Waves in Geophysics
July 11, 2005 — July 15, 2005
Coordinator:
- John Grue (University of Oslo, Blindern, Oslo, Norway)
Waves on the ocean surface, internal tides and internal solitons, their phenomenological and mathematical descriptions, and how to perform advanced simulations of the waves, represent the main objectives of the course.
Tsunami forecasting: nonlinear generation by landslide motion and volcano eruption, wave run-up, breaking, distribution tsunami heights, real and prognostic events, includes a selection of approximately 80 tsunami events during the last decade, with waves of 30 mt in Japan and Kamchatka, and in the Mediterranean in 2003. Wind-generated ocean surface waves, their directional spectra, overshoot in fetch-limited and duration limited spectra, “saturation”, equilibrium, nonlinear wave-wave interactions and wind input are modeled comparing with field experiments.
Freak waves are individual waves in a wave field, significantly higher and steeper than what is expected from traditional wave statistics. Their occurrence in the open ocean, far from strong current gradients or topography, is explained as a possible consequence of nonlinearity in the wave field such as self-modulation.
Energetic internal tides—hot spots—are formed by the barotropic tide interacting with submarine ridges and shelves. Observations, data interpretation, modeling, extreme internal tide generation at near critical latitudes are described as well as shorter steep internal solitons propagating in layered oceans, including the wave induced velocity fields, shear and convective instabilities, surface and bottom currents.
Korteweg-de Vries (KdV) type of equations, the Davey-Stewardson, the nonlinear Schrödinger equation and extensions, and fully nonlinear modeling is outlined. Statistical properties of wave fields are deduced from large ensembles of deterministic simulations.
Statistical modeling of wind-generated waves includes a propagation structure using ray theory or a differential grid system for the action balance equation, parametric models of the degree of wind forcing of the waves, of the limiting process of wave breaking and of the nonlinear interactions among waves. Fully nonlinear internal wave models are compared with Benjamin-Ono, KdV-, intermediate-depth theory, as well as observations. Extensions of these equations are used to model internal tides and their transformation to high-frequency internal waves.
The course is addressed to PhD students, hydrodynamists, ocean forecasters, engineers, scientists, applied mathematicians, working with forecasting of real ocean waves, novel computations of very steep waves, modeling of internal tides and conversion to short internal solitons.