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Title: Odd surface waves in two-dimensional incompressible fluids

Journal Article · · SciPost Physics
 [1];  [2];  [3]
  1. Stony Brook Univ., NY (United States)
  2. City Univ. of New York (CUNY), NY (United States)
  3. City College of New York; Stony Brook University; Stony Brook Univ., NY (United States)

We consider free surface dynamics of a two-dimensional incompressible fluid with odd viscosity. The odd viscosity is a peculiar part of the viscosity tensor which does not result in dissipation and is allowed when parity symmetry is broken. For the case of incompressible fluids, the odd viscosity manifests itself through the free surface (no stress) boundary conditions. We first find the free surface wave solutions of hydrodynamics in the linear approximation and study the dispersion of such waves. As expected, the surface waves are chiral and even exist in the absence of gravity and vanishing shear viscosity. In this limit, we derive effective nonlinear Hamiltonian equations for the surface dynamics, generalizing the linear solutions to the weakly nonlinear case. Within the small surface angle approximation, the equation of motion leads to a new class of non-linear chiral dynamics governed by what we dub the {\it chiral} Burgers equation. The chiral Burgers equation is identical to the complex Burgers equation with imaginary viscosity and an additional analyticity requirement that enforces chirality. We present several exact solutions of the chiral Burgers equation. For generic multiple pole initial conditions, the system evolves to the formation of singularities in a finite time similar to the case of an ideal fluid without odd viscosity. We also obtain a periodic solution to the chiral Burgers corresponding to the non-linear generalization of small amplitude linear waves.

Research Organization:
State Univ. of New York (SUNY), Albany, NY (United States); Stony Brook Univ., NY (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division
Grant/Contract Number:
SC0017662
OSTI ID:
1461900
Alternate ID(s):
OSTI ID: 1596115; OSTI ID: 1805206
Journal Information:
SciPost Physics, Vol. 5, Issue 1; ISSN 2542-4653
Publisher:
SciPost FoundationCopyright Statement
Country of Publication:
United States
Language:
English

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Cited By (7)

Odd-viscosity-induced stabilization of viscous thin liquid films journal September 2019
The odd free surface flows of a colloidal chiral fluid journal September 2019
Free-Surface Variational Principle for an Incompressible Fluid with Odd Viscosity journal April 2019
Free surface variational principle for an incompressible fluid with odd viscosity text January 2018
Nonlinear shallow water dynamics with odd viscosity journal September 2021
Free-Surface Variational Principle for an Incompressible Fluid with Odd Viscosity journal April 2019
The free surface of a colloidal chiral fluid: waves and instabilities from odd stress and Hall viscosity preprint January 2018