The Response of a Weakly Stratified Layer to Buoyancy Forcing

Joseph Pedlosky Woods Hole Oceanographic Institution, Woods Hole, Massachusetts

Search for other papers by Joseph Pedlosky in
Current site
Google Scholar
PubMed
Close
Restricted access

Abstract

The response of a weakly stratified layer of fluid to a surface cooling distribution is investigated with linear theory in an attempt to clarify recent numerical results concerning the sinking of cooled water in polar ocean boundary currents.

A channel of fluid is forced at the surface by a cooling distribution that varies in the down-channel as well as the cross-channel directions. The resulting geostrophic flow in the central region of the channel impinges on its boundaries, and regions of strong downwelling are observed. For the parameters of the problem investigated, the downwelling occurs in a classical Stewartson layer but the forcing of the layer leads to an unusual relation with the interior flow, which is forced to satisfy the thermal condition on the boundary while the geostrophic normal flow in the interior is brought to rest in the boundary layer.

As a consequence of the layer’s dynamics, the resulting long-channel flow exhibits a nonmonotonic approach to the interior flow, and the strongest vertical velocities are limited to the boundary layer whose scale is so small that numerical models resolve the region only with great difficulty. The analytical model presented here is able to reproduce key features of the previous nonlinear numerical calculations.

Corresponding author address: Joseph Pedlosky, Woods Hole Oceanographic Institution, Woods Hole, MA 02543. Email: jpedlosky@whoi.edu

Abstract

The response of a weakly stratified layer of fluid to a surface cooling distribution is investigated with linear theory in an attempt to clarify recent numerical results concerning the sinking of cooled water in polar ocean boundary currents.

A channel of fluid is forced at the surface by a cooling distribution that varies in the down-channel as well as the cross-channel directions. The resulting geostrophic flow in the central region of the channel impinges on its boundaries, and regions of strong downwelling are observed. For the parameters of the problem investigated, the downwelling occurs in a classical Stewartson layer but the forcing of the layer leads to an unusual relation with the interior flow, which is forced to satisfy the thermal condition on the boundary while the geostrophic normal flow in the interior is brought to rest in the boundary layer.

As a consequence of the layer’s dynamics, the resulting long-channel flow exhibits a nonmonotonic approach to the interior flow, and the strongest vertical velocities are limited to the boundary layer whose scale is so small that numerical models resolve the region only with great difficulty. The analytical model presented here is able to reproduce key features of the previous nonlinear numerical calculations.

Corresponding author address: Joseph Pedlosky, Woods Hole Oceanographic Institution, Woods Hole, MA 02543. Email: jpedlosky@whoi.edu

Save
  • Barcilon, V., and J. Pedlosky, 1967: A unified theory of homogeneous and stratified rotating fluids. J. Fluid Mech., 29 , 609621.

  • Greenspan, H. P., 1968: The Theory of Rotating Fluids. Cambridge University Press, 327 pp.

  • LaCasce, J. H., 2004: Diffusivity and viscosity dependence in the linear thermocline. J. Mar. Res., 62 , 743769.

  • Marotzke, J., 1997: Boundary mixing and the dynamics of the three-dimensional thermohaline circulations. J. Phys. Oceanogr., 27 , 17131728.

    • Search Google Scholar
    • Export Citation
  • Marotzke, J., and J. R. Scott, 1999: Convective mixing and thermohaline circulation. J. Phys. Oceanogr., 29 , 29622970.

  • Marshall, J., C. Hill, L. Perlman, and A. Adcroft, 1997: Hydrostatic, quasi-hydrostatic and nonhydrostatic ocean modeling. J. Geophys. Res., 102 , 57335752.

    • Search Google Scholar
    • Export Citation
  • Pedlosky, J., 1968: Linear theory of the circulation of a stratified ocean. J. Fluid Mech., 35 , 185205.

  • Pedlosky, J., and M. Spall, 2005: Boundary intensification of vertical velocity in a β-plane basin. J. Phys. Oceanogr., 35 , 24872500.

    • Search Google Scholar
    • Export Citation
  • Spall, M. A., 2008: Buoyancy-forced downwelling in boundary currents. J. Phys. Oceanogr., 38 , 27042721.

  • Stewartson, K., 1957: On almost rigid rotations. J. Fluid Mech., 6 , 1726.

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 120 53 18
PDF Downloads 96 63 6