Thesis (Ph. D.)--University of Washington, 2001. / Vita. Includes bibliographical references (leaves 93-99).

Thesis (M. Phil.)--Hong Kong University of Science and Technology, 2003. / Includes bibliographical references (leaves 56-58). Also available in electronic version. Access restricted to campus users.

Thesis (Ph. D.)--University of Texas at Austin, 2000. / Vita. Includes bibliographical references (leaves 212-219). Available also in a digital version from Dissertation Abstracts.

Thesis (DTech. degree in the Dept. of Mathematics and Statistics.)-Tshwane University of Technology, 2008.

The two-dimensional, viscous flow around an elliptic cylinder undergoing prescribed unsteady motions is analyzed. The fluid is taken to be incompressible. Departing from the conventional vorticity-stream function approach, the Biot-Savart law of induced velocities is utilized to account for the contribution to the velocity field of the different vorticity fields comprising the flow. These include the internal vorticity due to the rotation of the body, the free vorticity in the fluid surrounding the body, and the bound vorticity distributed along the body contour. In order to apply the method, the body must be assumed to be replaced by fluid of the same density as the undisturbed surroundings. The replacement fluid must have a rigid motion exactly the same as the actual body motion. This can be achieved by placing suitable distributed vorticity fields within and on the surface of the body. The bound vorticity on the body surface is in the form of a vortex sheet, and its distribution is governed by a Fredholm integral equation of the second kind. The equation is derived in detail. It is solved numerically. The motion of the free vorticity in the flow field is governed by the Navier-Stokes equations written in terms of vorticity. The descretized vorticity transport equation is derived for a control volume and is solved numerically using an explicit method with a forward-difference for the time derivative, and a central-difference for the diffusive terms. An upwind method is used for convection terms. The results obtained using the present method are compared with a number of special cases available in the literature. Viscous flows around a circular cylinder rotating in any arbitrary fashion possess an exact solution, as presented in Chapter 2. Two cases of this flow are chosen for comparison. In the first case the circular cylinder is initially given an impulsive twist such that it rotates with a constant velocity about its axis. In the second case, the angular velocity of the circular cylinder increases with time exponentially. For a Reynolds number of 100, based on the cylinder radius and the internal vorticity, the exact solutions are compared with the numerical results. Viscous flow around an elliptic cylinder of .0996 aspect ratio rotating with a constant angular velocity is another special case, available in the literature, which is chosen for comparison. For this case the Reynolds number, based on the cylinder semi-major-axis and internal vorticity is 202. The agreement in all above-mentioned cases is excellent. Finally, viscous flow around an elliptic cylinder of .25 aspect ratio undergoing a combined translation and pitching oscillation is presented. A Reynolds number of 500, based on the semi-major-axis and body translational velocity, is chosen for this case. No similar case has been reported until now. This case, however, is only one of the many cases that can be handled by the present method.

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We study the evolution of shear-free spherically symmetric charged fluids in general relativity. This requires the analysis of the coupled Einstein-Maxwell system of equations. Within this framework, the master field equation to be integrated is yxx = f(x)y2 + g(x)y3 We undertake a comprehensive study of this equation using a variety of ap- proaches. Initially, we find a first integral using elementary techniques (subject to integrability conditions on the arbitrary functions f(x) and g(x)). As a re- sult, we are able to generate a class of new solutions containing, as special cases, the models of Maharaj et al (1996), Stephani (1983) and Srivastava (1987). The integrability conditions on f(x) and g(x) are investigated in detail for the purposes of reduction to quadratures in terms of elliptic integrals. We also obtain a Noether first integral by performing a Noether symmetry analy- sis of the master field equation. This provides a partial group theoretic basis for the first integral found earlier. In addition, a comprehensive Lie symmetry analysis is performed on the field equation. Here we show that the first integral approach (and hence the Noether approach) is limited { more general results are possible when the full Lie theory is used. We transform the field equation to an autonomous equation and investigate the conditions for it to be reduced to quadrature. For each case we recover particular results that were found pre- viously for neutral fluids. Finally we show (for the first time) that the pivotal equation, governing the existence of a Lie symmetry, is actually a fifth order purely differential equation, the solution of which generates solutions to the master field equation. / Thesis (Ph.D.)-University of KwaZulu-Natal, Westville, 2011.