Nonlinear Dispersive Waves and Applications to Geophysical Fluid Flows

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This project is organized around two leading themes in internal gravity wave propagation in stratified fluids: (a) interplay between nonlinearity and dispersion, and (b) instabilities and resonances. Within the first theme, the long term goal is to provide a model of internal waves in layered stratification that correctly accounts for dispersion and high nonlinearity, to be used in alternative to the currently adopted non-dispersive and weakly nonlinear models. The aim is to retain the advantage of the simplicity of these theories with respect to the full Euler (or Navier-Stokes) governing motion equations, while still maintaining the ability to describe wave dynamics of practical interest. Highly nonlinear regimes often generate instabilities. The causes and evolution of these instabilities for fully nonlinear internal waves are the focus within the second theme. In particular, stability criteria based on the Howard-Miles theorem for stationary shear flows and parametric instability occurring at stable Richardson's number will be revisited in the context of internal gravity waves.This research focuses on an area of wave propagation which has widespread atmospheric and oceanic applications, and, therefore, large societal implications. For instance, large internal waves generated by wind forcing of the upper ocean may have a strong feedback effect on the intensity of hurricanes. Thus, numerical codes based on models capable of representing accurately large amplitude waves and their dispersive behavior (responsible for the spreading of wave energy over increasingly larger regions) can play an important role in hurricane forecasts, at little additional cost with respect to the currently employed hydrostatic codes. The award will support work that will help establish the theoretical and technical foundations of such improved computational codes.