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Exponential decay of the power spectrum of turbulence. (English) Zbl 1081.35505
Summary: The analyticity on a strip of the solutions of Navier-Stokes equations in 2D is shown to explain the observed fast decay of the frequency power spectrum of the turbulent velocity field. Some subtleties in the application of Wiener-Khinchine method to turbulence are resolved by showing that the frequency power spectrum of turbulent velocities is in fact a measure exponentially decaying for frequency \(\to \pm \infty\). Our approach also shows that the conventional procedures used in analyzing data in turbulence experiments are valid even in the absence of the ergodic property in the flow.

MSC:
35Q30 Navier-Stokes equations
76F99 Turbulence
76M25 Other numerical methods (fluid mechanics) (MSC2010)
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