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.