Nonlinear shallow water dynamics with odd viscosity

  title={Nonlinear shallow water dynamics with odd viscosity},
  author={Gustavo M. Monteiro and Sriram Ganeshan},
  journal={Physical Review Fluids},
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… 

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