A note on the general concept of wave breaking for Rossby and gravity waves |
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| Authors: | M E McIntyre T N Palmer |
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| Institution: | (1) Department of Applied Mathematics and Theoretical Physics, Silver St., CB3 9EW Cambridge, U.K.;(2) European Centre for Medium Range Weather Forecasts, Shinfield Park, RG2 9AX Reading, U.K. |
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| Abstract: | A recently proposed general definition of wave breaking is further discussed, in order to deal with some points on which misunderstanding appears to have arisen. As with surface and internal gravity waves, the classification of Rossby waves into  breaking and not breaking is a generic classification based on dynamical considerations, and not a statement about any unique signature or automatically recognizable shape. Nor is it a statement about passive tracers uncorrelated with potential vorticity on isentropic surfaces. A strong motivation for the definition is that proofs of the nonacceleration theorem of wave, mean-flow interaction theory rely, explicitly or implicitly, on a hypothesis that the waves do not break in the sense envisaged.The general definition refers to the qualitative behaviour of a certain set of material contours, namely those, and only those, which would undulate reversibly, with small slopes, under the influence of the waves' restoring mechanism, in those circumstances for which linearized, nondissipative wave theory is a self-consistent approximation to nonlinear reality. The waves' restoring mechanism depends upon the basic-state vertical potential density gradient in the case of gravity waves, and upon the basic-state isentropic gradient of potential vorticity in the case of Rossby waves. In the usual linearized theory of planetary scale Rossby waves on a zonal shear flow, the relevant material contours lie along latitude circles when undisturbed. |
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| Keywords: | wave propagation linear Rossby wave theory stratospheric planetary waves potential vorticity passive tracers critical layers wave breaking wave mean-flow interaction reversibility |
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