Nonlinear shallow water dynamics with odd viscosity

@article{Monteiro2021NonlinearSW,
  title={Nonlinear shallow water dynamics with odd viscosity},
  author={Gustavo M. Monteiro and Sriram Ganeshan},
  journal={Physical Review Fluids},
  year={2021}
}
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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References

SHOWING 1-10 OF 51 REFERENCES

Odd surface waves in two-dimensional incompressible fluids

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

Hydrodynamics of two-dimensional compressible fluid with broken parity: Variational principle and free surface dynamics in the absence of dissipation

We consider an isotropic compressible non-dissipative fluid with broken parity subject to free surface boundary conditions in two spatial dimensions. The hydrodynamic equations describing the bulk

Ordering of two small parameters in the shallow water wave problem

The classical problem of irrotational long waves on the surface of a shallow layer of an ideal fluid moving under the influence of gravity as well as surface tension is considered. A systematic

Odd viscosity in chiral active fluids

TLDR
A hydrodynamic theory of chiral active fluids is developed and odd viscosity is connected, which was previously considered an abstract concept.

The free surface of a colloidal chiral fluid: waves and instabilities from odd stress and Hall viscosity

In simple fluids, such as water, invariance under parity and time-reversal symmetry imposes that the rotation of constituent 'atoms' are determined by the flow and that viscous stresses damp motion.

The odd free surface flows of a colloidal chiral fluid

In simple fluids, such as water, invariance under parity and time-reversal symmetry imposes that the rotation of constituent ‘atoms’ is determined by the flow and that viscous stresses damp motion.

Torsional anomalies, Hall viscosity, and bulk-boundary correspondence in topological states

We study the transport properties of topological insulators, encoding them in a generating functional of gauge and gravitational sources. Much of our focus is on the simple example of a free massive

Kubo formulas for viscosity: Hall viscosity, Ward identities, and the relation with conductivity

We derive from first principles the Kubo formulas for the stress-stress response function at zero wavevector that can be used to define the full complex frequency-dependent viscosity tensor, both

Topological Waves in Fluids with Odd Viscosity.

TLDR
This work shows how this odd viscosity has a dramatic effect on topological sound waves in fluids, including the number and spatial profile of topological edge modes.

Hydrodynamic Electron Flow and Hall Viscosity.

TLDR
This work discusses how to measure the effects of both the even and odd components of the viscosity using hydrodynamic electronic transport in mesoscopic samples under applied magnetic fields and breaks time-reversal symmetry.
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