Edge‐, bottom‐, and Rossby waves in a rotating stratified fluid

TLDR

The waves could appear as an internal tide at the continental rise or as baroclinic meandering of currents over a slope. The low‑frequency limit, αS ≪ 1, is studied in detail. The authors analyze the low‑frequency limit αS ≪ 1, examining exponential decay of edge waves, their interaction with topographic‑planetary waves, and the influence of large‑scale boundaries and Coriolis parameter variations. Edge (bottom) waves exist at all frequencies below N sin α, propagate leftward with phase and energy, merge with topographic‑planetary waves for wavelengths > ≈ 450 km, and the β‑effect generates complementary modes isolated from the bottom.

Abstract

Abstract It is found that in a rotating stratified fluid bounded by a single rigid wall, edge waves may occur at all frequencies less than or equal to N sin a (a is the angle of the wall from the horizontal and N the Brunt‐Vaisala frequency). These decay exponentially away from the boundary, in a distance of O(S) wavelengths, for α = O(1), or O(S ‐1) wavelengths, for αS ≤ O(1), where S is the ratio of N to the Coriolis parameter f, taken for illustration to be large. The phase and energy both move with a component to the left, facing shallow water. The waves could, for example, appear as an internal tide at the continental rise or as baroclinic meandering of currents over a slope. The low‐frequency limit, αS ≪ 1, is studied in detail. To allow for large scales of motion other rigid boundaries and variations in f are included. The edge (actually "bottom") waves then merge with topographic‐planetary waves as the wavelengths increase; the familiar depth‐independent mode is found to be possible in the sea for wavelengths exceeding about 450 km. The ß‐effect introduces modes complementary to that trapped at the bottom, which instead are isolated from it.