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We study the effect of confinement on the three-dimensional linearinstability of fastly rotating two-dimensional turbulent flows. Using the largescale friction to model the effect of top and bottom boundaries, we study theonset of three-dimensional perturbations on a rapidly rotating flow. Thefriction term is taken to affect both the evolution of the two-dimensionalturbulent flow and the perturbations that evolve on top of it. Using directnumerical simulations, the threshold for the onset of three-dimensionalperturbations is traced out as a function of the control parameters. Asreported in the earlier work (K. Seshasayanan and B. Gallet. 2020. Onset ofthree-dimensionality in rapidly rotating turbulent flows), two differentmechanisms, namely the centrifugal and parametric type instabilities, areresponsible for the destabilisation across the wide range of parametersexplored in this study. In the turbulent regime, we find that the large scalefriction term does not affect the threshold in the case of centrifugalinstability while in the case of the parametric instability the instabilitythreshold is shifted to larger Rossby numbers. For the parametric instability,the length scale of the unstable mode is found to scale as the inverse squareroot of the rotation rate and the growth rate of the unstable mode is found tobe correlated with the minimum of the determinant of the strain rate tensor ofthe underlying two-dimensional turbulent flow, showing resemblance withelliptical type instabilities. Results from the turbulent flow are thencompared with the oscillatory Kolmogorov flow, which undergoes a parametricinstability resulting into inertial waves. The dependence of the threshold onthe aspect ratio of the system is discussed for both the turbulent and theoscillating Kolmogorov flows.

Effect of confinement on the transition from 2D to 3D fast rotating flows