• Benilov, E. S., 1994: The effect of continuous shear upon the two-layer model of baroclinic instability. Geophys. Astrophys. Fluid Dyn.78, 95–113.

  • ——, 1995: Baroclinic instability of quasi-geostrophic flows localized in a thin layer. J. Fluid Mech.,288, 175–199.

  • Charney, J. G., 1947: The dynamics of long waves in a baroclinic westerly current. J. Meteor.4, 135–163.

  • Dormand, J. R., and P. J. Prince, 1980: A family of embedded Runge–Kutta formulae. J. Comput. Appl. Math.,6, 19–26.

  • Eady, E. T., 1949: Long waves and cyclone waves. Tellus,1, 33–52.

  • Fukamachi, Y., J. P. McCreary, and J. A. Proehl, 1995: Instability of density fronts in layer and continuously stratified models. J. Geophys. Res.,100, 2559–2577.

  • Gill, A. E., J. S. A. Green, and A. J. Simmons, 1974: Energy partition in the large-scale ocean circulation and the production of mid-ocean eddies. Deep-Sea Res.,21, 499–528.

  • Green, J. S. A., 1960: A problem in baroclinic stability. Quart. J. Roy. Meteor. Soc.,86, 237–251.

  • Hairer, E., S. P. Norsett, and G. Wanner, 1993: Solving Ordinary Differential Equations 1: Nonstiff Problems. Springer-Verlag, 528 pp.

  • Killworth, P. D., D. B. Chelton, and R. A. DeSzoeke, 1997: The speed of observed and theoretical long extratropical planetary waves. J. Phys. Oceanogr.,27, 1946–1966.

  • Lee, C. M., and C. C. Eriksen, 1996: The subinertial momentum balance of the North Atlantic subtropical convergence zone. J. Phys. Oceanogr.,26, 1690–1704.

  • Olson, D. B., 1991: Rings in the ocean. Ann. Rev. Earth Planet. Sci.,19, 283–311.

  • Pedlosky, J., 1987: Geophysical Fluid Dynamics. Springer-Verlag, 710 pp.

  • Phillips, N. A., 1954: Energy transformation and meridional circulation associated with simple baroclinic waves in a two-level, quasi-geostrophic model. Tellus,6, 273–286.

  • Roden, G. I., 1975: On the North Pacific temperature, salinity, sound velocity and density fronts and their relation to the wind and energy flux fields. J. Phys. Oceanogr.,5, 557–571.

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 136 136 0
PDF Downloads 5 5 0

On the Linear Approximation of Velocity and Density Profiles in the Problem of Baroclinic Instability

View More View Less
  • 1 Department of Mathematics, University of Tasmania, Launceston, Australia
© Get Permissions Rent on DeepDyve
Restricted access

Abstract

The linear approximation of density and velocity profiles is compared to more realistic models with vertically inhomogeneous density gradients and nonzero anomalous vorticity (i.e., the nonplanetary part of potential vorticity). Calculations based on the parameters of “real life” currents in the Northern Pacific demonstrate that these effects, acting together, can make baroclinic instability 2.5–6 times stronger and dramatically expand the spectral range of unstable disturbances toward the short-wave region (by a factor of more than 20–30).

* Current affiliation: Department of Mathematics, University of Limerick, Limerick, Ireland.

Corresponding author address: Dr. Eugene S. Benilov, Department of Mathematics, University of Limerick, Limerick, Ireland.

Email: eugene@maths.warwick.ac.uk

Abstract

The linear approximation of density and velocity profiles is compared to more realistic models with vertically inhomogeneous density gradients and nonzero anomalous vorticity (i.e., the nonplanetary part of potential vorticity). Calculations based on the parameters of “real life” currents in the Northern Pacific demonstrate that these effects, acting together, can make baroclinic instability 2.5–6 times stronger and dramatically expand the spectral range of unstable disturbances toward the short-wave region (by a factor of more than 20–30).

* Current affiliation: Department of Mathematics, University of Limerick, Limerick, Ireland.

Corresponding author address: Dr. Eugene S. Benilov, Department of Mathematics, University of Limerick, Limerick, Ireland.

Email: eugene@maths.warwick.ac.uk

Save