Wave capture and wave–vortex duality

OLIVER BÜHLER, MICHAEL E. McINTYRE
2005 Journal of Fluid Mechanics  
New and unexpected results are presented regarding the nonlinear interactions between a wavepacket and a vortical mean flow, with an eye towards internal wave dynamics in the atmosphere and oceans and the problem of 'missing forces' in atmospheric gravity-wave parametrizations. The present results centre around a prewave-breaking scenario termed 'wave capture', which differs significantly from the standard such scenarios associated with critical layers or mean density decay with altitude. We
more » ... ith altitude. We focus on the peculiar wave-mean interactions that accompany wave capture. Examples of these interactions are presented for layerwise-two-dimensional, layerwise-non-divergent flows in a three-dimensional Boussinesq system, in the strongstratification limit. The nature of the interactions can be summarized in the phrase 'wave-vortex duality', whose key points are firstly that wavepackets behave in some respects like vortex pairs, as originally shown in the pioneering work of Bretherton (1969) , and secondly that a collection of interacting wavepackets and vortices satisfies a conservation theorem for the sum of wave pseudomomentum and vortex impulse, provided that the impulse is defined appropriately. It must be defined as the rotated dipole moment of the Lagrangian-mean potential vorticity (PV). This PV differs crucially from the PV evaluated from the curl of either the Lagrangian-mean or the Eulerian-mean velocity. The results are established here in the strong-stratification limit for rotating (quasi-geostrophic) as well as for non-rotating systems. The concomitant momentum budgets can be expected to be relatively complicated, and to involve far-field recoil effects in the sense discussed in Bühler & McIntyre (2003) . The results underline the three-way distinction between impulse, pseudomomentum, and momentum. While momentum involves the total velocity field, impulse and pseudomomentum involve, in different ways, only the vortical part of the velocity field. † This is a controversial topic. Within a big literature one may cite, for instance, the complementary discussions and bibliographies in Nazarenko, Zabusky & Scheidegger (1995) and Stone (2000) .
doi:10.1017/s0022112005004374 fatcat:tbwni5t5ibdmfebqrhj3bwkwey