Critical transition in fast-rotating turbulence within highly elongated domains

Abstract

Abstract

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

“…Such states have been observed by Le Reun et al (2017), Le Reun et al (2019) and Brunet et al (2020), but a systematic investigation of their existence in various realisations of rotating turbulence remains to be carried out. In the future, our study could help bridge the gap between finite Rossby number experiments and simulations of turbulence (Godeferd & Moisy 2015) and asymptotic models of rotating turbulence (Galtier 2003;Bellet et al 2006;van Kan & Alexakis 2019).…”

Onset of three-dimensionality in rapidly rotating turbulent flows

“…For the latter situation, one can prove that the flow becomes exactly 2-D when the Rossby number is reduced at fixed (but arbitrarily large) Reynolds number and fixed aspect ratio of the fluid domain, using rigorous upper bound theory. This has important consequences for the energy dissipation rate of rapidly rotating turbulent flows: the anomalous dissipation associated with the forward energy cascade of 3-D turbulence is replaced by the laminar-like viscous dissipation of the domain-scale velocity structures that arise from the 2-D inverse energy cascade (Alexakis & Doering 2006;van Bokhoven et al 2009;Campagne et al 2014;Deusebio et al 2014;Campagne et al 2016;Buzzicotti et al 2018;van Kan & Alexakis 2020;Pestana & Hickel 2019). Mapping the energy dissipation rate of rotating turbulence in parameter space requires determination of the transition between exactly 2-D and partially 3-D rapidly rotating flows.…”

“…2016; Buzzicotti et al. 2018; van Kan & Alexakis 2020; Pestana & Hickel 2019). Mapping the energy dissipation rate of rotating turbulence in parameter space requires determination of the transition between exactly 2-D and partially 3-D rapidly rotating flows.…”

Is the Taylor–Proudman theorem exact in unbounded domains? Case study of the three-dimensional stability of a vortex pair in a rapidly rotating fluid

“…2011; Davidson 2013; Deusebio et al. 2014; Godeferd & Moisy 2015; van Kan & Alexakis 2020; and references therein). This may originate from a violation of one assumption behind the Taylor–Proudman theorem, for example: if the Rossby number is not sufficiently small, if boundary layers are present or if there are thermal effects like in rotating convection.…”

“…However, when the flow is unbounded, some authors have argued that an exact two-dimensionalization cannot occur even for infinite rotation rate because there always exist three-dimensional inertial waves with the same time scale as advective motions so that they can couple (Cambon, Rubinstein & Godeferd 2004; Nazarenko & Schekochihin 2011; Deusebio et al. 2014; Alexakis & Biferale 2018; van Kan & Alexakis 2020).…”