Large-Scale Propagating Disturbances: Approximation by Vertical Normal Modes

Abstract

Propagating features and waves occur everywhere in the ocean. This paper derives a concise description of how such small-amplitude, large-scale oceanic internal disturbances propagate dynamically against a slowly varying background mean flow and stratification, computed using oceanic data. For a flat-bottomed ocean, assumed here, the linear internal modes, computed using the local stratification, form a useful basis for expanding the oceanic shear modes of propagation. Remarkably, the shear modal structure is largely independent of orientation of the flow. The resulting advective velocities, which are termed pseudovelocities, comprise background flow decomposed onto normal modes, and westward planetary wave propagation velocities. The diagonal entries of the matrix of pseudovelocities prove to be reasonably accurate descriptors of the speed and direction of propagation of the shear modes, which thus respond as if simply advected by this diagonal-entry velocity field. The complicated three-dimensional propagation problem has thus been systematically reduced to this simple rule. The first shear mode is dominated by westward propagation, and possesses a midlatitude speed-up over the undisturbed linear first-mode planetary wave. The pseudovelocity for the second shear mode, in contrast, while still dominated by westward propagation at lower latitudes, shows a gyrelike structure at latitudes above 30°. This resembles in both shape and direction the geostrophic baroclinic flow between about 500- and 1000-m depth, but are much slower than the flow at these depths. Features may thus be able to propagate some distance around a subtropical or subpolar gyre, but not, in general, at the speed of the circulation.