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Resonance phenomenon for the Galerkin-truncated Burgers and Euler equations
It is shown that the solutions of inviscid hydrodynamical equations with suppression of all spatial Fourier modes having wave numbers in excess of a threshold ${K}_{\mathrm{G}}$ exhibit unexpected features. The study is carried out for both the one-dimensional Burgers equation and the two-dimensional incompressible Euler equation. For large ${K}_{\mathrm{G}}$ and …