Asymptotic analysis on the modelling of the shallow-water waves with the Coriolis effect

PDE Seminar
Wednesday, March 29, 2017 - 15:05
1 hour (actually 50 minutes)
Skiles 006
University Of Texas At Arlington
In this talk, a mathematical model of long-crested water waves propagating mainly in one direction with the effect of Earth's rotation is derived by following the formal asymptotic procedures. Such a model equation is analogous to the Camassa-Holm approximation of the two-dimensional incompressible and  irrotational Euler equations and has a formal bi-Hamiltonian structure.  Its solution corresponding to physically relevant initial perturbations is more accurate on a much longer time scale. It is shown that the deviation of the free surface can be determined by the horizontal velocity at a certain depth in the second-order approximation.  The  effects of the Coriolis force caused by the Earth rotation and  nonlocal higher nonlinearities on blow-up criteria and wave-breaking phenomena are also investigated. Our refined analysis is approached by applying the method of characteristics and conserved quantities to the  Riccati-type differential inequality.