Seminar Event Detail

Applied Interdisciplinary Mathematics (AIM)

Date:  Friday, April 19, 2019
Location:  1084 East Hall (3:00 PM to 4:00 PM)

Title:  Ocean wave turbulence - from theory to computation

Abstract:   In this presentation, we seek a first-principles understanding of the stationary and invariant form of ocean wave spectrum based on wave turbulence theory, which describes the statistical property of an ensemble of waves in weakly nonlinear interactions. The starting point of the research is on capillary waves, which dominate the small-scale dynamics of ocean surface. Allowing triad resonant interactions, capillary waves represent a most fundamental system which yields a stationary wave turbulence spectrum. In theory, we reformulate the theoretical stationary solution of the capillary wave spectrum, with a correction on the value of the Kolmogorov constant, quantifying the proportionality between spectral amplitude and spectral energy flux. In computation, we develop a numerical method to simulate the phase-resolved evolution of a nonlinear capillary wave field. The simulations confirm the new theoretical development, and additionally uncover the effect of finite domain on the wave spectrum evolution. Inspired by the numerical findings, a new model named "quasi-resonant kinetic equation" is developed, which incorporates the effect of finite domain in the wave turbulence framework.


Speaker:  Yulin Pan
Institution:  University of Michigan, Naval Architecture and Marine Engineering

Event Organizer:   Charlie Doering


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