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.

Laboratory Experiments on Eddy Generation by a Buoyant Coastal Current Flowing over Variable Bathymetry*

“…As mentioned previously, the ratio of the isopycnal slope to the bathymetric slope sЈ/s is the principle parameter controlling the strength of the interaction between the current and the bathymetry (Yankovsky and Chapman 1997;Lentz and Helfrich 2002). This parameter is large (small) when the bathymetric slope is gentle (steep) relative to the slope of the isopycnals.…”

“…Several authors have proposed scale variables that can be used to classify buoyant coastal currents using parameters that can be controlled or measured at the source. The most convenient for the purposes of this study are those derived and tested in a series of laboratory experiments by Lentz and Helfrich (2002). An idealized representation of the flow studied by these authors is shown in Fig.…”

“…The third and fourth scales are simply the Rossby radius R D and internal gravity wave speed c based on the depth of the foot of the front h, respectively. The final scale, the nose speed c n , was proposed by Lentz and Helfrich (2002) …”

“…The foot remains fixed as the current widens, so the velocity of the current must decrease to conserve the total flux of buoyant fluid. The spreading mechanism has not been definitively explained, but Lentz and Helfrich (2002) suggest that it may result from an offshore flux of water in an interfacial Ekman layer between the buoyant and ambient waters.…”

Laboratory modelling of the effects of temporal changes of estuarine-fresh-water discharge rates on the propagation speed of oceanographic coastal currents

“…Previous studies of coastal currents (e.g. Griffiths & Hopfinger 1983, Griffiths 1986, Davies, Jacobs & Mofor 1993, Simpson 1997, Thomas & Linden 1998, Boyer, Haidvogel & Pèrenne 2001, Avicola & Huq 2002, Lentz & Helfrich 2002, Avicola & Huq 2003a,b, Rivas, Velasco Fuentes & Ochoa 2005, Horner-Devine et al 2006 have dealt with the current speed, depth and width, and examined their stability and the effects of bottom topography on the current dynamics or the characteristics of the gyre that forms near the estuary where the river water enters the ocean. Here we examine the response of the propagation speed of the currents following a change of the volumetric discharge rate of fresh water at the source.…”