DIFFER Seminar: The (Unconventional) Physics of Steady States in Instability-Driven Turbulence

Abstract: Instability driven turbulence is fed by inherently virulent sources: instabilities typically grow exponentially and would diverge to infinity were there no nonlinearity. In turbulence the key nonlinear process is spectral transfer, i.e., energy transfer between scales. This transfer is often thought of as being largely free of dissipation for turbulence to even exist. Turbulence can, however, eventually reach microscales where dissipation is strong, providing at the opposite end of an extended range of scales, a sink that balances the instability. This picture has dominated thinking about turbulent steady states since first proposed by Kolmogorov in 1941, whether the turbulence is stirred or driven by instability. While Kolomogorov’s picture provides a compelling description of stirred turbulence, recent advances indicate that it is fundamentally inconsistent with the steady states of instability-driven turbulence. This talk will show that in instability driven turbulence, account must be taken of collective modes that are damped, be they other roots of the instability dispersion relation, zeros of a plasma dielectric, or modes of oscillation that are intrinsically nonlinear. These modes do not decay into oblivion, as long assumed, but are actively pumped by the nonlinearity, providing a nonlinearly accessed sink of energy at the large scales of the instability drive, and depriving Kolmogorov cascades to small scales of energy.

A variety of aspects of instability-driven turbulence related to this theme will be introduced. These include the fluctuation bases needed to capture the salient features of instability-driven turbulence, the energy flow characteristics among the Fourier modes of a Kolmogorov cascade versus those of a basis of large-scale stable modes, and nonlinear similarity regimes in transfer to stable modes. Models for saturation of instability driven turbulence in fusion microturbulence and astrophysically relevant shear-flow driven turbulence will be presented, such that proper parameter scalings and transient behavior are recovered. The ability of such models to describe regimes of suppressed transport which had long eluded satisfactory explanation will be described, along with analyses of the origins of intermittency observed in these regimes. Observations of excitation of intrinsically nonlinear fluctuations that mimic linearly stable modes will be described, along with an explanation for the behavior. The nonlinear correlation time of three-wave interactions is found to play a central role in all of these scenarios, hence the origin and physics of this interaction will be described.