Mathematics of Hele-Shaw beach evolution by breaking waves

Description

Mathematical modeling of beach evolution by breaking waves will never be anything less than complicated: large-scale numerical computations are necessary, but because of the large number of (sand) grains involved, as well as the fine-scale water motion, brute-force computations remain too demanding. Creative approaches to computational multi-scale modeling are required in order to reduce the degrees of freedom involved.
Inspired by the strongly visual approach to applied mathematics of the late Howell Peregrine, I devised a simplified, quasi-two-dimensional, or `Hele-Shaw', mathematical model that captures the essentials of wave breaking and beach evolution. I then built a corresponding table-top experiment and subsequently returned to modeling its dynamics. The laboratory reality proves that the reduced model is not a mere mathematical construct. I will present: the applied mathematics which lead to the reduced model; a live demonstration of the table-top experiment; and, an overview of our wave modeling expertise in compatible numerical schemes and finite element models with hydraulic jumps.
Finally, I will sketch some multi-scale modeling approaches that enable feasible three-dimensional, numerical computations.

Period	17 Nov 2011
Held at	Centre for Analysis, Scientific computing and Applications (CASA), Netherlands
Degree of Recognition	National