime of the aperiodic fluctuations in acoustic pressure fluctuations. At a higher Reynolds number, we observe an abrupt transition from one limit cycle oscillation (LCO) to another limit cycle oscillation during the shift in whistling frequency. Further, we use synchronisation theory to investigate the coupled behaviour of the acoustic and the hydrodynamic fields. The acoustic pressure ($p'$) and hydrodynamic ($v'$) fluctuations during LCO exhibit phase synchronisation. Thus, we conclude that the shift in whistling frequency is a transition between the two phase synchronised limit cycle oscillations that occurs either through the state of intermittency or abruptly. The periodic bursts of intermittency correspond to the phase-synchronised periodic $p'$ and $v'$, and the aperiodic epochs correspond to the desynchronised aperiodic $p'$ and $v'$.
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Frequency Shifts During Whistling Occurs as Transition between Two Phase Synchronised Limit Cycles Via a State of Intermittency or Abruptly

2023-01-01
Ramesh S. Bhavi , Induja Pavithran , R. I. Sujith
Self-sustained oscillations arising from the interactions between the hydrodynamic and the acoustic field are disastrous in engineering systems such as segmented solid rocket motors and large gas pipelines. These self-sustained … Self-sustained oscillations arising from the interactions between the hydrodynamic and the acoustic field are disastrous in engineering systems such as segmented solid rocket motors and large gas pipelines. These self-sustained oscillations (limit cycle oscillations) are also referred to as aeroacoustic instabilities, which can be heard as a whistle. Understanding the change in dynamical state by altering the control parameter in an aeroacoustic system is critical in designing control strategies for aeroacoustic instabilities. In this study, as the control parameter Reynolds number ($Re$) is varied, we hear a change in the whistling frequency. We show that this change in frequency occurs via the state of intermittency, which has bursts of periodic fluctuations amidst the regime of the aperiodic fluctuations in acoustic pressure fluctuations. At a higher Reynolds number, we observe an abrupt transition from one limit cycle oscillation (LCO) to another limit cycle oscillation during the shift in whistling frequency. Further, we use synchronisation theory to investigate the coupled behaviour of the acoustic and the hydrodynamic fields. The acoustic pressure ($p'$) and hydrodynamic ($v'$) fluctuations during LCO exhibit phase synchronisation. Thus, we conclude that the shift in whistling frequency is a transition between the two phase synchronised limit cycle oscillations that occurs either through the state of intermittency or abruptly. The periodic bursts of intermittency correspond to the phase-synchronised periodic $p'$ and $v'$, and the aperiodic epochs correspond to the desynchronised aperiodic $p'$ and $v'$.
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Explosive synchronization in a turbulent reactive flow system

2023-01-01
Amal Joseph , Induja Pavithran , R. I. Sujith
The occurrence of abrupt dynamical transitions in the macroscopic state of a system has received growing attention. We present experimental evidence for abrupt transition via explosive synchronization in a real-world … The occurrence of abrupt dynamical transitions in the macroscopic state of a system has received growing attention. We present experimental evidence for abrupt transition via explosive synchronization in a real-world complex system, namely a turbulent reactive flow system. In contrast to the paradigmatic continuous transition to a synchronized state from an initially desynchronized state, the system exhibits a discontinuous synchronization transition with a hysteresis. We consider the fluctuating heat release rate from the turbulent flames at each spatial location as locally coupled oscillators that are coupled to the global acoustic field in the confined system. We analyze the synchronization between these two subsystems during the transition to a state of oscillatory instability and discover that explosive synchronization occurs at the onset of oscillatory instability. Further, we explore the underlying mechanism of interaction between the subsystems and construct a mathematical model of the same.
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Emergence of order from chaos through a continuous phase transition in a turbulent reactive flow system

2023-01-01
Sivakumar Sudarsanan , Amitesh Roy , Induja Pavithran +2 more
As the Reynolds number is increased, a laminar fluid flow becomes turbulent, and the range of time and length scales associated with the flow increases. Yet, in a turbulent reactive … As the Reynolds number is increased, a laminar fluid flow becomes turbulent, and the range of time and length scales associated with the flow increases. Yet, in a turbulent reactive flow system, as we increase the Reynolds number, we observe the emergence of a single dominant time scale in the acoustic pressure fluctuations, as indicated by its loss of multifractality. Such emergence of order from chaos is intriguing and has hardly been studied. We perform experiments in a turbulent reactive flow system consisting of flame, acoustic, and hydrodynamic subsystems interacting nonlinearly. We study the evolution of short-time correlated dynamics between the acoustic field and the flame in the spatiotemporal domain of the system. The order parameter, defined as the fraction of the correlated dynamics, increases gradually from zero to one. We find that the susceptibility of the order parameter, correlation length, and correlation time diverge at a critical point between chaos and order. Our results show that the observed emergence of order from chaos is a continuous phase transition. Moreover, we provide experimental evidence that the critical exponents characterizing this transition fall in the universality class of directed percolation. Our study demonstrates how a real-world complex, non-equilibrium turbulent reactive flow system exhibits universal behavior near a critical point.
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Early warnings are too late when parameters change rapidly

2024-07-30
Rohit Radhakrishnan , Induja Pavithran , Valerie Livina +2 more
Early warning signals (EWSs) forewarn a sudden transition (or tipping) from a desirable state to an undesirable state. However, we observe that EWSs detect an impending tipping past bifurcation points … Early warning signals (EWSs) forewarn a sudden transition (or tipping) from a desirable state to an undesirable state. However, we observe that EWSs detect an impending tipping past bifurcation points when control parameters are varied fast; this questions the applicability of EWSs in real-world systems. When a control parameter is changed at a finite rate, the tipping is also delayed, providing a borrowed stability (in the parameter space) before the system tips. In this study, we use the Hurst exponent as EWS in a thermoacoustic system - a horizontal Rijke tube. We find that upon receiving an EWS alert, a quick reversal of the control parameter within the region of borrowed stability cannot always prevent tipping in real-world systems. We show this failure is due to the (i) delay in receiving the EWS alert and (ii) dispersion observed in the warning points received. For fast variation of parameters, where preventive measures fall short, we demonstrate EWS-based control actions to rescue the system after tipping. Our results in a real-world system for a fast variation of parameter highlight the limits of applicability of EWSs in preventing tipping.
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The role of disordered dynamics on the nature of transition in a turbulent reactive flow system

2024-09-21
Sivakumar Sudarsanan , Induja Pavithran , R. I. Sujith
The transition from a chaotic to a periodic oscillatory state can be smooth or abrupt in real-world turbulent systems. Although there have been several mathematical studies, the occurrence of abrupt … The transition from a chaotic to a periodic oscillatory state can be smooth or abrupt in real-world turbulent systems. Although there have been several mathematical studies, the occurrence of abrupt transitions in real-world systems such as turbulent reactive flow systems is not well understood. A turbulent reactive flow system consists of the flame, the acoustic field, and the hydrodynamic field interacting nonlinearly. Generally, as the Reynolds number is increased, a laminar flow becomes turbulent, and the range of time scales associated with the flow broadens. Yet, as the Reynolds number is increased in a turbulent reactive flow system, a single dominant time scale emerges in the acoustic pressure oscillations, indicated by its loss of multifractality. For such smooth and abrupt transitions from chaos to order, we study the evolution of correlated and uncorrelated dynamics between the acoustic pressure and the heat release rate oscillations in the spatiotemporal domain of the turbulent reactive system. The correlated dynamics that add or remove energy from the acoustic field are defined as conformists and contrarians, respectively. The uncorrelated dynamics, neither adds nor removes energy is defined as disorder. Conformist dynamics dominate the contrarian dynamics as order emerges from chaos. We discover that the spatial extent of the disordered dynamics plays a critical role in deciding the nature of the transition. During the smooth transition, we observe a significant presence of disordered dynamics in the spatial domain. In contrast, abrupt transitions are accompanied by the disappearance of disordered dynamics from the spatial domain.
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The role of disordered dynamics on the nature of transition in a turbulent reactive flow system

2024-09-21
Sivakumar Sudarsanan , Induja Pavithran , R. I. Sujith
The transition from a chaotic to a periodic oscillatory state can be smooth or abrupt in real-world turbulent systems. Although there have been several mathematical studies, the occurrence of abrupt … The transition from a chaotic to a periodic oscillatory state can be smooth or abrupt in real-world turbulent systems. Although there have been several mathematical studies, the occurrence of abrupt transitions in real-world systems such as turbulent reactive flow systems is not well understood. A turbulent reactive flow system consists of the flame, the acoustic field, and the hydrodynamic field interacting nonlinearly. Generally, as the Reynolds number is increased, a laminar flow becomes turbulent, and the range of time scales associated with the flow broadens. Yet, as the Reynolds number is increased in a turbulent reactive flow system, a single dominant time scale emerges in the acoustic pressure oscillations, indicated by its loss of multifractality. For such smooth and abrupt transitions from chaos to order, we study the evolution of correlated and uncorrelated dynamics between the acoustic pressure and the heat release rate oscillations in the spatiotemporal domain of the turbulent reactive system. The correlated dynamics that add or remove energy from the acoustic field are defined as conformists and contrarians, respectively. The uncorrelated dynamics, neither adds nor removes energy is defined as disorder. Conformist dynamics dominate the contrarian dynamics as order emerges from chaos. We discover that the spatial extent of the disordered dynamics plays a critical role in deciding the nature of the transition. During the smooth transition, we observe a significant presence of disordered dynamics in the spatial domain. In contrast, abrupt transitions are accompanied by the disappearance of disordered dynamics from the spatial domain.
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Early warnings are too late when parameters change rapidly

2024-07-30
Rohit Radhakrishnan , Induja Pavithran , Valerie Livina +2 more
Early warning signals (EWSs) forewarn a sudden transition (or tipping) from a desirable state to an undesirable state. However, we observe that EWSs detect an impending tipping past bifurcation points … Early warning signals (EWSs) forewarn a sudden transition (or tipping) from a desirable state to an undesirable state. However, we observe that EWSs detect an impending tipping past bifurcation points when control parameters are varied fast; this questions the applicability of EWSs in real-world systems. When a control parameter is changed at a finite rate, the tipping is also delayed, providing a borrowed stability (in the parameter space) before the system tips. In this study, we use the Hurst exponent as EWS in a thermoacoustic system - a horizontal Rijke tube. We find that upon receiving an EWS alert, a quick reversal of the control parameter within the region of borrowed stability cannot always prevent tipping in real-world systems. We show this failure is due to the (i) delay in receiving the EWS alert and (ii) dispersion observed in the warning points received. For fast variation of parameters, where preventive measures fall short, we demonstrate EWS-based control actions to rescue the system after tipping. Our results in a real-world system for a fast variation of parameter highlight the limits of applicability of EWSs in preventing tipping.
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Emergence of order from chaos through a continuous phase transition in a turbulent reactive flow system

2024-06-20
Sivakumar Sudarsanan , Amitesh Roy , Induja Pavithran +2 more
As the Reynolds number is increased, a laminar fluid flow becomes turbulent, and the range of time and length scales associated with the flow increases. Yet, in a turbulent reactive … As the Reynolds number is increased, a laminar fluid flow becomes turbulent, and the range of time and length scales associated with the flow increases. Yet, in a turbulent reactive flow system, as we increase the Reynolds number, we observe the emergence of a single dominant timescale in the acoustic pressure fluctuations, as indicated by its loss of multifractality. Such emergence of order from chaos is intriguing. We perform experiments in a turbulent reactive flow system consisting of flame, acoustic, and hydrodynamic subsystems interacting nonlinearly. We study the evolution of short-time correlated dynamics between the acoustic field and the flame in the spatiotemporal domain of the system. The order parameter, defined as the fraction of the correlated dynamics, increases gradually from zero to one. We find that the susceptibility of the order parameter, correlation length, and correlation time diverge at a critical point between chaos and order. Our results show that the observed emergence of order from chaos is a continuous phase transition. Moreover, we provide experimental evidence that the critical exponents characterizing this transition fall in the universality class of directed percolation. Our paper demonstrates how a real-world complex, nonequilibrium turbulent reactive flow system exhibits universal behavior near a critical point.
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Explosive synchronization in a turbulent reactive flow system

2024-02-01
Amal Joseph , Induja Pavithran , R. I. Sujith
The occurrence of abrupt dynamical transitions in the macroscopic state of a system has received growing attention. We present experimental evidence for abrupt transition via explosive synchronization in a real-world … The occurrence of abrupt dynamical transitions in the macroscopic state of a system has received growing attention. We present experimental evidence for abrupt transition via explosive synchronization in a real-world complex system, namely, a turbulent reactive flow system. In contrast to the paradigmatic continuous transition to a synchronized state from an initially desynchronized state, the system exhibits a discontinuous synchronization transition with a hysteresis. We consider the fluctuating heat release rate from the turbulent flames at each spatial location as locally coupled oscillators that are coupled to the global acoustic field in the confined system. We analyze the synchronization between these two subsystems during the transition to a state of oscillatory instability and discover that explosive synchronization occurs at the onset of oscillatory instability. Further, we explore the underlying mechanism of interaction between the subsystems and construct a mathematical model of the same.
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Early warnings of tipping in a non-autonomous turbulent reactive flow system: Efficacy, reliability, and warning times

2024-01-01
Ankan Banerjee , Induja Pavithran , R. I. Sujith
Real-world complex systems such as the earth's climate, ecosystems, stock markets, and combustion engines are prone to dynamical transitions from one state to another, with catastrophic consequences. State variables of … Real-world complex systems such as the earth's climate, ecosystems, stock markets, and combustion engines are prone to dynamical transitions from one state to another, with catastrophic consequences. State variables of such systems often exhibit aperiodic fluctuations, either chaotic or stochastic in nature. Often, the parameters describing a system vary with time, showing time dependency. Constrained by these effects, it becomes difficult to be warned of an impending critical transition, as such effects contaminate the precursory signals of the transition. Therefore, a need for efficient and reliable early-warning signals (EWSs) in such complex systems is in pressing demand. Motivated by this fact, in the present work, we analyze various EWSs in the context of a non-autonomous turbulent thermoacoustic system. In particular, we investigate the efficacy of different EWS in forecasting the onset of thermoacoustic instability (TAI) and their reliability with respect to the rate of change of the control parameter. This is the first experimental study of tipping points in a non-autonomous turbulent thermoacoustic system. We consider the Reynolds number (Re) as the control parameter, which is varied linearly with time at finite rates. The considered EWSs are derived from critical slowing down, spectral properties, and fractal characteristics of the system variables. The state of TAI is associated with large amplitude acoustic pressure oscillations that could lead thermoacoustic systems to break down. We consider acoustic pressure fluctuations as a potential system variable to perform the analysis. Our analysis shows that irrespective of the rate of variation of the control parameter, the Hurst exponent and variance of autocorrelation coefficients warn of an impending transition well in advance and are more reliable than other EWS measures. Additionally, we show the variation in the warning time to an impending TAI with rates of change of the control parameter. We also investigate the variation in amplitudes of the most significant modes of acoustic pressure oscillations with the Hurst exponent. Such variations lead to scaling laws that could be significant in prediction and devising control actions to mitigate TAI.
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Tipping in complex systems under fast variations of parameters

2023-08-01
Induja Pavithran , P. R. Midhun , R. I. Sujith
Abrupt changes in the state of a system are often undesirable in natural and human-made systems. Such transitions occurring due to fast variations of system parameters are called rate-induced tipping … Abrupt changes in the state of a system are often undesirable in natural and human-made systems. Such transitions occurring due to fast variations of system parameters are called rate-induced tipping (R-tipping). While a quasi-steady or sufficiently slow variation of a parameter does not result in tipping, a continuous variation of the parameter at a rate greater than a critical rate results in tipping. Such R-tipping would be catastrophic in real-world systems. We experimentally demonstrate R-tipping in a real-world complex system and decipher its mechanism. There is a critical rate of change of parameter above which the system undergoes tipping. We discover that there is another system variable varying simultaneously at a timescale different from that of the driver (control parameter). The competition between the effects of processes at these two timescales determines if and when tipping occurs. Motivated by the experiments, we use a nonlinear oscillator model, exhibiting Hopf bifurcation, to generalize such type of tipping to complex systems where multiple comparable timescales compete to determine the dynamics. We also explain the advanced onset of tipping, which reveals that the safe operating space of the system reduces with the increase in the rate of variations of parameters.
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Imprints of log-periodicity in thermoacoustic systems close to lean blowout

2023-02-28
Ankan Banerjee , Induja Pavithran , R. I. Sujith
In the context of statistical physics, critical phenomena are accompanied by power laws having a singularity at the critical point where a sudden change in the state of the system … In the context of statistical physics, critical phenomena are accompanied by power laws having a singularity at the critical point where a sudden change in the state of the system occurs. In this work we show that lean blowout (LBO) in a turbulent thermoacoustic system is accompanied by a power law leading to finite-time singularity. As a crucial discovery of the system dynamics approaching LBO, we unravel the existence of the discrete scale invariance (DSI). In this context, we identify the presence of log-periodic oscillations in the temporal evolution of the amplitude of the dominant mode of low-frequency oscillations (A_{f}) existing in pressure fluctuations preceding LBO. The presence of DSI indicates the recursive development of blowout. Additionally, we find that A_{f} shows a faster-than-exponential growth and becomes singular when blowout occurs. We then present a model that depicts the evolution of A_{f} based on log-periodic corrections to the power law associated with its growth. Using the model, we find that blowouts can be predicted even several seconds earlier. The predicted time of LBO is in good agreement with the actual time of occurrence of LBO obtained from the experiment.
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Early warnings of tipping in a non-autonomous turbulent reactive flow system: efficacy, reliability, and warning times

2023-01-01
Ankan Banerjee , Induja Pavithran , R. I. Sujith
Real-world complex systems such as the climate, ecosystems, stock markets, and combustion engines are prone to dynamical transitions from one state to another, with catastrophic consequences. State variables of such … Real-world complex systems such as the climate, ecosystems, stock markets, and combustion engines are prone to dynamical transitions from one state to another, with catastrophic consequences. State variables of such systems often exhibit aperiodic fluctuations, either chaotic or stochastic in nature. Often, the parameters describing a system vary with time, showing time dependency. Constrained by these effects, it becomes difficult to be warned of an impending critical transition, as such effects contaminate the precursory signals of the transition. Therefore, a need for efficient and reliable early-warning signals (EWS) in such complex systems is in pressing demand. Motivated by this fact, in the present work, we analyze various EWS in the context of a non-autonomous turbulent thermoacoustic system. In particular, we investigate the efficacy of different EWS in forecasting the onset of thermoacoustic instability (TAI) and their reliability with respect to the rate of change of the control parameter. We consider the Reynolds number (Re) as the control parameter, which is varied linearly with time at finite rates. The considered EWS are derived from critical slowing down, spectral properties, and fractal characteristics of the system variables. The state of TAI is associated with large amplitude acoustic pressure oscillations that could lead thermoacoustic systems to break down. Our analysis shows that irrespective of the rate of variation of the control parameter, the Hurst exponent and variance of autocorrelation coefficients warn of an impending transition well in advance and are more reliable than other EWS measures. We also investigate the variation of amplitudes of the most significant modes of acoustic pressure oscillations with the Hurst exponent. Such variations lead to scaling laws which could be significant in prediction and devising control actions to mitigate TAI.
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Frequency shifts during whistling occurs as transition between two phase synchronised limit cycles via a state of intermittency or abruptly

2023-01-01
Ramesh S. Bhavi , Induja Pavithran , R. I. Sujith
Self-sustained oscillations arising from the interactions between the hydrodynamic and the acoustic field are disastrous in engineering systems such as segmented solid rocket motors and large gas pipelines. These self-sustained … Self-sustained oscillations arising from the interactions between the hydrodynamic and the acoustic field are disastrous in engineering systems such as segmented solid rocket motors and large gas pipelines. These self-sustained oscillations (limit cycle oscillations) are also referred to as aeroacoustic instabilities, which can be heard as a whistle. Understanding the change in dynamical state by altering the control parameter in an aeroacoustic system is critical in designing control strategies for aeroacoustic instabilities. In this study, as the control parameter Reynolds number ($Re$) is varied, we hear a change in the whistling frequency. We show that this change in frequency occurs via the state of intermittency, which has bursts of periodic fluctuations amidst the regime of the aperiodic fluctuations in acoustic pressure fluctuations. At a higher Reynolds number, we observe an abrupt transition from one limit cycle oscillation (LCO) to another limit cycle oscillation during the shift in whistling frequency. Further, we use synchronisation theory to investigate the coupled behaviour of the acoustic and the hydrodynamic fields. The acoustic pressure ($p'$) and hydrodynamic ($v'$) fluctuations during LCO exhibit phase synchronisation. Thus, we conclude that the shift in whistling frequency is a transition between the two phase synchronised limit cycle oscillations that occurs either through the state of intermittency or abruptly. The periodic bursts of intermittency correspond to the phase-synchronised periodic $p'$ and $v'$, and the aperiodic epochs correspond to the desynchronised aperiodic $p'$ and $v'$.
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Frequency Shifts During Whistling Occurs as Transition between Two Phase Synchronised Limit Cycles Via a State of Intermittency or Abruptly

2023-01-01
Ramesh S. Bhavi , Induja Pavithran , R. I. Sujith
Self-sustained oscillations arising from the interactions between the hydrodynamic and the acoustic field are disastrous in engineering systems such as segmented solid rocket motors and large gas pipelines. These self-sustained … Self-sustained oscillations arising from the interactions between the hydrodynamic and the acoustic field are disastrous in engineering systems such as segmented solid rocket motors and large gas pipelines. These self-sustained oscillations (limit cycle oscillations) are also referred to as aeroacoustic instabilities, which can be heard as a whistle. Understanding the change in dynamical state by altering the control parameter in an aeroacoustic system is critical in designing control strategies for aeroacoustic instabilities. In this study, as the control parameter Reynolds number ($Re$) is varied, we hear a change in the whistling frequency. We show that this change in frequency occurs via the state of intermittency, which has bursts of periodic fluctuations amidst the regime of the aperiodic fluctuations in acoustic pressure fluctuations. At a higher Reynolds number, we observe an abrupt transition from one limit cycle oscillation (LCO) to another limit cycle oscillation during the shift in whistling frequency. Further, we use synchronisation theory to investigate the coupled behaviour of the acoustic and the hydrodynamic fields. The acoustic pressure ($p'$) and hydrodynamic ($v'$) fluctuations during LCO exhibit phase synchronisation. Thus, we conclude that the shift in whistling frequency is a transition between the two phase synchronised limit cycle oscillations that occurs either through the state of intermittency or abruptly. The periodic bursts of intermittency correspond to the phase-synchronised periodic $p'$ and $v'$, and the aperiodic epochs correspond to the desynchronised aperiodic $p'$ and $v'$.
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Explosive synchronization in a turbulent reactive flow system

2023-01-01
Amal Joseph , Induja Pavithran , R. I. Sujith
The occurrence of abrupt dynamical transitions in the macroscopic state of a system has received growing attention. We present experimental evidence for abrupt transition via explosive synchronization in a real-world … The occurrence of abrupt dynamical transitions in the macroscopic state of a system has received growing attention. We present experimental evidence for abrupt transition via explosive synchronization in a real-world complex system, namely a turbulent reactive flow system. In contrast to the paradigmatic continuous transition to a synchronized state from an initially desynchronized state, the system exhibits a discontinuous synchronization transition with a hysteresis. We consider the fluctuating heat release rate from the turbulent flames at each spatial location as locally coupled oscillators that are coupled to the global acoustic field in the confined system. We analyze the synchronization between these two subsystems during the transition to a state of oscillatory instability and discover that explosive synchronization occurs at the onset of oscillatory instability. Further, we explore the underlying mechanism of interaction between the subsystems and construct a mathematical model of the same.
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Emergence of order from chaos through a continuous phase transition in a turbulent reactive flow system

2023-01-01
Sivakumar Sudarsanan , Amitesh Roy , Induja Pavithran +2 more
As the Reynolds number is increased, a laminar fluid flow becomes turbulent, and the range of time and length scales associated with the flow increases. Yet, in a turbulent reactive … As the Reynolds number is increased, a laminar fluid flow becomes turbulent, and the range of time and length scales associated with the flow increases. Yet, in a turbulent reactive flow system, as we increase the Reynolds number, we observe the emergence of a single dominant time scale in the acoustic pressure fluctuations, as indicated by its loss of multifractality. Such emergence of order from chaos is intriguing and has hardly been studied. We perform experiments in a turbulent reactive flow system consisting of flame, acoustic, and hydrodynamic subsystems interacting nonlinearly. We study the evolution of short-time correlated dynamics between the acoustic field and the flame in the spatiotemporal domain of the system. The order parameter, defined as the fraction of the correlated dynamics, increases gradually from zero to one. We find that the susceptibility of the order parameter, correlation length, and correlation time diverge at a critical point between chaos and order. Our results show that the observed emergence of order from chaos is a continuous phase transition. Moreover, we provide experimental evidence that the critical exponents characterizing this transition fall in the universality class of directed percolation. Our study demonstrates how a real-world complex, non-equilibrium turbulent reactive flow system exhibits universal behavior near a critical point.
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Abrupt transitions in turbulent thermoacoustic systems

2022-11-30
Ramesh S. Bhavi , Induja Pavithran , Amitesh Roy +1 more
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Extreme COVID-19 waves reveal hyperexponential growth and finite-time singularity

2022-04-01
Induja Pavithran , R. I. Sujith
Coronavirus disease 2019 (COVID-19) has rapidly spread throughout our planet, bringing human lives to a standstill. Understanding the early transmission dynamics of a wave helps plan intervention strategies such as … Coronavirus disease 2019 (COVID-19) has rapidly spread throughout our planet, bringing human lives to a standstill. Understanding the early transmission dynamics of a wave helps plan intervention strategies such as lockdowns that mitigate further spread, minimizing the adverse impact on humanity and the economy. Exponential growth of infections was thought to be the defining feature of an epidemic in its initial growth phase. Here we show that, contrary to common belief, early stages of extreme COVID-19 waves have an unbounded growth and finite-time singularity accompanying a hyperexponential power-law. The faster than exponential growth phase is hazardous and would entail stricter regulations to minimize further spread. Such a power-law description allows us to characterize COVID-19 waves better using single power-law exponents, rather than using piecewise exponentials. Furthermore, we identify the presence of log-periodic patterns decorating the power-law growth. These log-periodic oscillations may enable better prediction of the finite-time singularity. We anticipate that our findings of hyperexponential growth and log-periodicity will enable accurate modeling of outbreaks of COVID-19 or similar future outbreaks of other emergent epidemics.
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Imprints of log-periodicity in thermoacoustic systems close to lean blowout

2022-01-01
Ankan Banerjee , Induja Pavithran , R. I. Sujith
In the context of statistical physics, critical phenomena are accompanied by power laws having a singularity at the critical point where a sudden change in the state of the system … In the context of statistical physics, critical phenomena are accompanied by power laws having a singularity at the critical point where a sudden change in the state of the system occurs. In this work, we show that lean blowout (LBO) in a turbulent thermoacoustic system can be viewed as a critical phenomenon. As a crucial discovery of the system dynamics approaching LBO, we unravel the existence of the discrete scale invariance (DSI). In this context, we identify the presence of log-periodic oscillations in the temporal evolution of the amplitude of dominant mode of low-frequency oscillations $(A_f)$ exist in pressure fluctuations preceding LBO. The presence of DSI indicates the recursive development of blowout. Additionally, we find that $A_f$ shows a faster than exponential growth and becomes singular when blowout occurs. We then present a model that depicts the evolution of $A_f$ based on log-periodic corrections to the power law associated with its growth. Using the model, we find that blowout can be predicted even several seconds earlier. The predicted time of LBO in good agreement with the actual time of occurrence of LBO obtained from the experiment.
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Tipping in complex systems under fast variations of parameters

2022-01-01
Induja Pavithran , P. R. Midhun , R. I. Sujith
Sudden transitions in the state of a system are often undesirable in natural and human-made systems. Such transitions under fast variation of system parameters are called rate-induced tipping. We experimentally … Sudden transitions in the state of a system are often undesirable in natural and human-made systems. Such transitions under fast variation of system parameters are called rate-induced tipping. We experimentally demonstrate rate-induced tipping in a real-world complex system and decipher its mechanism. There is a critical rate of change of parameter above which the system undergoes tipping. We show that another system parameter, not under our control, changes simultaneously at a different rate, and the competition between the effects of that parameter and the control parameter determines if and when tipping occurs. Motivated by the experiments, we use a nonlinear oscillator model exhibiting Hopf bifurcation to generalize this tipping to complex systems in which slow and fast parameters compete to determine the system dynamics.
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Extreme COVID-19 waves reveal hyperexponential growth and finite-time singularity

2021-10-20
Induja Pavithran , R. I. Sujith
Abstract Coronavirus disease 2019 (COVID-19) has rapidly spread throughout our planet, bringing human lives to a standstill. Understanding the early transmission dynamics helps plan intervention strategies such as lockdowns that … Abstract Coronavirus disease 2019 (COVID-19) has rapidly spread throughout our planet, bringing human lives to a standstill. Understanding the early transmission dynamics helps plan intervention strategies such as lockdowns that mitigate further spread, minimizing the adverse impact on humanity and the economy 1–3 . Exponential growth of infections was thought to be the defining feature of an epidemic in its initial growth phase 4–7 ; any variation from an exponential growth was described by adjusting the parameters of the exponential model 7,8 . Here, we show that, contrary to common belief, early stages of extreme COVID-19 waves display an unbounded growth and finite-time singularity accompanying a hyperexponential power-law. The faster than exponential growth phase is hazardous and would entail stricter regulations. Such a power-law description allows us to characterize COVID-19 waves with single power-law exponents, better than piece-wise exponentials. Furthermore, we identify the presence of log-periodic patterns decorating the power-law growth. These log-periodic oscillations may enable better prediction of the finite-time singularity. We anticipate that our findings of hyperexponential growth and log-periodicity will help model the COVID-19 transmission more accurately.
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Effect of rate of change of parameter on early warning signals for critical transitions

2021-01-01
Induja Pavithran , R. I. Sujith
Many dynamical systems exhibit abrupt transitions or tipping as the control parameter is varied. In scenarios where the parameter is varied continuously, the rate of change of the control parameter … Many dynamical systems exhibit abrupt transitions or tipping as the control parameter is varied. In scenarios where the parameter is varied continuously, the rate of change of the control parameter greatly affects the performance of early warning signals (EWS) for such critical transitions. We study the impact of variation of the control parameter with a finite rate on the performance of EWS for critical transitions in a thermoacoustic system (a horizontal Rijke tube) exhibiting subcritical Hopf bifurcation. There is a growing interest in developing early warning signals for tipping in real systems. First, we explore the efficacy of early warning signals based on critical slowing down and fractal characteristics. From this study, lag-1 autocorrelation (AC) and Hurst exponent (H) are found to be good measures to predict the transition well before the tipping point. The warning time, obtained using AC and H, reduces with an increase in the rate of change of the control parameter following an inverse power law relation. Hence, for very fast rates, the warning time may be too short to perform any control action. Furthermore, we report the observation of a hyperexponential scaling relation between the AC and the variance of fluctuations during such a dynamic Hopf bifurcation. We construct a theoretical model for noisy Hopf bifurcation wherein the control parameter is continuously varied at different rates to study the effect of rate of change of the parameter on EWS. Similar results, including the hyperexponential scaling, are observed in the model as well.
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Universality in spectral condensation

2020-10-15
Induja Pavithran , Vishnu R. Unni , Alan John Varghese +6 more
Abstract Self-organization is the spontaneous formation of spatial, temporal, or spatiotemporal patterns in complex systems far from equilibrium. During such self-organization, energy distributed in a broadband of frequencies gets condensed … Abstract Self-organization is the spontaneous formation of spatial, temporal, or spatiotemporal patterns in complex systems far from equilibrium. During such self-organization, energy distributed in a broadband of frequencies gets condensed into a dominant mode, analogous to a condensation phenomenon. We call this phenomenon spectral condensation and study its occurrence in fluid mechanical, optical and electronic systems. We define a set of spectral measures to quantify this condensation spanning several dynamical systems. Further, we uncover an inverse power law behaviour of spectral measures with the power corresponding to the dominant peak in the power spectrum in all the aforementioned systems.
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Universality in the emergence of oscillatory instabilities in turbulent flows

2020-02-24
Induja Pavithran , Vishnu R. Unni , Alan John Varghese +4 more
Spontaneous emergence of periodic oscillations due to self-organization is ubiquitous in turbulent flows. The emergence of such oscillatory instabilities in turbulent fluid mechanical systems is often studied in different system-specific … Spontaneous emergence of periodic oscillations due to self-organization is ubiquitous in turbulent flows. The emergence of such oscillatory instabilities in turbulent fluid mechanical systems is often studied in different system-specific frameworks. We uncover the existence of a universal scaling behaviour during self-organization in turbulent flows leading to oscillatory instability. Our experiments show that the spectral amplitude of the dominant mode of oscillations scales inversely with the Hurst exponent of a fluctuating state variable following an inverse power law relation. Interestingly, we observe the same power law behaviour with a constant exponent near -2 across various turbulent systems such as aeroacoustic, thermoacoustic and aeroelastic systems.
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Coauthor Papers Together
R. I. Sujith 15
R. I. Sujith 4
Ramesh S. Bhavi 3
Jürgen Kurths 3
Amitesh Roy 3
Sivakumar Sudarsanan 3
Ankan Banerjee 3
Amal Joseph 2
P. R. Midhun 2
Abhishek Saha 2
Vishnu R. Unni 2
Norbert Marwan 2
Alan John Varghese 2
Rohit Radhakrishnan 1
Shruti Tandon 1
Shruti Tandon 1
Ankan Banerjee 1
Premraj Durairaj 1
Valerie Livina 1
C. Vijayan 1
R. I. Sujith 1