Editorial Type:
Article
Article Type:
Research Article

Shallow Convection and Buoyancy Equilibration in an Idealized Coastal Polynya

David C. Chapman Woods Hole Oceanographic Institution, Woods Hole, Massachusetts

Search for other papers by David C. Chapman in
Current site
Google Scholar
PubMed Close
and
Glen Gawarkiewicz Woods Hole Oceanographic Institution, Woods Hole, Massachusetts

Search for other papers by Glen Gawarkiewicz in
Current site
Google Scholar
PubMed Close
Print Publication:
01 Apr 1997
DOI:
https://doi.org/10.1175/1520-0485(1997)027<0555:SCABEI>2.0.CO;2
Page(s):
555–566
Restricted access

Abstract

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 te and the equilibrium density anomaly ρe are given by
i1520-0485-27-4-555-eq1
where B0 is the imposed buoyancy flux, b the offshore width of the constant forcing region, H the water depth, f the Coriolis parameter, ρ0 a reference density, and g the gravitational acceleration. Finally, β = [π/2α′E(1 − b2/a2)]1/2, where a is the length of the constant forcing region along the coast, α′ 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 times more efficient than in open-ocean deep convection. Some implications for Arctic coastal polynyas are discussed.

Corresponding author address: Dr. David C. Chapman, Woods Hole Oceanographic Institution, Woods Hole, MA 02543.

Abstract

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 te and the equilibrium density anomaly ρe are given by
i1520-0485-27-4-555-eq1
where B0 is the imposed buoyancy flux, b the offshore width of the constant forcing region, H the water depth, f the Coriolis parameter, ρ0 a reference density, and g the gravitational acceleration. Finally, β = [π/2α′E(1 − b2/a2)]1/2, where a is the length of the constant forcing region along the coast, α′ 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 times more efficient than in open-ocean deep convection. Some implications for Arctic coastal polynyas are discussed.

Corresponding author address: Dr. David C. Chapman, Woods Hole Oceanographic Institution, Woods Hole, MA 02543.

Save
Cover Journal of Physical Oceanography
Journal of Physical Oceanography

  • Abramowitz, M., and I. Stegun, 1965: Handbook of Mathematical Functions. Dover, 1046 pp.

  • Brickman, D., 1995: Heat flux partitioning in open-ocean convection. J. Phys. Oceanogr.,25, 2609–2623.

  • Cavalieri, D. J., and S. Martin, 1994: The contributions of Alaskan, Siberian, and Canadian coastal polynyas to the cold halocline layer of the Arctic Ocean. J. Geophys. Res.,99, 18 343–18 362.

  • Coates, M. J., G. N. Ivey, and J. R. Taylor, 1995: Unsteady, turbulent convection into a rotating, linearly stratified fluid: Modeling deep ocean convection. J. Phys. Oceanogr.,25, 3032–3050.

  • Gawarkiewicz, G., and D. C. Chapman, 1995: A numerical study of dense water formation and transport on a shallow, sloping continental shelf. J. Geophys. Res.,100, 4489–4507.

  • Haidvogel, D., J. Wilkin, and R. Young, 1991: A semi-spectral primitive equation ocean circulation model using vertical sigma and orthogonal curvilinear horizontal coordinates. J. Comput. Phys.,94, 151–185.

  • Ivey, G. N., J. R. Taylor, and M. J. Coates, 1995: Convectively driven mixed layer growth in a rotating, stratified fluid. Deep-Sea Res.,42, 331–349.

  • Jones, H., and J. Marshall, 1993: Convection with rotation in a neutral ocean: A study of open-ocean deep convection. J. Phys. Oceanogr.,23, 1009–1039.

  • Manley, T. O., and K. Hunkins, 1985: Mesoscale eddies of the Arctic Ocean. J. Geophys. Res.,90, 4911–4930.

  • Maxworthy, T., and S. Narimousa, 1994: Unsteady, turbulent convection into a homogeneous, rotating fluid, with oceanographic applications. J. Phys. Oceanogr.,24, 865–887.

  • Melling, H., 1993: The formation of a haline shelf front in wintertime in an ice-covered arctic sea. Contin. Shelf Res.,13, 1123–1147.

  • Pease, C. H., 1987: The size of wind-driven coastal polynyas. J. Geophys. Res.,92, 7049–7059.

  • Schumacher, J. D., K. Aagaard, C. H. Pease, and R. B. Tripp, 1983: Effects of a shelf polynya on flow and water properties in the northern Bering Sea. J. Geophys. Res.,88, 2723–2732.

  • Visbeck, M., J. Marshall, and H. Jones, 1996: Dynamics of isolated convective regions in the ocean. J. Phys. Oceanogr.,26, 1721–1934.

  • Whitehead, J.A., J. Marshall, and G. E. Hufford, 1996: Localized convection in rotating stratified fluid. J. Geophys. Res.,101, 25 705-25 722.

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 473 214 56
PDF Downloads 179 44 3