linear Rossby wave theory
stratospheric planetary waves
wave mean-flow interaction
Springer Online Journal Archives 1860-2000
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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