Gravity current down a steeply inclined slope in a rotating fluid

The sinking of dense water down a steep continental slope is studied using laboratory experiments, theoretical analysis and numerical simulation. The experiments were made in a rotating tank containing a solid cone mounted on the tank floor and originally filled with water of constant density. A bottom gravity current was produced by injecting more dense coloured water at the top of the cone. The dense water plume propagated from the source down the inclined cone wall and formed a bottom front separating the dense and light fluids. The location of the bottom front was measured as a function of time for various experimental parameters. In the majority of runs a stable axisymmetric flow was observed. In certain experiments, the bottom layer became unstable and was broken into a system of frontal waves which propagated down the slope. The fluid dynamics theory was developed for a strongly non-linear gravity current forming a near-bottom density front. The theory takes into account both bottom and interfacial friction as well as deviation of pressure from the hydrostatic formula in the case of noticeable vertical velocities. Analytical and numerical solutions were found for the initial (t < 1=f ), intermediate (t 1=f ), and main …t 1=f † stages, where f is the Coriolis parameter. The model results show that during the initial stage non-linear inertial oscillations are developed. During the main stage, the gravity current is concentrated in the bottom layer which has a thickness of the order of the Ekman scale. The numerical solutions are close to the same analytical one. Stability analysis shows that the instability threshold depends mainly on the Froude number and does not depend on the Ekman number. The results of laboratory experiments confirm the similarity properties of the bottom front propagation and agree well with the theoretical predictions. Introduction The sinking of dense water over the continental slope is a significant contributor to water exchange between the shelf-slope zone and the open ocean. Dense water accumulates on shelves, migrates to the shelf edge, and flows across the continental slope forming a gravity current. This process is thought to be important in the formation of oceanic bottom and deep waters, and particularly of Antarctic bottom water (Whitehead, 1987). Other examples are bottom gravity currents in the South Australian Gulfs (Bowers and Lennon, 1987), the Denmark Straits overflow (Dickson et al., 1990), the Mediterranean outflow into the Atlantic (Price et al., 1993) and into the Black Sea (Latif et al., 1991). Despite recent progress, bottom gravity currents over the continental slope have not been well investigated experimentally or theoretically. This is because, firstly, they often occur sporadically and in barely accessible regions, and secondly, the theoretical description of currents over a steep slope must be extended beyond geostrophic or quasi-geostrophic models to include friction and the vertical component of the Coriolis force. In recent years, gravity currents on horizontal and inclined bottoms have been a subject of theoretical and laboratory studies (Zatsepin et al., 1982; Shapiro, 1982; Kostianoy and Shapiro, 1985; Mory et al., 1987; Simpson, 1987; Whitehead et al., 1990; Speer et al., 1993; Nagata et al., 19931; Zhmur et al., 1994). The research has been restricted mainly to the case of a horizontal or slightly sloping bottom or a non-rotating fluid. In the theoretical studies, bottom friction has usually been considered in the ‘‘boundary layer’’ approximation (Whitehead, 1990; Speer et al., 1993) Correspondence to: G. I. Shapiro This reference was brought to our attention by Dr. P. Baines after the manuscript had been submitted. In general, both the experiments and the theories are significantly different. However, one of our figures (Fig. 5) looks similar to Fig. 12 of Nagata et al. (1993) Ann. Geophysicae 15, 366–374 (1997)  EGS – Springer-Verlag 1997