On Heisenberg's elementary theory of turbulence

Abstract

In this paper the spectrum of turbulence is considered on the basis of an elementary theory recently developed by Heisenberg. Explicit solutions for the spectrum have been obtained both when the conditions are stationary and an equilibrium spectrum obtains and when the conditions are non-stationary and the turbulence is decaying. In the former case the problem admits of an explicit solution. In the latter case the problem reduces to determining a one-parametric family of solutions of a certain second-order differential equation. The decay spectra for various values of the Reynolds number (which remains constant during the decay) are illustrated.