Scaling analysis for the interaction between a buoyant coastal current and the continental shelf: Experiments and observations

Abstract

This paper addresses how the geometrical parameters (ambient ocean depth, H; bottom slope, α) of coastal bathymetry affect the evolution of buoyant coastal currents flowing over a sloping continental shelf. Scaling arguments are presented that show the coastal current dynamics can be classified by a two-variable nondimensional parameter space: the ambient depth parameter, h/H, and the bottom slope parameter, R/yb. The ratio h/H is the fraction of the available depth occupied by the buoyant layer: the bottom slope parameter is the ratio of two horizontal length scales, the internal Rossby radius R to the bottom-trapped width yb. The scale depth h is derived from geostrophic dynamics and is representative of the depth of the buoyant layer of the coastal current. The resulting parameter space is delineated by surface-advected currents that do not depend upon the bottom slope parameter and bottom-trapped currents that do. For bottom-trapped coastal currents, the across-shore width and downstream velocities are dependent upon the magnitude of the bottom slope parameter, R/yb. The bottom slope parameter is also a ratio of the buoyant layer isopycnal slope to the shelf slope. Experiments are conducted in the laboratory in order to test the scaling. Measurements of coastal current width and nose velocities are taken, together with mean density cross sections, for a number of coastal currents. Experimental observations and oceanic datasets are examined in terms of the proposed scaling arguments; it is shown that these experimental measurements and oceanic observations are in accord.