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We estimate the number of degrees of freedom of solutions of the 2DNavier-Stokes equation, proving that its mathematical analog, the number ofdetermining modes, is bounded by the Kraichnan number squared. In particular,this provides new bounds on the number of determining modes in term of theGrashof number for solutions that are not highly intermittent.

The number of degrees of freedom for the 2D Navier-Stokes equation: a connection with Kraichnan's theory of turbulence