Non-perturbative Methods in Statistical Descriptions of Turbulence by Jan Friedrich

Author:Jan Friedrich
Language: eng
Format: epub
ISBN: 9783030519773
Publisher: Springer International Publishing

4.4.2 Primitive Perturbative Treatment of the Nonlinearity in the Navier-Stokes Equation

In this section, we outline a procedure that treats the nonlinear character of the Navier-Stokes equation in a perturbative sense. The treatment implies that the zeroth-order approximation can be obtained from the usual heat equation with an additional stirring force. Perturbation expansions can then be based on the zeroth-order approximation which leads to a switch on of nonlinear interactions, similar to the procedure in QED discussed in the preceding section.

The starting point for the procedure that was developed in the seminal work by Kraichnan [4] is the Navier-Stokes equation in Fourier space

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