A rare event algorithm links transitions in turbulent flows with activated nucleations

Abstract

Many turbulent flows undergo drastic and abrupt configuration changes with huge impacts. As a paradigmatic example we study the multistability of jet dynamics in a barotropic beta plane model of atmosphere dynamics. It is considered as the Ising model for Jupiter troposphere dynamics. Using the adaptive multilevel splitting, a rare event algorithm, we are able to get a very large statistics of transition paths, the extremely rare transitions from one state of the system to another. This new approach opens the way for addressing a set of questions that are out of reach through direct numerical simulations. We demonstrate for the first time the concentration of transition paths close to instantons, in a numerical simulation of genuine turbulent flows. We show that the transition is a noise-activated nucleation of vorticity bands. We address for the first time the existence of Arrhenius laws in turbulent flows. The methodology we developed shall prove useful to study many other transitions related to drastic changes for the turbulent dynamics of climate, geophysical, astrophysical and engineering applications. This opens a new range of studies impossible so far, and bring turbulent phenomena in the realm of non-equilibrium statistical mechanics.

8 pages, 7 figures, one table

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• Random changes of flow topology in two dimensional and geophysical turbulence
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• Universal profile of the vortex condensate in two-dimensional turbulence
• Bi-stability in turbulent, rotating spherical Couette flow
• Velocity statistics inside coherent vortices generated by the inverse cascade of $2d$ turbulence
• Theoretical prediction of Reynolds stresses and velocity profiles for barotropic turbulent jets

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