Coupling of damped and growing modes in unstable shear flow
Abstract
Analysis of the saturation of the KelvinHelmholtz instability is undertaken to determine the extent to which the conjugate linearly stable mode plays a role. For a piecewisecontinuous mean flow profile with constant shear in a fixed layer, it is shown that the stable mode is nonlinearly excited, providing an injectionscale sink of the fluctuation energy similar to what has been found for gyroradiusscale driftwave 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:

 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) (SC24)
 OSTI Identifier:
 1425380
 Alternate Identifier(s):
 OSTI ID: 1363831; OSTI ID: 1438569
 Grant/Contract Number:
 FG0289ER53291
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Physics of Plasmas
 Additional Journal Information:
 Journal Volume: 24; Journal Issue: 6; Journal ID: ISSN 1070664X
 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 KelvinHelmholtz instability is undertaken to determine the extent to which the conjugate linearly stable mode plays a role. For a piecewisecontinuous mean flow profile with constant shear in a fixed layer, it is shown that the stable mode is nonlinearly excited, providing an injectionscale sink of the fluctuation energy similar to what has been found for gyroradiusscale driftwave 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 = {2017},
month = {6}
}
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