Nearly time-periodic water waves

Non-equilibrium Dynamics and Random Matrices
Topic:Nearly time-periodic water waves
Speaker:Jon Wilkening
Affiliation:University of California, Berkeley
Date:Tuesday, February 25
Time/Room:2:00pm - 3:00pm/S-101
Video Link:https://video.ias.edu/nedrm/2014/0225-JonWilkening

We compute new families of time-periodic and quasi-periodic solutions of the free-surface Euler equations involving extreme standing waves and collisions of traveling waves of various types. A Floquet analysis shows that many of the new solutions are linearly stable to harmonic perturbations. Evolving such perturbations (nonlinearly) over tens of thousands of cycles suggests that the solutions remain nearly time-periodic forever. We also discuss resonance and re-visit a long-standing conjecture of Penney and Price that the standing water wave of greatest height should form wave crests with sharp, 90 degree interior corner angles.