Journal of the Australian Mathematical Society  Series B
Vol. 40 Part 2 (1998)
The effect of randomness on the stability of deep water
surface gravity waves in the presence of a thin thermocline
Sudebi Bhattacharyya
Department of Mathematics
Scottish Church
College
1 & 3
Urquhart Square
Calcutta700006
India.
and
K. P. Das
Department of Applied Mathematics
University of
Calcutta
92
Acharya Prafulla Chandra Road
Calcutta700009
India
Abstract:
The effect of randomness on the stability of deep water surface
gravity waves in the presence of a thin thermocline is studied. A
previously derived fourth order nonlinear evolution equation is used to
find a spectral transport equation for a narrow band of surface gravity
wave trains. This equation is used to study the stability of an initially
homogeneous Lorentz shape of spectrum to small long wavelength
perturbations for a range of spectral widths. The growth rate of the
instability is found to decrease with the increase of spectral widths. It
is found that the fourth order term in the evolution equation produces a
decrease in the growth rate of the instability. There is stability if the
spectral width exceeds a certain critical value. For a vanishing bandwidth
the deterministic growth rate of the instability is recovered. Graphs
have been plotted showing the variations of the growth rate of the
instability against the wavenumber of the perturbation for some different
values of spectral width, thermocline depth, angle of perturbation and
wave steepness.
PDF file size:
134K
© Copyright 1998, Australian Mathematical Society
TeXAdel Scientific Publishing
19980918
