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.

Marsh vegetation is widely considered to offer protection against coastal storm damage, and vegetated flow has thus become a key area of hydrodynamic research. This study investigates the utility of simulated Spartina alterniora marsh vegetation as storm protection using an ADV measurement technique, and is the first to apply jet self-similarity analysis to characterize the overall mean and turbulent flow properties of a three-dimensional axisymmetric jet through a vegetated array. The mean axial flow of a horizontal axisymmetric turbulent jet is obstructed by three configurations of staggered arrays of vertical rigid plant stems. The entire experiment is repeated over five sufficiently high jet Reynolds number conditions to ensure normalization and subsequent collapse of data by nozzle velocity so that experimental error is obtained. All self-similarity parameters for the unobstructed free jet correspond to typical published values: the axial decay coefficient B is 5:8 +/- 0:2, the Gaussian spreading coefficient c is 85 +/- 5, and the halfwidth spreading rate eta_(1/2) is 0:093 +/- 0:003. Upon the introduction of vegetation, from partially obstructed to fully obstructed, B falls from 5:1+/- 0:2 to 4:2 +/- 0:2 and finally 3:7 +/-0:1 for the fully obstructed case, indicating that vegetation reduces axial jet velocity. Cross-sectionally averaged momentum for the unobstructed free jet is M=M0 = 1:05 +/- 0:07, confirming conservation of momentum. Failure of conservation of momentum is most pronounced in the fully obstructed scenario – M=M0 = 0:54 +/- 0:05. The introduction of vegetation increases spreading of the impinging jet. The entrainment coefficient alpha for the free jet case is 0.0575; in the fully obstructed case, alpha = 0:0631. Mean advection of mean and turbulent kinetic energy demonstrates an expected reduction in turbulence intensity within the vegetated array. In general, turbulent production decreases as axial depth of vegetation increases, though retains the bimodal profile of the free jet case; the fully vegetated case, however, exhibits clear peaks behind plant stems. Turbulent transport was shown to be unaffected by vegetation and appears to be primarily a function of axial distance from the jet nozzle. An analysis of rate of dissipation revealed that not only does the cumulative effect of upstream wakes overall depress the magnitude of spectral energy density across all wavenumbers but also that plant stems dissipate large anisotropic eddies in centerline streamwise jet flow. This study, thus, indicates that sparse emergent vegetation both reduces axial flow velocity and has a dissipative effect on jet flow. Typically, however, storm surge does not exhibit the lateral spreading demonstrated by an axisymmetric jet; therefore, the results of this study cannot conclusively support the claim that coastal vegetation reduces storm surge axial velocity.

The labyrinth seal is a non-contact annular type sealing device used to reduce the internal leakage of the working fluid which is caused by the pressure difference between each stage in a turbomachine. Reducing the leakage mass flow rate of the working fluid through the labyrinth seal is desirable because it improves the efficiency of the turbomachine. The carry-over coefficient, based on the divergence angle of the jet, changed with flow parameters with fixed seal geometry while earlier models expressed the carry-over coefficient solely as a function of seal geometry. For both compressible and incompressible flows, the Reynolds number based on clearance was the only flow parameter which could influence the carry-over coefficient. In the case of incompressible flow based on the simulations for various seal geometries and operating conditions, for a given Reynolds number, the carry-over coefficient strongly depended on radial clearance to tooth width ratio. Moreover, in general, the lower the Reynolds number, the larger is the divergence angle of the jet and this results in a smaller carry-over coefficient at lower Reynolds numbers. However, during transition from laminar to turbulent, the carry-over coefficient reduced initially and once the Reynolds number attained a critical value, the carry-over coefficient increased again. In the case of compressible flow, the carry-over coefficient had been slightly increased if radial clearance to tooth width ratio and radial clearance to tooth pitch ratio were increased. Further, the carry-over coefficient did not considerably change if only radial clearance to tooth width ratio was decreased. The discharge coefficient for compressible and incompressible flows depended only on the Reynolds number based on clearance. The discharge coefficient of the tooth in a single cavity labyrinth seal was equivalent to that in a multiple tooth labyrinth seal indicating that flow downstream had negligible effect on the discharge coefficient. In particular, for compressible fluid under certain flow and seal geometric conditions, the discharge coefficient did not increase with an increase in the Reynolds number. It was correlated to the pressure ratio, Pr. Moreover, it was also related to the fact that the flow of the fluid through the constriction became compressible and the flow eventually became choked. At low pressure ratios (less than 0.7), Saikishan’s incompressible model deviated from CFD simulation results. Hence, the effects of compressibility became significant and both the carry-over coefficient compressibility factor and the discharge coefficient compressibility factor needed to be considered and included into the leakage model. The carry-over coefficient compressibility factor, phi, had two linear relationships with positive and negative slopes regarding the pressure ratios. This result was not associated with the seal geometry because the seal geometry ratios for each instance were located within the nearly same ranges. Further, the phi-Pr relationship was independent of the number of teeth regardless of single and multiple cavity labyrinth seals. The discharge coefficient compressibility factor, psi, was a linear relationship with pressure ratios across the tooth as Saikishan predicted. However, in certain flow and seal geometric conditions, Saikishan’s model needed to be modified for the deviation appearing when the pressure ratios were decreased. Hence, a modified psi-Pr relationship including Saikishan’s model was presented in order to compensate for the deviation between the simulations and his model.