On the motion of gravity-capillary waves with odd viscosity Articles uri icon

publication date

  • March 2022

start page

  • 1

end page

  • 33

issue

  • 28

volume

  • 32

International Standard Serial Number (ISSN)

  • 0938-8974

abstract

  • We develop three asymptotic models of surface waves in a non-Newtonian fluid with
    odd viscosity. This viscosity is also known as Hall viscosity and appears in a number
    of applications such as quantum Hall fluids or chiral active fluids. Besides the odd
    viscosity effects, these models capture both gravity and capillary forces up to quadratic
    interactions and take the form of nonlinear and nonlocal wave equations. Two of
    these models describe bidirectional waves, while the third PDE studies the case of
    unidirectional propagation. We also prove the well-posedness of these asymptotic
    models in spaces of analytic functions and in Sobolev spaces. Finally, we present a
    number of numerical simulations for the unidirectional model.

keywords

  • waves; odd viscosity; hall viscosity; moving interfaces; free-boundary problems