Predictability of the large scales of freely evolving three and two-dimensional turbulence

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Abstract
The predictability of freely evolving three and two‐dimensional turbulence is studied within the formalism developed by Kraichnan and Lorenz, using the EDQNM theory. In the three‐dimensional case, the time when the wavenumber characteristic of the error reaches the energy containing range is increased by more than a factor of 10 compared to the case of stationary turbulence. But the times to which the ratio r(t) of decorrelated energy over total energy equals 0.5 are only increased by a factor of 2 in the decaying case. In two‐dimensional turbulence, one verifies that the wavenumber characteristic of the error first decreases exponentially in the enstrophy cascade, the total error remaining low. Then in a second phase,it decreases as (t−t 0)− 1 (t 0 being the time at which the error is initially injected), while r(t) increases rapidly. The times such that r(t)=0.5 are, in units of large eddy turnover times at t=t 0, increased by a factor 1.8 when one compares the decaying case to the forced case. These results would allow the understanding of the appearance of three‐dimensionality on the spanwise ‘‘coherent’’ vortices in the free shear layers.

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