Impact of domain anisotropy on the inverse cascade in geostrophic turbulent convection

Abstract

The effect of domain anisotropy on the inverse cascade occurring within the geostrophic turbulence regime of rapidly rotating Rayleigh-Bénard convection (RRBC) is investigated. In periodic domains with square cross-section in the horizontal a domainfilling dipole state is present. For rectangular periodic domains a Kolmogorov-like flow consisting of a periodic array of alternating unidirectional jets with embedded vortices is observed, together with an underlying weak meandering transverse jet. Similar transitions occurring in weakly dissipative two-dimensional flows driven by externally imposed small amplitude noise as well as in classical hydrostatic geostrophic turbulence are a consequence of inviscid conservation of energy and potential enstrophy and can be understood using statistical mechanics considerations. RRBC represents an important three-dimensional system with only one inviscid invariant that nonetheless exhibits largescale structures driven by intrinsically generated fluctuations.

Jets and large-scale vortices in rotating Rayleigh-Bénard convection

“…The reduced model, which assumes the dominance of the planetary vorticity over the planetary vorticity, is however unable to capture any asymmetry between cyclonic and anticyclonic motions. Interestingly, the effect of domain horizontal anisotropy on the formation of large-scale flows in rotating Rayleigh-Bénard convection has been recently investigated with the reduced system by Julien et al (2017). They find that unidirectional jets with embedded persistent LSVs form for aspect ratios L y /L x in excess of 1.1, in good agreement with our 3D numerical results.…”

“…They find that unidirectional jets with embedded persistent LSVs form for aspect ratios L y /L x in excess of 1.1, in good agreement with our 3D numerical results. The asymptotically reduced system of Julien et al (2017) would therefore be a valuable tool to study the confinement effects of the large-scale dynamics in the limit of small Rossby number.…”

The Effect of Rotation on Fingering Convection in Stellar Interiors

“…Studies of rapidly rotating convection and oscillatory double-diffusive convection in the polar configuration (i.e. with rotation aligned with gravity) have generally concluded that LSVs are only observed in a rotationally constrained (low Rossby number) and yet also strongly turbulent (high Reynolds number) regime (Guervilly et al (2014);Julien et al (2018); Seshasayanan & Alexakis (2018)), which is also what we found here. The first of these conditions can be understood by noting that strong rotation is required to trigger an inverse energy cascade.…”

“…Inspection of the horizontal kinetic energy spectrum demonstrates that the LSV forms through a rotationally-driven inverse cascade that draws its energy from the basic instability at the finger scale. The LSV formation and dynamics are strongly reminiscent of those observed in a variety of other rapidly rotating turbulent systems, such as convection (Guervilly et al (2014); Julien et al (2018)), stratified turbulence (Marino et al (2013); Oks et al (2017)) and oscillatory double-diffusive convection (Moll & Garaud (2017)).…”

“…The emergence of such LSVs is reminiscent of similar findings in the work by Moll & Garaud (2017) (for the ODDC case) as well as in studies of rapidly rotating convection (Guervilly et al (2014)). In all such cases, LSVs are always seen to fill the domain, and have also been interpreted as resulting from an inverse cascade (Julien et al (2018)). 6.…”