Buoyant gravity currents along a sloping bottom in a rotating fluid

The dynamics of buoyant gravity currents in a rotating reference frame is a classical problem relevant to geophysical applications such as river water entering the ocean. However, existing scaling theories are limited to currents propagating along a vertical wall, a situation almost never realized in the ocean. A scaling theory is proposed for the structure (width and depth), nose speed and flow field characteristics of buoyant gravity currents over a sloping bottom as functions of the gravity current transport Q, density anomaly g', Coriolis frequency f, and bottom slope alpha. The nose propagation speed is c(p) similar to c(w) /(1 + c(w)/c(alpha)) and the width of the buoyant gravity current is W-p similar to c(w)/f (1 + c(w)/c(alpha)), where c(w) = (2Qg'f)(1/4) is the nose propagation speed in the vertical wall limit (steep bottom slope) and c(alpha) = alphag'/f is the nose propagation speed in the slope-controlled limit (small bottom slope). The key non-dimensional parameter is c(w)/c(alpha), which indicates whether the bottom slope is steep enough to be considered a vertical wall (c(w)/c(alpha) --> 0) or approaches the slope-controlled limit (c(w)/c(alpha) --> infinity). The scaling theory compares well against a new set of laboratory experiments which span steep to gentle bottom slopes (c(w)/c(alpha) = 0.11-13.1). Additionally, previous laboratory and numerical model results are reanalysed and shown to support the proposed scaling theory.