Study of the Hopf functional equation for turbulence: Duhamel principle and dynamical scaling
Study of the Hopf functional equation for turbulence: Duhamel principle and dynamical scaling
We consider a formulation for the Hopf functional differential equation which governs statistical solutions of the Navier-Stokes equations. By introducing an exponential operator with a functional derivative, we recast the Hopf equation as an integro-differential functional equation by the Duhamel principle. On this basis we introduce a successive approximation to …