Lecture I: Internal waves in continuously stratified fluids
A survey of the governing equations and basic properties of internal
gravity
waves in continuously stratified fluids. Geophysical significance of
internal
waves in the oceans and atmosphere.
Lecture II: Nonlinear internal gravity wave beams
Internal gravity waves are anisotropic since gravity provides a preferred
direction. As a result, the response to localized time-harmonic forcing
features, rather than circular wavefronts, beam-like disturbances
propagating
along specific directions depending on the driving frequency. Recent
advances
in understanding the propagation and nonlinear interactions of
finite-amplitude
wave beams will be discussed.
Lecture III: Reflecting tidal wave beams and local generation of
solitary waves in the ocean thermocline.
A nonlinear long-wave model will be presented of how internal wave beams,
that
are induced by tidal flow over bottom topography and then reflect from the
ocean thermocline at a significant distance from the continental shelf,
may
give rise to solitary waves. Comparison of the theoretical predictions
against
field observations will be made, supporting this local generation
mechanism.