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Ekman-inertial instability

Nicolas Grisouard* and Varvara E. Zemskova

  • Department of Physics, University of Toronto, 60 St. George Street, Toronto, Ontario, Canada M5S 1A7

  • *nicolas.grisouard@utoronto.ca
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Phys. Rev. Fluids 5, 124802 – Published 10 December, 2020

DOI: https://doi.org/10.1103/PhysRevFluids.5.124802

Abstract

We report on an instability arising in subsurface, laterally sheared geostrophic flows. When the lateral shear of a horizontal flow in geostrophic balance has a sign opposite to the Coriolis parameter and exceeds it in magnitude, embedded perturbations are subjected to inertial instability, albeit modified by viscosity. When the perturbation arises from the surface of the fluid, the initial response is akin to a Stokes problem, with an initial flow aligned with the initial perturbation. The perturbation then grows quasi-inertially, rotation deflecting the velocity vector, which adopts a well-defined angle with the mean flow, and viscous stresses, transferring horizonal momentum downward. The combination of rotational and viscous effects in the dynamics of inertial instability prompts us to call this process “Ekman-inertial instability.” While the perturbation initially grows superinertially, the growth rate then becomes subinertial, eventually tending back to the inertial value. The same process repeats downward as time progresses. Ekman-inertial transport aligns with the asymptotic orientation of the flow and grows exactly inertially with time once the initial disturbance has passed. Because of the strongly superinertial initial growth rate, this instability might compete favorably against other instabilities arising in ocean fronts.

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Physics Subject Headings (PhySH)

Corrections

12 May, 2021

Correction: Two quantities representing the lateral shear production were incorrectly presented after Eq. (20) and have been set right.

Article Text

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Outline

Information

Phys. Rev. Fluids 5, 124802– Published 10 December, 2020
  • Received 26 June 2020
  • Accepted 13 November 2020
  • Corrected 12 May 2021
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