¡@¡@The main purpose of this paper is to analyze the surface progressive gravity waves propagating on a gentle sloping beach in two dimension. Instead of using the method of Eulerian system by the previous investigators, we introduce the governing equations completely in the Lagrangian system directly. All the characteristics of the wave system is expressed by a suitable perturbation expansion in the bottom slope under linearizing the problem in wave amplitude, then all the governing equations are systematically expanded to order. The solution of the wave system is to be solved to second order , even to high order could also be obtained. Based on the obtained results, the velocity potential, pressure and motion of the fluid particle in the wave system in time and space is therefore presented, and we can see that the bottom slope is a main factor to screw the wave field to deform to break. Finally, the experimental result is cited to compare and verify.

Thesis (Ph. D.)--University of Texas at Austin, 2000. / Vita. Includes bibliographical references (leaves 293-298). Available also in a digital version from Dissertation Abstracts.

Title from PDF of title page (University of Missouri--Columbia, viewed on Feb 25, 2010). The entire thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file; a non-technical public abstract appears in the public.pdf file. Dissertation advisor: Dr. Brent L. Rosenblad. Vita. Includes bibliographical references.

The use of patterned metallic surfaces for the control of the transmission of microwave radiation has been reinvigorated in recent years due to the success and interest in metamaterial research. These metallic periodic structures, commonly referred to as frequency selective screens (FSSs), allow responses to be tailored according to the geometry of the metallic structure as opposed to the material composition. A consequence of the presence of a metallic corrugation is the possible excitation of surfaces waves (commonly referred to as surface plasmon polaritons at visible frequencies). Surface waves can be utilised to achieve further control of the transmission properties of a structure. In this thesis several highly original metallic structures are investigated which use FSS and surface wave concepts. These structures exhibit interesting and previously unexplained transmission behaviour. The experimental chapters within this thesis are divided into two areas. The first three experimental chapters (4-6) present original investigations into the excitation of diffractively coupled surface waves on metallic hole/patch arrays and their role in the enhanced transmission/reflection of microwave radiation. The importance of metallic connectivity within arrays is highlighted through measurements of the metallic filling fraction dependence on the transmission properties of regular periodic and random arrays. The last two experimental chapters (7-8) contain investigations into the transmission properties of two novel resonant cavities. The structure studied in chapter 7 provides a mechanism for remarkably enhanced microwave transmission on resonance through an otherwise opaque continuous thin metal film. The second resonant cavity structure in chapter 8 uses a resonant array of metallic crosses to form a ‘resonant mirror’ Fabry-Perot cavity. These resonant FSSs exhibit a frequency dependent transmission/reflection and phase response thus producing an interesting series of modes which have very different properties to those supported by a non-resonant mirror etalon.

No description available.

No description available.

The nonlinear interactions between long surface waves and interfacial waves in a two-layer fluid are studied theoretically. The fluid is density-stratified and the thicknesses of the top and bottom layers are both assumed to be shallow relative to the length of a typical surface wave and interfacial wave, respectively. A set of Boussinesq-type equations are derived for potential flow in this system. The equations are then analyzed for the dynamics of the nonlinear resonant interactions between a monochromatic surface wave and two oblique interfacial waves. The analysis uses a second order perturbation approach. Consequently, a set of coupled transient evolution equations of wave amplitudes is derived. Moreover, the effect of weak viscosity of the lower layer is incorporated in the problem and the influences of important parameters on surface and interfacial wave evolution (namely the directional angle of interfacial waves, density ratio of the layers, thickness of the fluid layers, surface wave frequency, surface wave amplitude, and lower layer viscosity) are investigated. The results of the parametric study are discussed and are generally in qualitative agreement with previous studies. In shallow water, a triad formed of surface waves (or interfacial waves) can be considered in near-resonant interaction. In contrast to the previous studies which limited the study to a triad (one surface wave and two interfacial waves or one interfacial and two surface waves), the problem is generalized by considering the nonlinear interactions between a triad of surface waves and three oblique pairs of interfacial waves. In this system, each surface wave is in near-resonance interaction with other surface waves and in exact resonance with a pair of oblique interfacial waves. Similarly, each interfacial wave is in near-resonance interaction with other interfacial waves which are propagating in the same direction. Inclusion of all the interactions considerably changes the pattern of evolution of waves and highlights the necessity of accounting for several wave harmonics. Effects of density ratio, depth ratio, and surface wave frequency on the evolution of waves are discussed. Finally, a formulation is derived for spatial evolution of one surface wave spectrum in nonlinear interaction with two oblique interfacial wave spectra. The two-layer Boussinesq-type equations are treated in frequency domain to study the nonlinear interactions of time-harmonic waves. Based on weakly two-dimensional propagation of each wave train, a parabolic approximation is applied to derive the formulation.

Thesis (Ph.D.)--University of Tulsa, 1993. / Includes bibliographical references (leaves 91-96).

Thesis (Ph.D.)--University of Tulsa, 1993. / Includes bibliographical references (leaves 91-96).

Thesis (Ph. D.)--Ohio University, June, 1998. / Title from PDF t.p.