Nonlinear shallow-water waves with vertical odd viscosity

Abstract

The breaking of detailed balance in fluids through Coriolis forces or odd-viscous stresses has profound effects on the dynamics of surface waves. Here we explore both weakly and strongly non-linear waves in a three-dimensional fluid with vertical odd viscosity with and without the Coriolis effect. Our model describes the free surface of a shallow fluid composed of nearly vertical vortex filaments, which all stand perpendicular to the surface. We find that the odd viscosity in this configuration induces previously unexplored non-linear effects in shallow-water waves, arising from both stresses on the surface and stress gradients in the bulk. By assuming weak nonlinearity, we find reduced equations including Korteweg-de Vries (KdV), Ostrovsky, and Kadomtsev-Petviashvilli (KP) equations with modified coefficients. At sufficiently large odd viscosity, the dispersion changes sign, allowing for compact two-dimensional solitary waves. We show that odd viscosity and surface tension have the same effect on the free surface, but distinct signatures in the fluid flow. Our results describe the collective dynamics of many-vortex systems, which can also occur in oceanic and atmospheric geophysics.

26 pages, 12 figures

References in corpus (22)

• Odd viscosity in chiral active fluids
• Measuring Hall Viscosity of Graphene's Electron Fluid
• Topological waves in fluids with odd viscosity
• "Embedded solitons": solitary waves in resonance with the linear spectrum
• Statistical mechanics of a chiral active fluid
• Odd viscosity in active matter: microscopic origin and 3D effects
• Anomalous Hydrodynamics of Two-Dimensional Vortex Fluid
• Anomalous bulk-edge correspondence in continuous media
• A bulk-interface correspondence for equatorial waves
• Finite volume and pseudo-spectral schemes for the fully nonlinear 1D Serre equations
• Odd surface waves in two-dimensional incompressible fluids
• Stokes flows in three-dimensional fluids with odd and parity-violating viscosities
• Investigating anisotropic quantum Hall states with bi-metric geometry
• Edge wave and boundary layer of vortex matter
• 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
• Nonlinear Schrödinger equations and the universal description of dispersive shock wave structure
• Viscoelastic response of quantum Hall fluids in a tilted field
• Cubic Hall viscosity in three-dimensional topological semimetals
• Non-linear shallow water dynamics with odd viscosity
• On the motion of gravity-capillary waves with odd viscosity
• Complete absorption of topologically protected waves