EXPONENTIAL DECAY OF THE POWER SPECTRUM OF TURBULENCE

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 po wer spectrum of the turbulent velocity field. Some subtleties in the a pplication of the Wiener-Khinchine method to turbulence are resolved b y showing that the frequency power spectrum of turbulent velocities is in fact a measure exponentially decaying for frequency --> +/- infini ty. Our approach also shows that the conventional procedures used in a nalyzing data in turbulence experiments are valid even in the absence of the ergodic property in the flow.