Abstract:
The development of nonlinear surface and internal wave
groups is investigated. Surface wave evolution was observed
in an unusually long wave channel as a function of steepness
and group length. Dissipation and frequency downshifting were
important characteristics of the long-time evolution. The
amplitude and phase modulations were obtained using the
Hilbert transform and specified as an initial condition to the
cubic nonlinear Schrodinger equation, which was solved
numerically. This equation is known to govern the slowly
varying complex modulation envelope of gravity waves on deep
water. When dissipation was included, the model compared
quite well with the observations. Phase modulation was used
to interpret the long-time behavior, using the phase evolution
of exact asymptotic solutions as a guide. The wave groups
exhibited a long-time coherence but not the recurrence
predicted by the inviscid theory.
An oceanic field study of the generation of groups of
large amplitude internal waves by stratified tidal flow over a
submarine ridge indicates that the large amplitude and
asymmetry of the topography are critical in determining the
type of flow response. The calculated Froude numbers
response length scale and duration differ markedly between the
two phases of the tide due to the asymmetry.
