On the Propagation of Free Topographic Rossby Waves near Continental Margins

in partial fulfillment of the requirements for the degree of Doctor of Philosophy ABSTRACT Observational work by Thompson (1977) and others has demonstrated that free topographic Rossby waves propaqate northward up the continental rise south of New England. To study the dynamical implications of these waves as they approach the shelf, Beardsley, Vermersch, and Brown conducted an experiment in 1976 (called NESS76) in which some moored instruments were strategically placed across the New England continental margin to measure current, temperature, and bottom pressure for about six months. An analytical model has been constructed to study the propagation of free topographic Rossby waves in an infinite weeqe filled with a uniformly stratified fluid. The problem is found after some coordinate transformations to be identical to the corresponding surface gravity wave problem in a homogeneous fluid, but with the roles of the surface and bottom boundaries interchanged. Analytical solutions are thus available for both progressive and trapped waves, forming continuous and discrete spectra in the frequency space. The separation occurs at a nondimensional frequency d= S, defined as (N/f) tangY*, where N and f are the Brunt-Vaisfl' and inertial frecruencies, and tane* is the bottom slope. Since an infinite wedge has no intrinsic length scales, the only relevant nondimensional parameters are the frequency d and the Burger number S. T hus, stratification and bottom slope play the same dynamical role, and the analysis is greatly simplified. Asymptotic solutions for the progressive waves have been obtained for both the far field and small S which enable us to examine the parameter dependence of some ,of the basic wave properties in the far field, and the spatial evolution of the wave amplitude and phase as they approach the apex when S is small. The general solution is then presented and discussed in some detail. The eigenfrequencies of the trapped modes decrease when S decreases and reduce to the short wave limit of Reid's (1q58) second class, barotropic edge waves when S approaches zero. The modal structure broadens as S increases to some critical value above which no such coastally-trapped modes exist. To simulate more closely the dynamical processes occurring near the continental margin, a numerical model incorporating a more realistic topography than an infinite wedge has been constructed. With stratification imposing an additional harrier, the model suggests that the maximum energy flux transmission coefficient obtained in Kroll and Niiler's barotropic model (1976) is likely …