Math 801: Waves in Fluids | UW Mathematics

Prerequisites:

Knowledge of Fluid Dynamics (705 or equivalent) and PDEs (703,704 or equivalent). Some experience with numerics helpful. Please contact the instructor for details.

Instructor:

Paul Milewski

Time and Place:

Tu, Th, 11-12:15

textbooks:

Reference Books:
Whitham, G. Linear and Nonlinear Waves
Lighthill, J. Waves in Fluids
Craik, A. D. D. Wave Interactions and Fluid Flows

Course Content:

This course will present the main concepts and equations of nonlinear waves using surface waves and internal waves as a physical context.
We shall cover the following topics: (i) Introduction/review of incompressible fluid dynamics, including free surface problems. (ii) Shallow water theory: hydraulic approximation, breaking waves and shocks. Mixing in fluids. (iii) Weakly dispersive models: Boussinesq, Korteweg-de Vries and Serre (Green-Naghdi). (iv) Dispersion - waves in deep water - phase and group speed and the kinematics of linear waves. (v) Dispersion and nonlinearity: the Nonlinear Schrodinger Equation. (vi) Solitary and generalized solitary waves. Solitons.

The goal is to give students both the tools and intuition for the dynamics of nonlinear and/or dispersive waves.