Event Type:

Applied Mathematics and Computation Seminar

Date/Time:

Friday, October 18, 2013 - 05:00 to 06:00

Location:

GLK 115

Event Link:

Guest Speaker:

Institution:

OSU CEOAS and Engineering

Abstract:

Models for surface gravity wave propagation in the presence of currents

often assume the current field to be quasi-stationary, which implies that the absolute wave frequency is time invariant. However, in the presence of unsteady currents or time-varying water depth, linear wave theory predicts a time variation of the absolute wave frequency ^Aand wavenumber. Herein, observations of wave frequency modulations from a large-scale laboratory experiment are presented. In this case, the modulations are caused by both unsteady depths and unsteady currents due to the presence of

low-frequency standing waves. These new observations allow a unique and

detailed verification of the theoretical predictions regarding variations in the absolute wave frequency. In addition, analytic solutions for the variations in frequency and wave height induced by the unsteady medium are found through a perturbation analysis. These solutions clarify the dependency of the wave frequency/wave height modulations on the characteristics of the unsteady medium. We also find that analytic

solutions for simplified basin configurations provide an order of magnitude estimate of the expected frequency modulation effect. Finally, the importance of this phenomenon in natural situations is discussed.

Also see our paper on the subject at

http://pof.aip.org/resource/1/phfle6/v19/i12/p126601_s1