Event Type:

Applied Mathematics and Computation Seminar

Date/Time:

Friday, September 29, 2017 - 12:00 to 12:45

Location:

STAG 260

Event Link:

Guest Speaker:

Abstract:

I first introduce the classic solutions of edge waves: Stokes’ mode, Ursell’s higher-mode, and Eckart’s shallow-water approximation. By the coordinate translation, Stokes-mode solution becomes identical to that of deep-water waves, in spite of the majority of edge-wave energy being in shallow water. In addition, the evolution equation of nonlinear edge waves turns out equivalent to that of deep-water waves: viz. the nonlinear Schrödinger equation. My laboratory experiments exhibit the behavior of Benjamin-Feir instability — one of the predictions from the nonlinear Schrödinger equation — but with significant energy attenuation for this boundary-dominated flows. The laboratory realization of the envelope soliton was also affected by the viscous attenuation. The viscous time scale in my experiments is comparable to that of evolution process.