Hostname: page-component-8448b6f56d-dnltx Total loading time: 0 Render date: 2024-04-23T23:29:24.127Z Has data issue: false hasContentIssue false
  • English
  • Français

Finite-amplitude evolution of two-layer geostrophic vortices

Published online by Cambridge University Press:  21 April 2006

Karl R. Helfrich  and
Uwe Send
Karl R. Helfrich
Affiliation:
Woods Hole Oceanographic Institution, Woods Hole, MA 02543, USA
Uwe Send
Affiliation:
Scripps Institution of Oceanography, La Jolla, CA 92093, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

The finite-amplitude evolution of circular two-layer quasi-geostrophic vortices with piecewise uniform potential vorticity in each layer (also termed ‘heton’ clouds by Hogg & Stommel 1985a and Pedlosky 1985) is studied using the contour dynamics method. The numerical investigations are preceded by a linear stability analysis which shows the stabilizing influence of deepening the lower layer. Net barotropic flow may be either stabilizing or destabilizing. The contour dynamics calculations for baroclinic vortices show that supercritical (i.e. linearly unstable) conditions may lead to explosive break up of the vortex via the generation of continuous hetons at the cloud boundary. The number of vortex pairs is equal to the azimuthal mode number of the initial disturbance. An additional weakly supercritical regime in which amplitude vacillation occurs, but not explosive growth, is identified. Vortices with net barotropic circulation behave similarly except that the layer with vorticity opposite to the barotropic circulation will break up first. Strong barotropic circulation can inhibit the development of hetons. The stronger layer may eject thin filaments, but remain mostly intact. Calculations for initial conditions composed of several unstable modes show that the linearly most unstable mode dominates at finite amplitude.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 197 , December 1988 , pp. 331 - 348
Copyright
© 1988 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Dahlquist, G. & Björck, Å, 1974 Numerical Methods. Prentice-Hall.
Flierl, G. R.1988 On the instability of geostrophic vortices. J. Fluid Mech. 197, 349–388.Google Scholar
Griffiths, R. W. & Linden, P. F.1981 The stability of vortices in a rotating, stratified fluid. J. Fluid Mech. 105, 283–316.Google Scholar
Hart, J. E.1981 Wavenumber selection in nonlinear baroclinic instability. J. Atmos. Sci. 38, 400–408.Google Scholar
Hogg, N. G. & Stommel, H. M.1985a Hetonic explosions: The breakup and spread of warm pools as explained by baroclinic point vortices. J. Atmos. Sci. 42, 1465–1476.Google Scholar
Hogg, N. G. & Stommel, H. M.1985b The heton, an elementary interaction between discrete baroclinic geostrophic vortices, and its implications concerning eddy heat-flow. Proc. R. Soc. Lond. A 397, 1–20.Google Scholar
Ikeda, M.1981 Instability and splitting of mesoscale rings using a two layer quasi-geostrophic model on an f-plane. J. Phys Oceanogr. 11, 987–998.Google Scholar
Klein, P. & Pedlosky, J.1986 A numerical study of baroclinic instability at large supercriticality. J. Atmos. Sci. 43, 1243–1262.Google Scholar
Kozlov, V. F., Makarov, V. G. & Sokolovskiy, M. A.1986 Numerical model of baroclinic instability of axially symmetric eddies in a two-layer ocean. Izv. Akad. Nauk, SSSR Atmos. Ocean. Phys. 22, 674–678.Google Scholar
Pedlosky, J.1979 Geophysical Fluid Dynamics. Springer.
Pedlosky, J.1981 The nonlinear dynamics of baroclinic wave ensembles. J. Fluid Mech. 102, 169–209.Google Scholar
Pedlosky, J.1985 The instability of continuous heton clouds. J. Atmos. Sci. 42, 1477–1486.Google Scholar
Pratt, L. J. & Stern, M. E.1986 Dynamics of potential vorticity fronts and eddy detachment. J. Phys. Oceanogr. 16, 1101–1120.Google Scholar
Young, W. R.1985 Some interactions between small numbers of baroclinic, geostrophic vortices. Geophys. Astrophys. Fluid Dyn. 33, 35–62.Google Scholar
Zabusky, N. J., Hughes, M. & Roberts, K. V.1979 Contour dynamics for the Euler equations in two dimensions. J. Comp. Phys. 30, 96–106.Google Scholar
Zabusky, N. J. & Overman, E. A.1983 Regularization of contour dynamical algorythms. 1. Tangential regularization. J. Comp. Phys. 52, 351–373.Google Scholar