A theoretical, two‐layer, reduced‐gravity model for descending dense water flow on continental shelves/slopes

Abstract

A theoretical, two‐layer, reduced‐gravity model for descending dense water flow on continental shelves/slopes has been developed to investigate the dynamics of bottom dense water plumes. The model is nonsteady state and includes vertical viscosity, the Coriolis force, and bottom friction. An integral solution rather than a perfect analytical expression is derived and, thus, the Simpson's 1/3 rule to approximate the integral is applied. At the very bottom, the dense water plume moves about 45° to the right (left) in the Northern (Southern) Hemisphere, looking downslope. From the bottom, the velocity vector rotates anticyclonically upward, indicating a bottom Ekman spiral that mimics the atmospheric Ekman boundary layer. The dense water within the bottom Ekman layer obeys a three‐force balance, while the dense water above the bottom Ekman layer is governed by a two‐force balance, which is a geostrophic flow with superimposed cycloidal inertial oscillations oriented from about 25° to 140° to the right (left) of the downslope direction in the Northern (Southern) Hemisphere. The transport within the bottom Ekman layer is directed about 60–70° to the right (left) of the downslope direction in the Northern (Southern) Hemisphere, forming an offshore (cross‐isobath) transport in the absence of eddy flux and wind‐forcing. The ratio of offshore transport to alongshore transport within the bottom Ekman layer is about 0.19 (19%), while the ratio above the bottom Ekman layer (i.e., geostrophic layer of the dense water) is only 3% (negligible compared to its alongshore transport), which, however, is equivalent in magnitude to its counterpart in the bottom Ekman layer if O(DE/h) ∼ 0.1 (where DE is the bottom Ekman layer thickness and h is the dense water layer thickness). In other words, the bottom Ekman layer and the geostrophic (dense) layer contribute equivalent dense water offshore (each contributes 50%). The magnitude of the descending dense water velocity depends linearly on reduced gravity and sin(θ) (slope angle).