• Letter

Nonlinear shallow water dynamics with odd viscosity

Gustavo M. Monteiro and Sriram Ganeshan
Phys. Rev. Fluids 6, L092401 – Published 7 September 2021

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 (νo) 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 exist two regimes with a sharp transition point within the applicability of the KdV dynamics, which we refer to as weak (|νo|<gh3/6) and strong (|νo|>gh3/6) 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.

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  • Received 2 September 2020
  • Accepted 16 August 2021

DOI:https://doi.org/10.1103/PhysRevFluids.6.L092401

©2021 American Physical Society

Physics Subject Headings (PhySH)

Fluid Dynamics

Authors & Affiliations

Gustavo M. Monteiro1 and Sriram Ganeshan1,2

  • 1Department of Physics, City College, City University of New York, New York, New York 10031, USA
  • 2CUNY Graduate Center, New York, New York 10031, USA

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Issue

Vol. 6, Iss. 9 — September 2021

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