2134/404
Oleg G. Derzho
Oleg G.
Derzho
Roger Grimshaw
Roger
Grimshaw
Rossby waves on a shear flow with recirculation cores
Loughborough University
2005
untagged
Mathematical Sciences not elsewhere classified
2005-08-16 14:48:04
Preprint
https://repository.lboro.ac.uk/articles/preprint/Rossby_waves_on_a_shear_flow_with_recirculation_cores/9384131
Large amplitude Rossby waves riding on a background flow with a weak shear can be calculated up to a critical amplitude for which the meridional velocity, in a frame travelling with the wave, approaches zero at some point. Here we consider waves with an amplitude slightly greater than the critical amplitude by incorporating a region of recirculating fluid ( vortex core ) near this critical point. The effect of the vortex core is to introduce an extra nonlinear term into the equation for the wave amplitude proportional to the 3/2 power of the difference between the wave amplitude and the critical amplitude. The main effect due to the vortex core is a broadening of the wave profile. Further we show that the vortex core family has a limiting amplitude, with the limiting amplitude corresponding to a semi-infinite bore.