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Near-resonant instability of geostrophic modes: beyond Greenspan's theorem

Abstract : We explore the near-resonant interaction of inertial waves with geostrophic modes in rotating fluids via numerical and theoretical analysis. When a single inertial wave is imposed, we find that some geostrophic modes are unstable above a threshold value of the Rossby number kRo based on the wavenumber and wave amplitude. We show this instability to be caused by triadic interaction involving two inertial waves and a geostrophic mode such that the sum of their eigenfrequencies is non-zero. We derive theoretical scalings for the growth rate of this near-resonant instability. The growth rate scaled by the global rotation rate is proportional to (kRo)2 at low kRo and transitions to a kRo scaling for larger kRo . These scalings are in excellent agreement with direct numerical simulations. This instability could explain recent experimental observations of geostrophic instability driven by waves.
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Submitted on : Monday, October 26, 2020 - 2:50:43 PM
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T. Le Reun, B. Gallet, B. Favier, M. Le Bars. Near-resonant instability of geostrophic modes: beyond Greenspan's theorem. Journal of Fluid Mechanics, 2020, 900, ⟨10.1017/jfm.2020.454⟩. ⟨hal-02978481⟩



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