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The effect of domain anisotropy on the inverse cascade occurring within thegeostrophic turbulence regime of rapidly rotating Rayleigh-B\'enard convection(RRBC) is investigated. In periodic domains with square cross-section in thehorizontal a domain-filling dipole state is present. For rectangular periodicdomains a Kolmogorov-like flow consisting of a periodic array of alternatingunidirectional jets with embedded vortices is observed, together with anunderlying weak meandering transverse jet. Similar transitions occurring inweakly dissipative two-dimensional flows driven by externally imposed smallamplitude noise as well as in classical hydrostatic geostrophic turbulence area consequence of inviscid conservation of energy and potential enstrophy andcan be understood using statistical mechanics considerations. RRBC representsan important three-dimensional system with only one inviscid invariant thatnonetheless exhibits large-scale structures driven by intrinsically generatedfluctuations.

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