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arXiv · 1412.4959

Dynamics of reversals and condensates in 2D Kolmogorov flows

Pankaj Kumar Mishra·Johann Herault·Stephan Fauve·Mahendra K. Verma
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Abstract

We present direct numerical simulations of the different two-dimensional flow regimes generated by a constant spatially periodic forcing balanced by viscous dissipation and large scale drag with a dimensionless damping rate $1/Rh$. The linear response to the forcing is a $6\times6$ square array of counter-rotating vortices, which is stable when the Reynolds number $Re$ or $Rh$ are small. After identifying the sequence of bifurcations that lead to a spatially and temporally chaotic regime of the flow when $Re$ and $Rh$ are increased, we study the transitions between the different turbulent regimes observed for large $Re$ by varying $Rh$. A large scale circulation at the box size (the condensate state) is the dominant mode in the limit of vanishing large scale drag ($Rh$ large). When $Rh$ is decreased, the condensate becomes unstable and a regime with random reversals between two large scale circulations of opposite signs is generated. It involves a bimodal probability density function of the large scale velocity that continuously bifurcates to a Gaussian distribution when $Rh$ is decreased further.

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Pankaj Kumar Mishra, Johann Herault, Stephan Fauve, Mahendra K. Verma. 2014-12-16. Dynamics of reversals and condensates in 2D Kolmogorov flows. https://doi.org/10.1103/physreve.91.053005

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