# American Institute of Mathematical Sciences

July  2012, 11(4): 1549-1561. doi: 10.3934/cpaa.2012.11.1549

## Effects of shear flow on KdV balance - applications to tsunami

 1 Fakultät für Mathematik, University of Vienna, Nordbergstr. 15, 1090 Vienna, Austria

Received  March 2011 Revised  June 2011 Published  January 2012

Building upon recent work in the applicability of soliton theory to tsunami propagation, we discuss the effects of shear flow on the KdV balance. This leads in the shallow-water limit to the Burns condition, and we see that for shear which does not yield critical layer solutions, the speeds determined by the Burns condition arise again in the KdV balance. In the event of waves propagating counter to the shear, KdV dynamics arise earlier, while their appearance is delayed in the case of waves propagating with the shear, the magnitude of this effect depending on the surface shear velocity.
Citation: Raphael Stuhlmeier. Effects of shear flow on KdV balance - applications to tsunami. Communications on Pure & Applied Analysis, 2012, 11 (4) : 1549-1561. doi: 10.3934/cpaa.2012.11.1549
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