Well-posedness of two-dimensional hydroelastic waves with mass
نویسندگان
چکیده
We study hydroelastic waves in interfacial flow of two-dimensional irrotational fluids. Each of the fluids is taken to be of infinite extent in one vertical direction, and bounded by a free surface in the other vertical direction. Elastic effects are considered at the free surface; this can describe physical settings such as the ocean bounded above by a layer of ice. A previous study proved well-posedness without considering the mass of the elastic surface; we now consider the effect of this mass. Under the assumption that a certain integral equation is solvable, we prove well-posedness of the initial value problem for the system. We are able to demonstrate that in some cases, such as the case of small mass parameter, the integral equation is indeed solvable. The proof uses geometric dependent variables, a normalized arclength parameterization, and a small-scale decomposition in the evolution equations.
منابع مشابه
Well-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 کاملSufficiently Strong Dispersion Removes Ill-posedness in Truncated Series Models of Water Waves
Truncated series models of gravity water waves are popular for use in simulation. Recent work has shown that these models need not inherit the well-posedness properties of the full equations of motion (the irrotational, incompressible Euler equations). We show that if one adds a sufficiently strong dispersive term to a quadratic truncated series model, the system then has a well-posed initial v...
متن کاملHydroelastic response of a floating runway to cnoidal waves
The hydroelastic response of mat-type Very Large Floating Structures (VLFSs) to severe sea conditions, such as tsunamis and hurricanes, must be assessed for safety and survivability. An efficient and robust nonlinear hydroelastic model is required to predict accurately the motion of and the dynamic loads on a VLFS due to such large waves. We develop a nonlinear theory to predict the hydroelasti...
متن کاملInteraction of hydro-elastic waves with a vertical wall
This study aims to gain knowledge on how hydroelastic waves interact with off-shore structures, for example off-shore wind turbines or oil rigs. The linear two-dimensional problem of hydroelastic waves reflected by a vertical wall is analysed. Water is of finite depth and is covered by ice. The fluid is assumed incompressible and inviscid. The ice sheet is assumed thin compared with both the wa...
متن کاملWell-posednesss of Strongly Dispersive Two-dimensional Surface Waves Boussinesq Systems
We consider in this paper the well-posedness for the Cauchy problem associated to two-dimensional dispersive systems of Boussinesq type which model weakly nonlinear long wave surface waves. We emphasize the case of the strongly dispersive ones with focus on the “KdV-KdV” system which possesses the strongest dispersive properties and which is a vector two-dimensional extension of the classical K...
متن کامل