The number of degrees of freedom for the 2D Navier-Stokes equation: a connection with Kraichnan's theory of turbulence
Abstract
We estimate the number of degrees of freedom of solutions of the 2D Navier-Stokes equation, proving that its mathematical analog, the number of determining modes, is bounded by the Kraichnan number squared. In particular, this provides new bounds on the number of determining modes in term of the Grashof number for solutions that are not highly intermittent.
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