Miller, A. J., 1986:

Barotropic planetary-topographic oscillations in ocean basins.

Ph.D. dissertation. Scripps Institution of Oceanography, University of California, San Diego, 133 pp.

Abstract. Basin-scale, low-frequency, linear fluctuations in idealized, rotating, ocean basins with planetary and/or topographic vorticity gradients are discussed in three free-standing chapters.
In Chapter I, free vorticity modes are numerically computed for square, mid-latitude, ocean basins with topography. It is found that strong coupling between planetary (Rossby) modes and topographic (shelf, ridge or seamount) modes can occur. This results in the generation of families of modes, the members of which exhibit spatial structures and time scales comparable to a flat-bottom counterpart mode. The mechanism provides an alternative to strong dissipation as an explantation for broadbandedness in spectral observations of planetary modes.
It is found in Chapter II that mesoscale turbulence, when confined to western-boundary regions of numerical models, can efficiently excite basin modes at resonance, with (parameterized) bottom friction limiting the response. Furthermore, the mid-ocean mesoscale eddy field, driven by Rossby-wave radiation from the turbulent region, is found to be remarkably similar to that of a stochastic-wind-driven model. This suggests that fluctuating winds and boundary-current radiation may be of comparable import as sources for the open-ocean mesoscale field. Topography is observed to significantly alter the amplitude but not the nature of the model fluctuations.
The long-period tides are discussed in Chapter III in the light of recent observations and theories. Quasigeostrophic solutions which include topography and friction are computed. Friction is found to decrease the effects of bottom roughness in the quasigeostrophic models. The divergent velocity field associated with a nearly-equilibrium tide is found to be comparable to equilibrium-tide vortex stretching in driving quasigeostrophic flows. However, quasigeostrophic solutions are shown to be insufficient for interpreting the observations. A divergent velocity field is suggested to be an important element of future long-period tide models.
The results suggest that oceanic planetary modes may yet be observed once calculations are extended to realistic basins and sea-level records are properly interpreted. Oceanic mesoscale turbulence may excite rather than dissipate basin, or sub-basin, modes, thus providing an excitation mechanism distinct from atmospheric forcing. Understanding the oceanic response to long-period tidal forcing provides an important benchmark for oceanic circulation theory.