Non-linear shallow water dynamics with odd viscosity

Abstract

In this letter, we derive the Korteweg-de Vries (KdV) equation corresponding to the surface dynamics of a shallow depth ($h$) two-dimensional fluid with odd viscosity (${\nu }_o$) subject to gravity ($g$) in the long wavelength weakly nonlinear limit. In the long wavelength limit, the odd viscosity term plays the role of surface tension albeit with opposite signs for the right and left movers. We show that there exists two regimes with a sharp transition point within the applicability of the KdV dynamics, which we refer to as weak $(|{\nu }_o|<\sqrt{g{h}^3}/6)$ and strong $(|{\nu }_o|>\sqrt{g{h}^3}/6)$ parity-breaking regimes. While the `weak' parity breaking regime results in minor qualitative differences in the soliton amplitude and velocity between the right and left movers, the `strong' parity breaking regime on the contrary results in solitons of depression (negative amplitude) in one of the chiral sectors.

arXiv comment6 pages, 4 figures, video abstract: https://www.youtube.com/watch?v=DgFZxyNmllQ&feature=youtu.be

References in corpus (35)

• Non-Abelian adiabatic statistics and Hall viscosity in quantum Hall states and p_x+ip_y paired superfluids
• Viscosity of Quantum Hall Fluids
• Geometrical Description of the Fractional Quantum Hall Effect
• Odd viscosity in chiral active fluids
• Hall Viscosity and Electromagnetic Response
• Measuring Hall Viscosity of Graphene's Electron Fluid
• Kubo formulas for viscosity: Hall viscosity, Ward identities, and the relation with conductivity
• Negative magnetoresistance in viscous flow of two-dimensional electrons
• Topological waves in fluids with odd viscosity
• Hydrodynamic Electron Flow and Hall Viscosity
• Torsional Anomalies, Hall Viscosity, and Bulk-boundary Correspondence in Topological States
• Framing Anomaly in the Effective Theory of Fractional Quantum Hall Effect
• Fractional Quantum Hall Effect in a Curved Space: Gravitational Anomaly and Electromagnetic Response
• Non-local transport and the Hall viscosity of 2D hydrodynamic electron liquids
• Odd viscosity in two-dimensional incompressible fluids
• Density-curvature response and gravitational anomaly
• Band mass anisotropy and the intrinsic metric of fractional quantum Hall systems
• Anomalous Hydrodynamics of Two-Dimensional Vortex Fluid
• Boundary effective action for quantum Hall states
• Geometry of Quantum Hall States: Gravitational Anomaly and Kinetic Coefficients
• Hall viscosity, topological states and effective theories
• Geometric adiabatic transport in quantum Hall states
• Effective theory of chiral two-dimensional superfluids
• Quantum Hall effect and Quillen metric
• Odd surface waves in two-dimensional incompressible fluids
• Ordering of two small parameters in the shallow water wave problem
• On the effective hydrodynamics of FQHE
• Collective Field Theory for Quantum Hall States
• Emergent Non-Eulerian Hydrodynamics of Quantum Vortices in Two Dimensions
• 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
• Magnetoelasticity theory of incompressible quantum Hall liquids
• A new collective mode in the fractional quantum Hall liquid
• Vortex flows on closed surfaces

Cited by in corpus (2)

• Hydrodynamics of Quantum Vortices on a Closed Surface
• Nonlinear shallow-water waves with vertical odd viscosity