Yz. Chen et Plf. Liu, NUMERICAL STUDY OF SURFACE SOLITARY WAVE AND KELVIN SOLITARY WAVE-PROPAGATION IN A WIDE CHANNEL, Fluid dynamics research, 19(1), 1997, pp. 27-45
The Petrov-Galerkin finite-element method is used to solve the unified
Kadomtsev-Petviashvili equation [Chen and Liu, J. Fluid Mech. 288 (19
95) 383]. Numerical experiments have been focused on studying the effe
ct of slowly varying topography on the propagation of surface solitary
waves in a stationary channel and Kelvin solitary waves in a rotating
channel. We find that in the absence of rotation, an oblique incident
solitary wave propagating over a three-dimensional shelf in a straigh
t wide channel will eventually develop into a series of uniform straig
ht-crested solitary waves, together with a train of small oscillatory
waves moving upstream. With proper phase shifts, the shapes of these f
inal two-dimensional solitary waves coincide with those of solitary wa
ves emerging from a corresponding normal incident solitary wave propag
ating over the corresponding two-dimensional shelf. In a two-layered r
otating channel, the variation of topography does not have much effect
on the propagation of a Kelvin solitary wave of depression, whereas i
t can have a significant influence on the propagation of a Kelvin soli
tary wave of elevation. Explanations for these numerical findings are
given.