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Title: Coupling of damped and growing modes in unstable shear flow

Abstract

Analysis of the saturation of the Kelvin-Helmholtz instability is undertaken to determine the extent to which the conjugate linearly stable mode plays a role. For a piecewise-continuous mean flow profile with constant shear in a fixed layer, it is shown that the stable mode is nonlinearly excited, providing an injection-scale sink of the fluctuation energy similar to what has been found for gyroradius-scale drift-wave turbulence. Quantitative evaluation of the contribution of the stable mode to the energy balance at the onset of saturation shows that nonlinear energy transfer to the stable mode is as significant as energy transfer to small scales in balancing energy injected into the spectrum by the instability. The effect of the stable mode on momentum transport is quantified by expressing the Reynolds stress in terms of stable and unstable mode amplitudes at saturation, from which it is found that the stable mode can produce a sizable reduction in the momentum flux.

Authors:
 [1];  [1];  [1];  [1]
  1. Univ. of Wisconsin, Madison, WI (United States)
Publication Date:
Research Org.:
Univ. of Wisconsin, Madison, WI (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Fusion Energy Sciences (FES) (SC-24)
OSTI Identifier:
1425380
Alternate Identifier(s):
OSTI ID: 1363831
Grant/Contract Number:
FG02-89ER53291
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Physics of Plasmas
Additional Journal Information:
Journal Volume: 24; Journal Issue: 6; Journal ID: ISSN 1070-664X
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; linear acoustics; crystallography; shear flows; turbulent flows; ionospheric physics; energy transfer; magnetospheric dynamics; physical optics; flow instabilities; fluid flows

Citation Formats

Fraser, A. E., Terry, P. W., Zweibel, E. G., and Pueschel, M. J. Coupling of damped and growing modes in unstable shear flow. United States: N. p., 2017. Web. doi:10.1063/1.4985322.
Fraser, A. E., Terry, P. W., Zweibel, E. G., & Pueschel, M. J. Coupling of damped and growing modes in unstable shear flow. United States. doi:10.1063/1.4985322.
Fraser, A. E., Terry, P. W., Zweibel, E. G., and Pueschel, M. J. Wed . "Coupling of damped and growing modes in unstable shear flow". United States. doi:10.1063/1.4985322. https://www.osti.gov/servlets/purl/1425380.
@article{osti_1425380,
title = {Coupling of damped and growing modes in unstable shear flow},
author = {Fraser, A. E. and Terry, P. W. and Zweibel, E. G. and Pueschel, M. J.},
abstractNote = {Analysis of the saturation of the Kelvin-Helmholtz instability is undertaken to determine the extent to which the conjugate linearly stable mode plays a role. For a piecewise-continuous mean flow profile with constant shear in a fixed layer, it is shown that the stable mode is nonlinearly excited, providing an injection-scale sink of the fluctuation energy similar to what has been found for gyroradius-scale drift-wave turbulence. Quantitative evaluation of the contribution of the stable mode to the energy balance at the onset of saturation shows that nonlinear energy transfer to the stable mode is as significant as energy transfer to small scales in balancing energy injected into the spectrum by the instability. The effect of the stable mode on momentum transport is quantified by expressing the Reynolds stress in terms of stable and unstable mode amplitudes at saturation, from which it is found that the stable mode can produce a sizable reduction in the momentum flux.},
doi = {10.1063/1.4985322},
journal = {Physics of Plasmas},
number = 6,
volume = 24,
place = {United States},
year = {Wed Jun 14 00:00:00 EDT 2017},
month = {Wed Jun 14 00:00:00 EDT 2017}
}

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