Shallow Convection and Buoyancy Equilibration in an Idealized Coastal Polynya*
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The recent theoretical approach of Visbeck, Marshall, and Jones is used to examine shallow convection and offshore transport of dense water from an idealized coastal polynya. A constant negative buoyancy flux is applied in a half-elliptical region adjacent to a coastal boundary, surrounded by a forcing decay region with uniform width W over which the imposed buoyancy flux decreases smoothly to zero. Initially, the density beneath the forcing increases linearly with time. A baroclinically unstable front forms at the edge of the forcing region. The width of the front is imposed by the width of the forcing decay region, provided this distance is larger than the baroclinic Rossby radius. Baroclinic eddies, whose velocities are inversely proportional to W develop along the front and exchange dense water from the forcing region with ambient water, eventually reaching an equilibrium in which the lateral buoyancy flux by eddies balances the prescribed surface buoyancy flux. The time to reach equilibrium t(e), and the equilibrium density anomaly rho(e) are given by t(e) = beta(fWb/B-0)(1/2); rho(e)=beta rho(0)/gH(fB(0)Wb)(1/2), where B-0 is the imposed buoyancy flux, b the offshore width of the constant forcing region, H the water depth, f the Coriolis parameter, rho(0), a reference density, and g the gravitational acceleration. Finally, beta = [pi/2 alpha’E(1-b(2)/a(2))](1/2), where a is the length of the constant forcing region along the coast, alpha’ is the efficiency of eddy exchange, and E is the complete elliptic integral of the second kind. These parameter dependencies are fundamentally different from previous results for deep or shallow convection (1/2 power rather than 1/3 or 2/3) owing to the influence of the forcing decay region. The scalings are confirmed with numerical calculations using a primitive equation model. Eddy exchange in shallow convection is several limes more efficient than in open-ocean deep convection. Some implications for Arctic coastal polynyas are discussed.