Near-resonant instability of geostrophic modes: beyond Greenspan's theorem. (10th October 2020)

• Record Type: Journal Article
• Authors: Le Reun, T.; Gallet, B.; Favier, B.; Le Bars, M.
• Is Part Of: Journal of fluid mechanics. Volume 900(2020)
• Publication Date: 2020-10-10
• Subjects: waves in rotating fluids, -- rotating flows; Fluid mechanics -- Periodicals; 532.005
• DOI: 10.1017/jfm.2020.454
• Languages: English
• ISSNs: 0022-1120

Abstract

Abstract: 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.