Thesis (Ph. D.)--University of Wisconsin--Madison, 1975. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 110-114).

Thesis (Ph. D.)--University of Wisconsin--Madison, 1908. / Reprinted from the Annals of mathematics, 2d series, v. 9, January, 1908. eContent provider-neutral record in process. Description based on print version record.

A global analysis for the hydrodynamical system defined for a homogeneous, incompressible layer of fluid on the β-plane is performed in both infinite and finite function space. Its application to global stability has yielded an algorithm for characterizing flows based on the existence of initially growing perturbations as opposed to the normal mode analysis; its application to the search for optimal initial perturbations has led to the least upper bound of energy growth rate; its application to multiple equilibria has given rise to a necessary condition for their existence; its application to the study of the relationship of modal to nonmodal growth rates has uncovered the cause underlying many aspects of the limitation of the modal stability analysis including the failure to predict transient growth of disturbances in stable flows and the underestimation of the intensity of initial development of instability in unstable flows. Numerical illustrations made for some specific flows have strengthened the general results, suggesting that a stability analysis of a hydrodynamical system without a global analysis is likely to be limited in many important aspects. The local analysis of asymptotic behavior of nonmodal disturbances to hyperbolic equilibria of the system have established: a) for any subcritical flow outside of monotonic, global stability regime, there exists a finite neighborhood around the origin of RM such that a disturbance initialized in this neighborhood will ultimately decay to zero after it exhibits Orr's temporal amplification; b) for any supercritical flow, there exists a finite neighborhood adjacent to the origin of RM such that a disturbance initialized in this neighborhood will persist as t→∞; and c) the nature of the persistent disturbances is related to the nature of the nonhyperbolic point in parameter space of interest. The numerical experiments are seen to confirm these predictions. Closure modeling of forced-dissipated statistical equilibrium of perturbed flows arising from initially uniform zonal flows over random topography is done with special regard to the correlation between disturbance and underlying topography and the resulting stress. Such an exercise has led to, on one hand, the numerical results for topographical stress suggesting clearly the significance of this force in overall momentum budget of large scale ocean circulations. On the other hand, it has led to an appreciation that the detailed conservation of energy and potential enstrophy, which holds regardless of the presence of dissipation in the system, provides a means for systematic investigation of nonlinear transfer of the these quantities among interacting triads, an area not accessible to other approaches. / Science, Faculty of / Earth, Ocean and Atmospheric Sciences, Department of / Graduate

The existence of a weak solution u(x, t) , in the -sense of J. Le'ray ([7]), is established for the initial-boundary value problem for the Navier-Stokes equations: [Formula omitted] The solution is required to satisfy the initial condition u(x, 0) = u[subscript]o (x) for x ɛΩ, and the boundary condition u(x, t) = 0 on ∂Ω x [0, T], where Ω is an open bounded domain in IR[superscript]n, with 2 ≤ n ≤ 4. Galerkin's method is employed to find a weak solution u as the limit of approximate solutions {u[subscript]m} . The convergence of the {u[subscript]m}is guaranteed by some compact embedding theorems, which depend on a priori estimates for the {u[subscript]m} and their fractional time derivatives of order Ƴ, 0<Ƴ<1/4. / Science, Faculty of / Mathematics, Department of / Graduate

A scalar theory of gravitation is used to construct stellar models which are static, spherically symmetric, isentropic, and composed of an ideal fluid obeying a power-law pressure-density relation. Such a relation holds for an isentropic non-degenerate perfect gas and for a degenerate Fermi gas In which the particles are non-relativistic or ultra-relativistic. A method for determining if a given static, spherically symmetric configuration is unstable against radial adiabatic perturbations is derived for the scalar theory. It is specialized to the particular models constructed. Numerical results on the structure and stability of the models are obtained and compared with general relativistic results. It Is found that the static results agree qualitatively with those given by general relativity but disagree quantitatively, e.g., a larger maximum mass for neutron stars is found using the scalar theory. The dynamical results are found to differ with those given in general relativity. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

The gravitational exchange of two fluids of different density through a convergent-divergent contraction is considered. Two-layer exchange flow theory is extended to include frictional effects with an emphasis on the interfacial friction. The magnitude of the interfacial friction is found to be greater than previously suggested and may be vital to the analysis of exchange flows. Experiments modelling gravitational exchange flow through a convergent-divergent contraction were conducted in the hydraulics laboratory at the University of British Columbia to test the hydraulic solutions that have been developed on two-layer exchange flow. A comparison of the theoretical solutions and experimental results is made. Experiments conducted provide data for evaluating the theoretical findings and help in locating the hydraulic controls of the experiment along with quantifying the magnitude of interfacial friction coefficient. A comparison is made between numerous values obtained for the interfacial friction coefficients by previous investigators and the experimental results of the present study. Flow visualization is used to study the Kelvin-Helmholtz and Holmboe instabilities that form at the interface of the two layers. / Applied Science, Faculty of / Civil Engineering, Department of / Graduate

44 leaves : illustrations

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