Slowly Modulated Baroclinic Waves in a Three-Layer Model

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  • 1 School of Mathematics, The University, Leeds LS2 9JT, UK and Geophysical Fluid Dynamics Laboratory, Meteorological Office, Bracknell, Berkshire RG12 2SZ, UK
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Abstract

A coupled pair of envelope equations is derived which describe the nonlinear evolution of slowly varying wave packets in a three-layer model of baroclinic instability on a βplane. The equations are identical in form to those obtained by Pedlosky (1972) to study wave-packet evolution in a two-layer model. They are transformable to the Self-Induced Transparency equations of nonlinear optics for complex wave amplitude, and to the sine-Gordon equation for real wave amplitude. Both are known to possess solution solutions, with associated highly predictable behavior.

The three-layer model therefore is another example of a mathematical model of baroclinic instability to exhibit solution behavior. The significance of such solutions to meteorology and oceanography is discussed.

Abstract

A coupled pair of envelope equations is derived which describe the nonlinear evolution of slowly varying wave packets in a three-layer model of baroclinic instability on a βplane. The equations are identical in form to those obtained by Pedlosky (1972) to study wave-packet evolution in a two-layer model. They are transformable to the Self-Induced Transparency equations of nonlinear optics for complex wave amplitude, and to the sine-Gordon equation for real wave amplitude. Both are known to possess solution solutions, with associated highly predictable behavior.

The three-layer model therefore is another example of a mathematical model of baroclinic instability to exhibit solution behavior. The significance of such solutions to meteorology and oceanography is discussed.

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