Interplay between Geostrophic Modes and Three Dimensionality in Rotating Turbulence near Phase transition

We study the saturation of three-dimensional unstable perturbations on a fastly rotating turbulent flow using direct numerical simulations (DNSs). Under the effect of Kolmogorov forcing at different scales, a critical transition between states dominated by geostrophic modes to states with three-dimensional variations was observed. The critical exponent near the threshold, which characterises such turbulent phase transitions, deviates from the mean-field value which manifests the inherently multiplicative nature of turbulent fluctuations. Near the transition, the intermittent behaviour in the order parameter reflects the signature of on-off intermittency. The destabilising mechanisms near the onset of transition turn out to be centrifugal instability. Linear stability analysis further validates the centrifugal instability and agrees well with the threshold obtained from the fully nonlinear results.