The Whitham equation for hydroelastic waves
نویسندگان
چکیده
منابع مشابه
Traveling Waves for the Whitham Equation
The existence of traveling waves for the original Whitham equation is investigated. This equation combines a generic nonlinear quadratic term with the exact linear dispersion relation of surface water waves of finite depth. It is found that there exist small-amplitude periodic traveling waves with sub-critical speeds. As the period of these traveling waves tends to infinity, their velocities ap...
متن کاملModelling nonlinear hydroelastic waves.
This paper uses the special Cosserat theory of hyperelastic shells satisfying Kirchoff's hypothesis and irrotational flow theory to model the interaction between a heavy thin elastic sheet and an infinite ocean beneath it. From a general discussion of three-dimensional motions, involving an Eulerian description of the flow and a Lagrangian description of the elastic sheet, a special case of two...
متن کاملGlobal Bifurcation for the Whitham Equation
We prove the existence of a global bifurcation branch of 2π-periodic, smooth, traveling-wave solutions of the Whitham equation. It is shown that any subset of solutions in the global branch contains a sequence which converges uniformly to some solution of Hölder class C, α < 1 2 . Bifurcation formulas are given, as well as some properties along the global bifurcation branch. In addition, a spec...
متن کاملWell-Posedness of Two-Dimensional Hydroelastic Waves
A well-posedness theory for the initial value problem for hydroelastic waves in two spatial dimensions is presented. This problem, which arises in numerous applications, describes the evolution of a thin elastic membrane in a two-dimensional potential flow. We use a model for the elastic sheet that accounts for bending stresses and membrane tension, but which neglects the mass of the membrane. ...
متن کاملA numerical study of the Whitham equation as a model for steady surface water waves
The object of this article is the comparison of numerical solutions of the so-called Whitham equation describing wave motion at the surface of a perfect fluid to numerical approximations of solutions of the full Euler free-surface water-wave problem. The Whitham equation ηt + 3 2 c0 h0 ηηx +Kh0∗ ηx = 0 was proposed by Whitham [33] as an alternative to the KdV equation for the description of sur...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Applied Ocean Research
سال: 2019
ISSN: 0141-1187
DOI: 10.1016/j.apor.2019.04.026