Free decay of isotropic turbulence as a test problem. When I began my postgraduate research in 1966, I quickly decided that there was one problem that I would never work on. That was the free decay of the kinetic energy of turbulence from some initial value. Although, as the subject of my postgraduate research wasContinue reading Free decay of isotropic turbulence as a test problem.

Stationary isotropic turbulence as a test problem. When I was first publishing, in the early 1970s, referees would often say something like `the author uses the turbulence in a box concept’ before going on to reveal a degree of incomprehension about what I might be doing, let alone what I actually was doing. A fewContinue reading Stationary isotropic turbulence as a test problem.

Asymptotic behaviour of the Direct Interaction Approximation. As mentioned previously, Kraichnan’s asymptotic solution of the DIA, for high Reynolds numbers and large wavenumbers, did not agree with the observed asymptotic behaviour of turbulence. His expression for the spectrum was , where is the root-mean-square velocity and is a constant. In 1964 (see [1] for theContinue reading Asymptotic behaviour of the Direct Interaction Approximation.

A brief summary of two-point renormalized perturbation theories. In the previous post we discussed the introduction of Kraichnan’s DIA, based on a combination of a mean-field assumption and a new kind of perturbation theory, and how it was supported by Wyld’s formalism, itself based on a conventional perturbation expansion of the NSE. This was notContinue reading A brief summary of two-point renormalized perturbation theories.