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Fluid Dynamics Seminar
Mon., Oct. 14, 2013,
2:30 PM
Cullimore, Room 611
New Jersey Institute of Technology
Waves Over Periodic Topographies
Jie Yu
Dept. of Civil, Construction and Environmental Engineering, North Carolina State University
Abstract
Wave propagation over variable topographies is a long-standing problem of importance in coastal and ocean engineering, as well as in oceanography. Such problems are mathematically challenging - even for linear waves over a simple sinusoidal bed, there have been no exact solutions known. Various approximate techniques have been derived, primarily for time-periodic waves, some semi-analytical and others essentially numerical. Hitherto the only case for which a really general treatment has been available is linear time-periodic waves over a horizontal flat bottom; here a complete basis of solutions has been known for many years. These are usually described as two oppositely directed propagating waves and two infinite families of evanescent waves. These linear modes have played important roles in various boundary value problems. In this talk, I shall present a new development of an exact Floquet theory for linear time-periodic waves over a spatially periodic topography of arbitrary amplitude and shape. The exact Floquet solutions give a complete basis for these situations which is analogous to the families of propagating and evanescent modes on a flat bed, and can similarly be used to solve boundary value problems. Examples of applications will be noted. Some recent work on extensions to weakly nonlinear waves over a large periodic seabed will be discussed.