Abstract
In this Letter, we derive the Korteweg–de Vries (KdV) equation corresponding to the surface dynamics of a shallow depth () two-dimensional fluid with odd viscosity () subject to gravity () 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 and strong 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.
- Received 2 September 2020
- Accepted 16 August 2021
DOI:https://doi.org/10.1103/PhysRevFluids.6.L092401
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