Mixed Topographic-Planetary Waves in an Exponentially Stratified Ocean

On the continental slope, a dispersion relation in terms of Bessel functions is found for mixed topographical-planetary waves in the approximation of a rigid-lid and an exponential stratification profile. It is numerically analyzed for both positive and negative meridional slopes of the topography. It is shown that taking into account exponential stratification, in comparison with a constant stratification profile, has a twofold effect. On the one hand, indeed, the exponential stratification profile leads to smaller vertical eigenvalues and, as a result, higher propagation velocities of topographical and planetary waves than on a constant stratification profile. On the other hand, the influence of topography on eigenvalues is negligible. If, during the transition from the baroclinic mode to the surface mode for a constant stratification profile, the topography can lead to a fourfold increase in the wave propagation velocity for the first baroclinic mode, then for the exponential profile such an effect is limited to 30%. As a result, mixed topographical-planetary waves do not possess hypersensitivity to the stratification profile, as previously established. The transition from the baroclinic mode to the surface mode with an exponential stratification profile, as with a constant stratification profile, occurs in the range of angles of inclination 10^–4~10^–2 for 100-km wavelengths.