Modelling quasi-two-dimensional turbulent shear flow

A two-length-scale turbulence model is introduced in this thesis for the computation of quasi-two-dimensional turbulent shear flow with two distinct length scales of motion. In the model, the turbulence motions of the two distinct length scales are computed separately. The small-scale turbulence is treated as a background component locally in equilibrium while the large-scale turbulence is simulated using a second-order closure procedure. The development of the turbulent shear flows depends on the rate of energy transfer from the large-scale to the small-scale turbulence. Two mechanisms are identified to have a significant effect on the rate of this energy transfer. On one hand, the rate is reduced due to the confinement of the large-scale turbulence to two-dimensional motion, since the nonlinear energy cascade process is less efficient in two-dimensional turbulent motion. On the other hand, the rate is enhanced due to the work done by the large-scale turbulent motion against the friction forces. The energy transfer rate due to friction is derived in the model using a two-step averaging procedure, whereas the transfer rate due to nonlinear cascade process is determined using a model equation. The data from a number of experimental investigations of quasi-two-dimensional turbulent shear flows are analyzed. These data support the notion of the two-length-scale turbulence model, that (i) the maintenance of the turbulent motion depends on the transfer of energy from the large-scale turbulence to the small-scale turbulence, and (ii) the transfer rate is subjected to confinement and friction influences as specified in the model. Numerical computations are conducted using the two-length-scale model and a single-length-scale model. The results are compared with the experimental data. The two-length-scale model is superior in performance compared with the single-length-scale model, particularly in the intermediate region of the flow where both length scales of the turbule