The inverse water wave problem of bathymetry detection

Journal of Fluid Mechanics - Tập 714 - Trang 562-590 - 2013
Vishal Vasan1, Bernard Deconinck2
1Department of Mathematics, Pennsylvania State University, University Park, PA 16802, USA
2Department of Applied Mathematics, University of Washington, Seattle, WA 98195, USA

Tóm tắt

AbstractThe inverse water wave problem of bathymetry detection is the problem of deducing the bottom topography of the seabed from measurements of the water wave surface. In this paper, we present a fully nonlinear method to address this problem in the context of the Euler equations for inviscid irrotational fluid flow with no further approximation. Given the water wave height and its first two time derivatives, we demonstrate that the bottom topography may be reconstructed from the numerical solution of a set of two coupled non-local equations. Owing to the presence of growing hyperbolic functions in these equations, their numerical solution is increasingly difficult if the length scales involved are such that the water is sufficiently deep. This reflects the ill-posed nature of the inverse problem. A new method for the solution of the forward problem of determining the water wave surface at any time, given the bathymetry, is also presented.

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Tài liệu tham khảo

Paley, 1934, Fourier Transforms in the Complex Domain, vol. 19

Guenther, 1996, Partial Differential Equations of Mathematical Physics and Integral Equations

Evans, 1998, Partial Differential Equations

10.1109/TGRS.2002.807578

10.1007/978-1-4757-3520-8

10.1090/S0894-0347-05-00484-4

10.1006/jcph.1993.1164

10.1098/rspa.2004.1367

10.1007/s00222-010-0288-1

10.1142/S0219530508001213

10.1017/S0022112011000073

Zakharov, 1968, Stability of periodic waves of finite amplitude on the surface of a deep fluid, Zh. Prikl. Mekh. Tekh. Fiz., 8, 86

10.1007/s00021-006-0231-9

10.1017/S0022112006001091

10.1016/S0378-3839(98)00035-0

10.1088/0266-5611/10/5/003

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Thông tin xuất bản

Journal of Fluid Mechanics

Tập 714

562-590

Thông tin tác giả