Sherwood 2015

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Universal instability, non-modal amplification, and subcritical turbulence

Author: Matt Landreman
Requested Type: Consider for Invited
Submitted: 2015-01-19 18:31:48

Co-authors: G. G. Plunk, T. M. Antonsen Jr, W. Dorland

Contact Info:
University of Maryland
A V Williams Building
College Park, MD   20742
United States

Abstract Text:
The ``universal instability'' has been discounted since several widely-cited papers in 1978 [1-3] concluded this drift wave was absolutely stable for any nonzero magnetic shear, but we challenge these earlier findings and demonstrate a variety of interesting behaviors in the system. First, contrary to [1-3], the drift wave in a sheared magnetic field can be absolutely unstable even with no temperature gradients, no trapped particles, and no magnetic curvature. Our findings differ from the 1978 results because the earlier work used an eigenmode equation limited to $k_x rho_i < 1$, whereas we find instability at $k_x rho_i > 1$ using a gyrokinetic approach that is not similarly limited. Second, even with parameters for which the system is linearly stable, many orders of magnitude of transient (non-modal) linear amplification can occur before exponential decay sets in. Non-modal amplification has been widely studied in other systems with sheared flows, but the drift-wave system provides a unique example in which large linear transients can arise without flow shear. Third, turbulence can be sustained nonlinearly in this system even when all eigenmodes are decaying, a phenomenon seen previously in some fluid models [6-7] and which we demonstrate kinetically. Generalizing an argument from neutral Navier-Stokes dynamics [8], we prove transient linear amplification (in the gyrokinetic free-energy norm) is required for sustained turbulence. While the standard eigenvalue analysis of the linearized problem cannot give a necessary condition for sustained turbulence, a modified eigenvalue problem does provide a necessary condition. [1] Ross & Mahajan, PRL 40, 324 (1978). [2] Tsang & Catto, PRL 40, 327 (1978). [3] Antonsen, PRL 41, 33 (1978). [4] Landreman, Antonsen, & Dorland, arXiv:1411.1807. [5] Landreman, Plunk, & Dorland, arXiv:1501.02980. [6] Scott, PRL 65, 3289 (1990). [7] Drake, Zeiler, & Biskamp, PRL 75, 4222 (1995). [8] DelSole, J Atmos Sci 61, 1086 (2004).


March 16-18, 2015
The Courant Institute, New York University