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