  The effect of domain anisotropy on the inverse cascade occurring within the
geostrophic turbulence regime of rapidly rotating Rayleigh-B\'enard convection
(RRBC) is investigated. In periodic domains with square cross-section in the
horizontal a domain-filling 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 large-scale structures driven by intrinsically generated
fluctuations.
