A numerical model has been developed which simulates the three-dimensional stability and transition of a periodically forced free shear layer in an incompressible fluid. Unlike previous simulations of temporally evolving shear layers, the current simulations examine spatial stability. The spatial model accommodates features of free shear flow, observed in experiments, which in the temporal model are precluded by the assumption of streamwise periodicity; e.g., divergence of the mean flow and wave dispersion. The Navier-Stokes equations in vorticity-velocity form are integrated using a combination of numerical methods tailored to the physical problem. A spectral method is adopted in the spanwise dimension in which the flow variables, assumed to be periodic, are approximated by finite Fourier series. In complex Fourier space, the governing equations are spatially two-dimensional. Standard central finite differences are exploited in the remaining two spatial dimensions. For computational efficiency, time evolution is accomplished by a combination of implicit and explicit methods. Linear diffusion terms are advanced by an Alternating Direction Implicit/Crank-Nicolson scheme whereas the Adams-Bashforth method is applied to convection terms. Nonlinear terms are evaluated at each new time level by the pseudospectral (collocation) method. Solutions to the velocity equations, which are elliptic, are obtained iteratively by approximate factorization. The spatial model requires that inflow-outflow boundary conditions be prescribed. Inflow conditions are derived from a similarity solution for the mean inflow profile onto which periodic forcing is superimposed. Forcing functions are derived from inviscid linear stability theory. A numerical test case is selected which closely parallels a well-known physical experiment. Many of the aspects of forced shear layer behavior observed in the physical experiment are captured by the spatial simulation. These include initial linear growth of the fundamental, vorticity roll-up, fundamental saturation, eventual domination of the subharmonic, vortex pairing, emergence of streamwise vorticity, and temporary stabilization of the secondary instability. Moreover, the spatial simulation predicts the experimentally observed superlinear growth of harmonics at rates 1.5 times that of the fundamental. Superlinear growth rates suggest nonlinear resonances between fundamental and harmonic modes which are not captured by temporal simulations.

Chen, Chao. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (leaves 43-46). / Abstract also in Chinese. / Abstract --- p.i / Acknowledgement --- p.iii / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Preliminaries --- p.7 / Chapter 3 --- The mathematical formulation of the problem and main results --- p.11 / Chapter 4 --- Reformulation of the problem --- p.17 / Chapter 5 --- Proof of the main theorems --- p.23 / Chapter 5.1 --- Proof of uniqueness --- p.23 / Chapter 5.2 --- Proof of non-existence --- p.31 / Chapter 6 --- Work in future --- p.40 / Chapter 7 --- Appendix --- p.41 / Bibliography --- p.43

by Wan Shan. / "June, 2003." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references. / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. Ann Arbor, MI : ProQuest Information and Learning Company, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.

Graduation date: 2006

Lake Kinneret is Israel's only fresh water lake (unless you count the Dead Sea). It spans roughly 20km from north to south, and about 12km at its widest east west extent. It is not quite 50m deep at its deepest point. In late spring, the lake stratifies significantly and remains stratified throughout the fall. During the time the lake is stratified, it exhibits low horizontal mode semi-diurnal inertial motions in response to surface forcing from diurnal winds. This internal motion is known to be important in the ecological and chemical balances of the lake, and is suspected to be responsible for episodes in which large numbers of fish are killed. The physical response of the lake to wind forcing is studied. The lake hydrodynamics is approximated by a (x,y,t) two and three layer model on the f-plane (rotating frame) with detailed bathymetry. The numerical method for the integration of the nonlinear partial differential equation is presented, as well as, the generation of the elliptic grid used in the spatial discretization of the Kinneret domain. A suite of numerical simulations are compared to the available data in the northwestern part of the lake. The nonlinear effects, as well as, the sloping beach problem are discussed in the appendixes. / Graduation date: 2000

Shocked porous granular material experiences pressure dependent compaction. D. John Pastine introduced a model in which the degree of compaction is dependent on the pressure induced by the shock wave, the shear strength of the material, and the distribution of void sizes. In the past, the model could only be approximated. Using computational techniques and higher speed computers, the response of this model to void size distributions may be displayed to a high degree of precision. / Graduation date: 1996

A time-domain model was developed to predict the fluid/structure interaction of a three-dimensional deformable body in a fluid domain subject to long-crested finite amplitude waves. These nonlinear waves induce transient motion in the body. In turn, the interaction of the body with the waves modifies the wave field, causing additional motion in the body. A time-domain simulation was required to describe these nonlinear motions of the body and the wave field. An implicit three-dimensional time-domain boundary element model of the fluid domain was developed and then coupled iteratively with a finite element model of the deformable body. Large body hydrodynamics and ideal fluid flow are assumed and the diffraction/radiation problem solved. Either linear waves or finite amplitude waves can be treated in the model. Thus the full nonlinear kinematic and dynamic free surface boundary conditions are solved in an iterative fashion. To implicitly include time in the governing field equations, Volterra's method was used. The approach is similar to that of the typical boundary element method for a fluid domain where the boundary element integral is derived from the governing field equation. The difference is that in Volterra's method the boundary element integral is derived from the time derivative of the governing field equation. The transient membrane motions are treated by discretizing the spatial domain with curved isoparametric elements. Newton-Raphson iterations are used to account for the geometric nonlinearities and the equations of motion are solved using an implicit numerical method. Examples are included to demonstrate the validity of the boundary element model of the fluid domain. The conditions in a wave channel were numerically modeled and compared to sinusoidal waves. The interaction of a submerged rigid horizontal cylinder with water waves was modeled and results compared to experimental and numerical results. The capability of the model to predict the interaction of highly deformable bodies and water waves was tested by comparing the numerical model to large-scale physical model experiment of a membrane cylinder placed horizontally in a wave channel. / Graduation date: 1992

Not available / text

Not available / text

published_or_final_version / abstract / Mechanical Engineering / Master / Master of Philosophy