Models for Damped Water Waves

@article{GraneroBelinchon2019ModelsFD,
  title={Models for Damped Water Waves},
  author={Rafael Granero-Belinch'on and Stefano Scrobogna},
  journal={SIAM J. Appl. Math.},
  year={2019},
  volume={79},
  pages={2530-2550}
}
In this paper we derive some new weakly nonlinear asymptotic models describing viscous waves in deep water with or without surface tension effects. These asymptotic models take into account several different dissipative effects and are obtained from the free boundary problems formulated in the works of Dias, Dyachenko and Zakharov (Physics Letters A, 2008), Jiang, Ting, Perlin and Schultz (Journal of Fluid Mechanics,1996) and Wu, Liu and Yue (Journal of Fluid Mechanics, 2006). 
View PDF on arXiv
13 Citations
Highly Influential Citations
1
Background Citations
5
Methods Citations
3
Results Citations
2

13 Citations

Citation Type

Citation Type

Well-posedness of water wave model with viscous effects
Starting from the paper by Dias, Dyachenko and Zakharov (\emph{Physics Letters A, 2008}) on viscous water waves, we derive a model that describes water waves with viscosity moving in deep water with…
Global well-posedness and decay for viscous water wave models
The motion of the free surface of an incompressible fluid is a very active research area. Most of these works examine the case of an inviscid fluid. However, in several practical applications, there…
Interfaces in incompressible flows
The motion of both internal and surface waves in incompressible fluids under capillary and gravity forces is a major research topic. In particular, we review the derivation of some new models…
On the Motion of Gravity-Capillary Waves with Odd Viscosity
We develop three asymptotic models of surface waves in a non-Newtonian fluid with odd viscosity. This viscosity is also known as Hall viscosity and appears in a number of applications such as quantum…
Well-posedness of the water-wave with viscosity problem
A P ] 2 2 D ec 2 02 0 GLOBAL WELL-POSEDNESS AND DECAY OF A VISCOUS WATER WAVE MODEL
The motion of the free surface of an incompressible fluid is a very active research area. Most of these works examine the case of an inviscid fluid. However, in several practical applications, there…
Reconciling different formulations of viscous water waves and their mass conservation
Surface tension stabilization of the Rayleigh-Taylor instability for a fluid layer in a porous medium
Gevrey regularity and finite time singularities for the Kakutani–Matsuuchi model
Well-posedness of an asymptotic model for capillarity-driven free boundary Darcy flow in porous media in the critical Sobolev space
...
...

References

SHOWING 1-10 OF 44 REFERENCES
Theory of weakly damped Stokes waves: a new formulation and its physical interpretation
A tractable theory for weakly damped, nonlinear Stokes waves on deep water was recently formulated by Ruvinsky & Friedman (1985a, b; 1987). In this paper we show how the theory can be simplified, and…
Dissipative Boussinesq equations
Theory of weakly damped free-surface flows: A new formulation based on potential flow solutions
Asymptotic models for free boundary flow in porous media
Well-posedness and analyticity of solutions to a water wave problem with viscosity
Numerical Simulation of a Weakly Nonlinear Model for Water Waves with Viscosity
TLDR
This work derives a weakly nonlinear model from the surface formulation of Zakharov complemented with physically-motivated viscous effects recently derived by Dias et al. (Phys. Lett. A 372:1297–1302, 2008).
Sufficiently 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…
Traveling Waves in Deep Water with Gravity and Surface Tension
TLDR
The purpose of this paper is apply the new numerical method, then compare small amplitude solutions of potential flow with those of the approximate model, and particular attention is paid to the behavior near quadratic resonances, an example of which is the Wilton ripple.
Visco-potential free-surface flows and long wave modelling
Viscous potential free-surface flows in a fluid layer of finite depth
...
...