Statistical theory of reversals in two-dimensional confined turbulent flows

Abstract : It is shown that the truncated Euler equation (TEE), i.e., a finite set of ordinary differential equations for the amplitude of the large-scale modes, can correctly describe the complex transitional dynamics that occur within the turbulent regime of a confined two-dimensional flow obeying Navier-Stokes equation (NSE) with bottom friction and a spatially periodic forcing. The random reversals of the NSE large-scale circulation on the turbulent background involve bifurcations of the probability distribution function of the large-scale circulation. We demonstrate that these NSE bifurcations are described by the related TEE microcanonical distribution which displays transitions from Gaussian to bimodal and broken ergodicity. A minimal 13-mode model reproduces these results.
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Vishwanath Shukla, Stephan Fauve, Marc Brachet. Statistical theory of reversals in two-dimensional confined turbulent flows. Physical Review E , American Physical Society (APS), 2016, 94 (6), pp.061101(R). ⟨10.1103/PhysRevE.94.061101⟩. ⟨hal-01446304⟩



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