Flux and dissipation of energy in the LET theory of turbulence

Abstract

The first part of this thesis examines and compares the separate closure formalisms of Wyld and Martin, Siggia, and Rose (MSR). The simplicity of Wyld’s perturbation scheme is offset by an incorrect renormalisation, this contrasts with the formally exact analysis of MSR. The work here shows that a slight change in Wyld’s renormalisation keeps the main results intact and, in doing so, demonstrates that this formalism is equivalent to MSR. The remainder of the thesis is concerned with turbulent dissipation. A numerical solution of the Local Energy Transfer theory, or LET, is reworked and extended to compute decaying and forced turbulence at large Reynolds numbers. Using this numerical simulation, the phenomenon of turbulent dissipation is investigated. In order to use decaying turbulence to study the turbulent dissipation rate as a function of Reynolds number, it is necessary to choose an appropriate time with which a measurement can be taken. Using phenomenological arguments of the evolution of a turbulent fluid, criteria for establishing such a time are developed. An important study in turbulence is the dissipation rate in the limit of vanishing viscosity, also known as the dissipation anomaly. This thesis derives an equation for the dissipation rate from the spectral energy balance equation. Using the LET computation for both decaying and forced turbulence, results are obtained that can be used along with the equation to study the mechanisms behind the dissipation anomaly. It is found that there is a difference in the behaviour of the normalised dissipation rate between decaying and forced turbulence and, for both cases, it is largely controlled by the energy flux.