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Recovering the Water-Wave Profile from Pressure Measurements
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In this article, a non-local nonlinear equation relating the pressure and the surface elevation was derived from the Euler formulation of the water-wave problem without approximation, and a variety of different asymptotic formulas were derived from this new equation.Abstract:
A new method is proposed to recover the water-wave surface elevation from pressure data obtained at the bottom of the fluid. The new method requires the numerical solution of a nonlocal nonlinear equation relating the pressure and the surface elevation which is obtained from the Euler formulation of the water-wave problem without approximation. From this new equation, a variety of different asymptotic formulas are derived. The nonlocal equation and the asymptotic formulas are compared with both numerical data and physical experiments. The solvability properties of the nonlocal equation are rigorously analyzed using the Implicit Function Theorem.read more
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New exact relations for easy recovery of steady wave profiles from bottom pressure measurements.
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References
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Stability of periodic waves of finite amplitude on the surface of a deep fluid
TL;DR: In this article, the stability of steady nonlinear waves on the surface of an infinitely deep fluid with a free surface was studied. And the authors considered the problem of stability of surface waves as part of the more general problem of nonlinear wave in media with dispersion.
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TL;DR: In this paper, the authors present an introduction to classical water wave theory for the college senior or first year graduate student, with a set of homework problems exercising and sometimes extending the material presented in the chapter.