An Improved Bound for the Complex Phase Speed of Baroclinic Instability

Roland A. de Szoeke College of Oceanic and Atmospheric Sciences, Oregon State University, Corvallis, Oregon

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Abstract

An improved bound is obtained for the radius of the semicircle in the complex plane containing the complex phase speed of baroclinically unstable plane wave disturbances. In the limit of long waves, this bound contains a term increasing with β and decreasing with the mean stratification (i.e., decreasing with the baroclinic Rossby radius of deformation). An extension of the bound, valid for finite wavelengths longer than order (δu/β)1/2, where δu is half the range of velocities in the mean shear flow, is also obtained.

Corresponding author address: Roland A. de Szoeke, 104 Ocean Administration Building, Oregon State University, Corvallis, OR 97331.

Email: szoeke@oce.orst.edu

Abstract

An improved bound is obtained for the radius of the semicircle in the complex plane containing the complex phase speed of baroclinically unstable plane wave disturbances. In the limit of long waves, this bound contains a term increasing with β and decreasing with the mean stratification (i.e., decreasing with the baroclinic Rossby radius of deformation). An extension of the bound, valid for finite wavelengths longer than order (δu/β)1/2, where δu is half the range of velocities in the mean shear flow, is also obtained.

Corresponding author address: Roland A. de Szoeke, 104 Ocean Administration Building, Oregon State University, Corvallis, OR 97331.

Email: szoeke@oce.orst.edu

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  • Cavallini, F., F. Crisciani, and R. Mosetti, 1988: Bounds on the eigenvalues of the planetary-scale baroclinic instability problem. Dyn. Atmos. Oceans,12, 71–80.

  • Chelton, D. B., R. A. de Szoeke, M. G. Schlax, K. El Naggar, and N. Siwertz, 1998: Geographical variability of the first baroclinic Rossby radius of deformation. J. Phys. Oceanogr.,28, 433–460.

  • Colin de Verdière, A., 1986: On mean flow instabilities within the planetary geostrophic equations. J. Phys. Oceanogr.,16, 1985–1990.

  • Frankignoul, C., P. Müller, and E. Zorita, 1997: A simple model of the decadal response of the ocean to stochastic forcing. J. Phys. Oceanogr.,27, 1533–1546.

  • Howard, L. N., 1961: Note on a paper of John Miles. J. Fluid Mech.,10, 509–512.

  • Jeffreys, H., and B. S. Jeffreys, 1956: Methods of Mathematical Physics, 3d ed., Cambridge University Press, 718 pp.

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

  • Pedlosky, J., 1963: Baroclinic instability in two layer systems. Tellus,15, 20–25.

  • ——, 1964: The stability of currents in the atmosphere and the oceans. Part I. J. Atmos. Sci.,21, 201–219.

  • ——, 1987: Geophysical Fluid Dynamics, 2d ed. Springer-Verlag, 710 pp.

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