A Geostrophic Adjustment Model of Two Buoyant Fluids

A combination of analytical calculations and laboratory experiments has been used to investigate the geostrophic adjustment of two buoyant fluids having different densities in a third denser ambient fluid. The frontal position, the depth profile, and the horizontal and vertical alignments of the two buoyant fluids at the final equilibrium state are determined by the ratio of the baroclinic Rossby radii of deformation Gamma(1) = lambda(31)/lambda(21) and Gamma(2) = lambda(32)/lambda(21) and the Burger numbers B-1 = lambda(31)/L-1 and B-2 = lambda(32)/L-2 of the two buoyant fluids, where lambda(ij) = (root g'H-ij(j)/f) is the baroclinic Rossby radius of deformation between fluids i and j. The buoyant fluids 1 and 2 have densities rho(1) and rho(2) (rho(1) < rho(2)), respectively; the ambient denser fluid has density rho(3); g' is the reduced gravity; H and L are the buoyant fluids' initial depth and width, respectively; and f is the Coriolis parameter. Laboratory rotating experiments confirmed the analytical prediction of the location of the two fronts. After reaching geostrophic equilibrium, the two buoyant currents align mainly horizontally when the extent of the fronts between fluids 1 and 3 and between fluids 2 and 3 is large compared to the extent of the front between fluids 1 and 2: that is, large values of lambda(31) and lambda(32) compared to lambda(21) or equivalently Gamma(1) >> 1 and Gamma(2) >> 1. Alternatively, if the extent of the fronts between the three fluids is similar (i.e., Gamma(1) approximate to Gamma(2) approximate to 1), the buoyant currents align mainly vertically. Furthermore, the Burger number of the lightest fluid B-1 controls the distance of the inner front from the coast, while B-2 controls the offshore extent of the outer front.