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Article Type:
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A Geostrophic Adjustment Model of Two Buoyant Fluids

Claudia Cenedese Department of Physical Oceanography, Woods Hole Oceanographic Institution, Woods Hole, Massachusetts

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James A. Lerczak College of Earth, Ocean, and Atmospheric Sciences, Oregon State University, Corvallis, Oregon

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Giuseppe Bartone Department of Civil, Building, and Environmental Engineering, Sapienza University of Rome, Rome, Italy

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Print Publication:
01 Nov 2012
DOI:
https://doi.org/10.1175/JPO-D-11-0169.1
Page(s):
1932–1944
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Abstract

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 Γ1 = λ31/λ21 and Γ2 = λ32/λ21 and the Burger numbers B1 = λ31/L1 and B2 = λ32/L2 of the two buoyant fluids, where is the baroclinic Rossby radius of deformation between fluids i and j. The buoyant fluids 1 and 2 have densities ρ1 and ρ2 (ρ1 < ρ2), respectively; the ambient denser fluid has density ρ3; 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 λ31 and λ32 compared to λ21 or equivalently Γ1 ≫ 1 and Γ2 ≫ 1. Alternatively, if the extent of the fronts between the three fluids is similar (i.e., Γ1 ≈ Γ2 ≈ 1), the buoyant currents align mainly vertically. Furthermore, the Burger number of the lightest fluid B1 controls the distance of the inner front from the coast, while B2 controls the offshore extent of the outer front.

Corresponding author address: Claudia Cenedese, Woods Hole Oceanographic Institution, 360 Woods Hole Rd., Woods Hole, MA 02536. E-mail: ccenedese@whoi.edu

Abstract

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 Γ1 = λ31/λ21 and Γ2 = λ32/λ21 and the Burger numbers B1 = λ31/L1 and B2 = λ32/L2 of the two buoyant fluids, where is the baroclinic Rossby radius of deformation between fluids i and j. The buoyant fluids 1 and 2 have densities ρ1 and ρ2 (ρ1 < ρ2), respectively; the ambient denser fluid has density ρ3; 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 λ31 and λ32 compared to λ21 or equivalently Γ1 ≫ 1 and Γ2 ≫ 1. Alternatively, if the extent of the fronts between the three fluids is similar (i.e., Γ1 ≈ Γ2 ≈ 1), the buoyant currents align mainly vertically. Furthermore, the Burger number of the lightest fluid B1 controls the distance of the inner front from the coast, while B2 controls the offshore extent of the outer front.

Corresponding author address: Claudia Cenedese, Woods Hole Oceanographic Institution, 360 Woods Hole Rd., Woods Hole, MA 02536. E-mail: ccenedese@whoi.edu
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