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Register a new userHysteretic behavior between quasi-two-dimensional flow and three-dimensional flow in forced rotating turbulence
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Conflict between formation of a cyclonic vortex and isotropization in forced homogeneous rotating turbulence is numerically investigated. It is well known that a large rotation rate of the system induces columnar vortices to result in quasi-two-dimensional (Q2D) flow, while a small rotation rate allows turbulence to be three-dimensional (3D). It is found that the transition from the Q2D turbulent flow to the 3D turbulent flow and the reverse transition occur at different values of the rotation rates. At the intermediate rotation rates, bistability of these two statistically steady states is observed. Such hysteretic behavior is also observed for the variation of the amplitude of an external force.
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Using complementary numerical approaches at high resolution, we study the late-time behaviour of an inviscid, incompressible two-dimensional flow on the surface of a sphere. Starting from a random initial vorticity field comprised of a small set of intermediate wavenumber spherical harmonics, we find that -- contrary to the predictions of equilibrium statistical mechanics -- the flow does not evolve into a large-scale steady state. Instead, significant unsteadiness persists, characterised by a population of persistent small-scale vortices interacting with a large-scale oscillating quadrupolar vorticity field. Moreover, the vorticity develops a stepped, staircase distribution, consisting of nearly homogeneous regions separated by sharp gradients. The persistence of unsteadiness is explained by a simple point vortex model characterising the interactions between the four main vortices which emerge.
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