Stratification-Dependent Enstrophy-Controlled Regime in Geostrophic Turbulence

We experimentally measure geostrophic turbulence in a rotating, differentially heated fluid annulus, which is bounded by convectively driven warm and cold flows at the outer and inner boundaries, respectively. The horizontal kinetic energy spectra exhibit a range at low wave number which scales as k^{-3}, where k denotes the horizontal wave number, with spectral amplitude that correlates with the square of the Brunt-Väisälä frequency at the same heights as the velocity measurements. The observed turbulent state exhibits a forward enstrophy cascade across all scales along with bidirectional energy transfer, which is evidenced by a reversal in the sign of the spectral energy flux at a scale proportional to the internal Rossby radius of deformation. These findings highlight the role of baroclinic instability in shaping the distribution of energy across scales, with implications for synoptic-scale turbulent flows near Earth's tropopause.