skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

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; OSTI ID: 1438569
Grant/Contract Number:  
FG02-89ER53291
Resource Type:
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 = {2017},
month = {6}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Save / Share:

Works referenced in this record:

Si iv COLUMN DENSITIES PREDICTED FROM NON-EQUILIBRIUM IONIZATION SIMULATIONS OF TURBULENT MIXING LAYERS AND HIGH-VELOCITY CLOUDS
journal, October 2015


Stellarator Turbulence: Subdominant Eigenmodes and Quasilinear Modeling
journal, February 2016


Stochasticity and the random phase approximation for three electron drift waves
journal, January 1982


Reduction of inward momentum flux by damped eigenmodes
journal, December 2009

  • Terry, P. W.; Baver, D. A.; Hatch, D. R.
  • Physics of Plasmas, Vol. 16, Issue 12
  • DOI: 10.1063/1.3271158

Generation and Stability of Zonal Flows in Ion-Temperature-Gradient Mode Turbulence
journal, December 2000


Evolution of Unmagnetized and Magnetized Shear Layers
journal, May 2008

  • Palotti, M. L.; Heitsch, F.; Zweibel, E. G.
  • The Astrophysical Journal, Vol. 678, Issue 1
  • DOI: 10.1086/529066

Scalings of Ion-Temperature-Gradient-Driven Anomalous Transport in Tokamaks
journal, July 1996


A validated non-linear Kelvin–Helmholtz benchmark for numerical hydrodynamics
journal, December 2015

  • Lecoanet, D.; McCourt, M.; Quataert, E.
  • Monthly Notices of the Royal Astronomical Society, Vol. 455, Issue 4
  • DOI: 10.1093/mnras/stv2564

Role of stable eigenmodes in saturated local plasma turbulence
journal, February 2006

  • Terry, P. W.; Baver, D. A.; Gupta, Sangeeta
  • Physics of Plasmas, Vol. 13, Issue 2
  • DOI: 10.1063/1.2168453

On the mechanism of shear flow instabilities
journal, October 1994


A Microscopic Analysis of Shear Acceleration
journal, December 2006

  • Rieger, Frank M.; Duffy, Peter
  • The Astrophysical Journal, Vol. 652, Issue 2
  • DOI: 10.1086/508056

Interacting vorticity waves as an instability mechanism for magnetohydrodynamic shear instabilities
journal, February 2015

  • Heifetz, E.; Mak, J.; Nycander, J.
  • Journal of Fluid Mechanics, Vol. 767
  • DOI: 10.1017/jfm.2015.47

Origin of Magnetic Stochasticity and Transport in Plasma Microturbulence
journal, June 2012


Stability of the Interface between Two Fluids in Relative Motion
journal, July 1968


Nonlinear stability and instability in collisionless trapped electron mode turbulence
journal, August 2002

  • Baver, D. A.; Terry, P. W.; Gatto, R.
  • Physics of Plasmas, Vol. 9, Issue 8
  • DOI: 10.1063/1.1491958

Structure of the atmosphere in the vicinity of large-amplitude Kelvin-Helmholtz billows
journal, July 1971

  • Browning, K. A.
  • Quarterly Journal of the Royal Meteorological Society, Vol. 97, Issue 413
  • DOI: 10.1002/qj.49709741304

The instability to long waves of unbounded parallel inviscid flow
journal, October 1962


Damped eigenmode saturation in plasma fluid turbulence
journal, January 2011

  • Makwana, K. D.; Terry, P. W.; Kim, J. -H.
  • Physics of Plasmas, Vol. 18, Issue 1
  • DOI: 10.1063/1.3530186

Origin of the Mass in Massive Star Outflows
journal, April 1997

  • Churchwell, E.
  • The Astrophysical Journal, Vol. 479, Issue 1
  • DOI: 10.1086/310578

Nonlinear inward particle flux component in trapped electron mode turbulence
journal, June 2006

  • Terry, P. W.; Gatto, R.
  • Physics of Plasmas, Vol. 13, Issue 6
  • DOI: 10.1063/1.2212403

Stability of Inviscid Plane Couette Flow
journal, January 1960