Observations and numerical experiments that suggest that sea-floor roughness can enhance the ratio of thermocline to abyssal eddy kinetic energy, motivate the study of linear free wave modes in a two layer quasi-geostrophic model for several eases of idealized variable bottom topography. The foeus is on topography with horizontal seale comparable to that of the waves, that is, on "rough" small-amplitude topography. Surface-intensified modes are found to exist at frequencies greater than the flat-bottom baroclinic cut-off frequency. These modes exist for topography that varies in both one and two horizontal dimensions. An approximate bound indicates that the maximum frequency of the surface-intensified modes is greater than the baroclinic cut-off by a factor equal to the total fluid depth divided by the lower layer depth. For fixed topographic wavenumber, there is not a simple dependence of the degree of surface-intensification on topographic amplitude, but rather a resonant structure with peaks at certain topographic amplitudes. These modes may be resonantly excited by surface forcing.
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