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

TL;DR

This paper establishes a mathematical bound linking the degrees of freedom in 2D Navier-Stokes solutions to Kraichnan's turbulence theory, providing new insights into turbulence modeling.

Contribution

It proves that the number of determining modes is bounded by the Kraichnan number squared, connecting turbulence theory with mathematical bounds.

Findings

Number of determining modes is bounded by Kraichnan number squared.

Provides new bounds on degrees of freedom in terms of Grashof number.

Results apply to solutions that are not highly intermittent.

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.