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Turbulence generation through an iterative cascade of the elliptical instability.

ABSTRACT: The essence of turbulent flow is the conveyance of energy through the formation, interaction, and destruction of eddies over a wide range of spatial scales-from the largest scales where energy is injected down to the smallest scales where it is dissipated through viscosity. Currently, there is no mechanistic framework that captures how the interactions of vortices drive this cascade. We show that iterations of the elliptical instability, arising from the interactions between counter-rotating vortices, lead to the emergence of turbulence. We demonstrate how the nonlinear development of the elliptical instability generates an ordered array of antiparallel secondary filaments. The secondary filaments mutually interact, leading to the formation of even smaller tertiary filaments. In experiments and simulations, we observe two and three iterations of this cascade, respectively. Our observations indicate that the elliptical instability could be one of the fundamental mechanisms by which the turbulent cascade develops.

SUBMITTER: McKeown R

PROVIDER: S-EPMC7048424 | biostudies-literature | 2020 Feb

REPOSITORIES: biostudies-literature

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Turbulence generation through an iterative cascade of the elliptical instability.

McKeown Ryan R Ostilla-Mónico Rodolfo R Pumir Alain A Brenner Michael P MP Rubinstein Shmuel M SM

Science advances 20200228 9

The essence of turbulent flow is the conveyance of energy through the formation, interaction, and destruction of eddies over a wide range of spatial scales-from the largest scales where energy is injected down to the smallest scales where it is dissipated through viscosity. Currently, there is no mechanistic framework that captures how the interactions of vortices drive this cascade. We show that iterations of the elliptical instability, arising from the interactions between counter-rotating vor ...[more]

PMID: 32158950

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Project description:Mesoscale cortical activity can be defined as the organization of activity of large neuron populations into collective action, forming time-dependent patterns such as traveling waves. Although collective action may play an important role in the cross-scale integration of brain activity and in the emergence of cognitive behavior, a comprehensive formulation of the laws governing its dynamics is still lacking. Because collective action processes are macroscopic with respect to neuronal activity, these processes cannot be described directly with methods and models developed for the microscale (individual neurons).To identify the characteristic features of mesoscopic dynamics, and to lay the foundations for a theoretical description of mesoscopic activity in the hippocampus, we conduct a comprehensive examination of observational data of hippocampal local field potential (LFP) recordings. We use the strong correlation between rat running-speed and the LFP power to parameterize the energy input into the hippocampus, and show that both the power and non-linearity of collective action (e.g., theta and gamma rhythms) increase with increased speed. Our results show that collective-action dynamics are stochastic (the precise state of a single neuron is irrelevant), weakly non-linear, and weakly dissipative. These are the principles of the theory of weak turbulence. Therefore, we propose weak turbulence a theoretical framework for the description of mesoscopic activity in the hippocampus. The weak turbulence framework provides a complete description of the cross-scale energy exchange (the energy cascade). It uncovers the mechanism governing major features of LFP spectra and bispectra, such as the physical meaning of the exponent α of power-law LFP spectra (e.g., f -α, where f is the frequency), the strengthening of theta-gamma coupling with energy input into the hippocampus, as well as specific phase lags associated with their interaction. Remarkably, the weak turbulence framework is consistent with the theory of self organized criticality, which provides a simple explanation for the existence of the power-law background spectrum. Together with self-organized criticality, weak turbulence could provide a unifying approach to modeling the dynamics of mesoscopic activity.

Dataset Information

Turbulence generation through an iterative cascade of the elliptical instability.

Publications

Turbulence generation through an iterative cascade of the elliptical instability.

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