Buoyant gravity currents along a sloping bottom in a rotating fluid

Abstract

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 α. The nose propagation speed is c p ∼ c w / (1 + c w / c α ) and the width of the buoyant gravity current is W p ∼ c w / f (1 + c w / c α ), where c w = (2 Qg ′ f ) 1/4 is the nose propagation speed in the vertical wall limit (steep bottom slope) and c α = α g / f is the nose propagation speed in the slope-controlled limit (small bottom slope). The key non-dimensional parameter is c w / c α , which indicates whether the bottom slope is steep enough to be considered a vertical wall ( c w / c α → 0) or approaches the slope-controlled limit ( c w / c α → ∞). The scaling theory compares well against a new set of laboratory experiments which span steep to gentle bottom slopes ( c w / c α = 0.11–13.1). Additionally, previous laboratory and numerical model results are reanalysed and shown to support the proposed scaling theory.