Near-resonant instability of geostrophic modes: beyond Greenspan's theorem - Archive ouverte HAL Access content directly
Journal Articles Journal of Fluid Mechanics Year : 2020

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.

Keywords

Fichier principal
Vignette du fichier
article.pdf (832.22 Ko) Télécharger le fichier
Origin Files produced by the author(s)
Loading...

Dates and versions

hal-02978481 , version 1 (26-10-2020)

Identifiers

Cite

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⟩
28 View
61 Download

Altmetric

Share

Gmail Mastodon Facebook X LinkedIn More