Taylor's (1935) dissipation surrogate reinterpreted

New results from direct numerical simulation of decaying isotropic turbulence show that Taylor’s expression for the viscous dissipation rate ε = CεU3/L is more appropriately interpreted as a surrogate for the inertial energy flux. As a consequence, the well known dependence of the Taylor prefactor Cε on Reynolds number Cε(RL)→Cε,∞ can be understood as corresponding to the onset of an inertial range

Flux and dissipation of energy in the LET theory of turbulence

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

Turbulent states in plane Couette flow with rotation

Shearing and rotational forces in fluids can significantly alter the transport of momentum.A numerical investigation was undertaken to study the role of these forces using plane Couette flow subject to rotation about an axis perpendicular to both wall-normal and streamwise directions. Using a set of progressively higher Reynolds numbers up to Re = 5200, we find that the torque for a given Re is a non-monotonic function of rotation number, Ro. For low-to-moderate turbulent Reynolds numbers we find a maximum that is associated with flow fields that are dominated by downstream vortices and calculations of 2-d vortices capture the maximum also quantitatively. For higher shear Reynolds numbers a second stronger maximum emerges at smaller rotation numbers, closer to non-rotating plane Couette flow. It is carried by flows with a markedly 3-d structure and cannot be captured by 2-d vortex studies. As the Reynolds number increases, this maximum becomes stronger and eventually overtakes the one associated with the 2-d flow state.Comment: 15 pages, 10 figure

Flux and dissipation of energy in the LET theory of turbulence

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.EThOS - Electronic Theses Online ServiceGBUnited Kingdo