On the propagation of free topographic Rossby waves near continental margins

Abstract

Observational work by Thompson (1977) and others has demonstrated that free topographic Rossby waves propagate 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 wedge 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 δ = S, defined as (N/f) tanθ*, where N and f are the Brunt-Väisälä and inertial frequencies, and tanθ* is the bottom slope. Since an infinite wedge has no intrinsic length scales, the only relevant nondimensiona1 parameters are the frequency δ and the Burger number S. Thus, 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 (1958) 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 an upper bound. Also in the presence of the finite slope changes, the baroclinic fringe waves generated near the slope-rise junction may form an amphidromic point at some mid-depth and locally reverse the direction of the phase propagation above it. These baroclinic fringe waves also cause an offshore heat flux over the continental rise which, combined with the onshore heat flux generated over the slope region in a frictionless model, induces, across the transect, a mean flow pattern of two counter-rotating gyres with downwelling occurring near the slope-rise junction. Bottom friction always generates an offshore heat flux and therefore modifies this mean flow pattern over the slope region. The induced longshore mean flow is approximately geostrophically balanced and generally points to the left facing the shoreline, but its direction can be reversed where the baroclinic fringe waves dominate. The mean thermal wind relation implies a generally denser slope water than that farther offshore. Some of the model predictions are compared with the data taken from NESS76. The comparisons are generally consistent, suggesting that topographic Rossby wave dynamics may play an important role for the low frequency motions near continental margins.