On the motion of gravity-capillary waves with odd viscosity

Abstract

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 Hall fluids or chiral active fluids. Besides the odd viscosity effects, these models capture both gravity and capillary forces up to quadratic interactions and take the form of nonlinear and nonlocal wave equations. Two of these models describe bidirectional waves while the third PDE studies the case of unidirectional propagation. We also prove the well-posedness of these asymptotic models in spaces of analytic functions and in Sobolev spaces. Finally, we present a number of numerical simulations for the unidirectional model.

arXiv comment3 figures

References in corpus (18)

• Viscosity of Quantum Hall Fluids
• Odd viscosity in chiral active fluids
• Topological waves in fluids with odd viscosity
• Theory of weakly damped free-surface flows: a new formulation based on potential flow solutions
• Odd viscosity in two-dimensional incompressible fluids
• Anomalous Hydrodynamics of Two-Dimensional Vortex Fluid
• Swimming at Low Reynolds Number in Fluids with Odd (Hall) Viscosity
• Viscous potential free-surface flows in a fluid layer of finite depth
• Dissipative Boussinesq equations
• Odd surface waves in two-dimensional incompressible fluids
• Visco-potential free-surface flows and long wave modelling
• Free surface variational principle for an incompressible fluid with odd viscosity
• Hydrodynamics of two-dimensional compressible fluid with broken parity: variational principle and free surface dynamics in the absence of dissipation
• Asymptotic models for free boundary flow in porous media
• The free surface of a colloidal chiral fluid: waves and instabilities from odd stress and Hall viscosity
• Reconciling different formulations of viscous water waves and their mass conservation
• An asymptotic model for internal capillary-gravity waves in deep water
• Global well-posedness and decay for viscous water wave models

Cited by in corpus (3)

• Nonlinear shallow-water waves with vertical odd viscosity
• Well-posedness, ill-posedness, and traveling waves for models of pulsatile flow in viscoelastic vessels
• Global well-posedness and decay for viscous water wave models