Two-dimensional density currents in a confined basin

Abstract

We present new experimental results on the mechanisms through which steady two-dimensional density currents lead to the formation of a stratification in a closed basin. A motivation for this work is to test the underlying assumptions in a diffusive “filling box” model that describes the oceanic thermohaline circulation (Hughes, G.O. and Griffiths, R.W., A simple convective model of the global overturning circulation, including effects of entrainment into sinking regions, Ocean Modeling, 2005, submitted.). In particular, they hypothesized that a non-uniform upwelling velocity is due to weak along-slope entrainment in density currents associated with a large horizontal entrainment ratio of E eq ∼ 0.1. We experimentally measure the relationship between the along-slope entrainment ratio, E, of a density current to the horizontal entrainment ratio, E eq, of an equivalent vertical plume. The along-slope entrainment ratios show the same quantitative decrease with slope as observed by Ellison and Turner (Ellison, T.H. and Turner, J.S., Turbulent entrainment in stratified flows, J. Fluid Mech., 1959, 6, 423–448.), whereas the horizontal entrainment ratio E eq appears to asymptote to a value of E eq = 0.08 at low slopes. Using the measured values of E eq we show that two-dimensional density currents drive circulations that are in good agreement with the two-dimensional filling box model of Baines and Turner (Baines, W.D. and Turner, J.S., Turbulent buoyant convection from a source in a confined region, J. Fluid. Mech., 1969, 37, 51–80.). We find that the vertical velocities of density fronts collapse onto their theoretical prediction that U =-2−2/3 B 1/3 E eq 2/3 (H/R) ζ, where U is the velocity, H the depth, B the buoyancy flux, R the basin width, E eq the horizontal entrainment ratio and ζ = z/H the dimensionless depth. The density profiles are well fitted with Δ = 2−1/3 B 2/3 E eq −2/3 H -1 [ln(ζ ) + τ ], where τ is the dimensionless time. Finally, we provide a simple example of a diffusive filling box model, where we show how the density stratification of the deep Caribbean waters (below 1850 m depth) can be described by a balance between a steady two-dimensional entraining density current and vertical diffusion in a triangular basin.