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Title: Kolmogorov flow in two dimensional strongly coupled dusty plasma

Abstract

Undriven, incompressible Kolmogorov flow in two dimensional doubly periodic strongly coupled dusty plasma is modelled using generalised hydrodynamics, both in linear and nonlinear regime. A complete stability diagram is obtained for low Reynolds numbers R and for a range of viscoelastic relaxation time τ{sub m} [0 < τ{sub m} < 10]. For the system size considered, using a linear stability analysis, similar to Navier Stokes fluid (τ{sub m} = 0), it is found that for Reynolds number beyond a critical R, say R{sub c}, the Kolmogorov flow becomes unstable. Importantly, it is found that R{sub c} is strongly reduced for increasing values of τ{sub m}. A critical τ{sub m}{sup c} is found above which Kolmogorov flow is unconditionally unstable and becomes independent of Reynolds number. For R < R{sub c}, the neutral stability regime found in Navier Stokes fluid (τ{sub m} = 0) is now found to be a damped regime in viscoelastic fluids, thus changing the fundamental nature of transition of Kolmogorov flow as function of Reynolds number R. A new parallelized nonlinear pseudo spectral code has been developed and is benchmarked against eigen values for Kolmogorov flow obtained from linear analysis. Nonlinear states obtained from the pseudo spectral code exhibit cyclicity and pattern formation in vorticity and viscoelasticmore » oscillations in energy.« less

Authors:
;  [1]
  1. Institute for Plasma Research, Bhat Gandhinagar, Gujarat 382 428 (India)
Publication Date:
OSTI Identifier:
22303743
Resource Type:
Journal Article
Journal Name:
Physics of Plasmas
Additional Journal Information:
Journal Volume: 21; Journal Issue: 7; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1070-664X
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; BENCHMARKS; DATA; FLUIDS; HYDRODYNAMICS; NAVIER-STOKES EQUATIONS; NONLINEAR PROBLEMS; PLASMA; RELAXATION TIME; REYNOLDS NUMBER; SOCIO-ECONOMIC FACTORS; STABILITY; TWO-DIMENSIONAL CALCULATIONS

Citation Formats

Gupta, Akanksha, Ganesh, R., E-mail: ganesh@ipr.res.in, and Joy, Ashwin. Kolmogorov flow in two dimensional strongly coupled dusty plasma. United States: N. p., 2014. Web. doi:10.1063/1.4890488.
Gupta, Akanksha, Ganesh, R., E-mail: ganesh@ipr.res.in, & Joy, Ashwin. Kolmogorov flow in two dimensional strongly coupled dusty plasma. United States. https://doi.org/10.1063/1.4890488
Gupta, Akanksha, Ganesh, R., E-mail: ganesh@ipr.res.in, and Joy, Ashwin. 2014. "Kolmogorov flow in two dimensional strongly coupled dusty plasma". United States. https://doi.org/10.1063/1.4890488.
@article{osti_22303743,
title = {Kolmogorov flow in two dimensional strongly coupled dusty plasma},
author = {Gupta, Akanksha and Ganesh, R., E-mail: ganesh@ipr.res.in and Joy, Ashwin},
abstractNote = {Undriven, incompressible Kolmogorov flow in two dimensional doubly periodic strongly coupled dusty plasma is modelled using generalised hydrodynamics, both in linear and nonlinear regime. A complete stability diagram is obtained for low Reynolds numbers R and for a range of viscoelastic relaxation time τ{sub m} [0 < τ{sub m} < 10]. For the system size considered, using a linear stability analysis, similar to Navier Stokes fluid (τ{sub m} = 0), it is found that for Reynolds number beyond a critical R, say R{sub c}, the Kolmogorov flow becomes unstable. Importantly, it is found that R{sub c} is strongly reduced for increasing values of τ{sub m}. A critical τ{sub m}{sup c} is found above which Kolmogorov flow is unconditionally unstable and becomes independent of Reynolds number. For R < R{sub c}, the neutral stability regime found in Navier Stokes fluid (τ{sub m} = 0) is now found to be a damped regime in viscoelastic fluids, thus changing the fundamental nature of transition of Kolmogorov flow as function of Reynolds number R. A new parallelized nonlinear pseudo spectral code has been developed and is benchmarked against eigen values for Kolmogorov flow obtained from linear analysis. Nonlinear states obtained from the pseudo spectral code exhibit cyclicity and pattern formation in vorticity and viscoelastic oscillations in energy.},
doi = {10.1063/1.4890488},
url = {https://www.osti.gov/biblio/22303743}, journal = {Physics of Plasmas},
issn = {1070-664X},
number = 7,
volume = 21,
place = {United States},
year = {Tue Jul 15 00:00:00 EDT 2014},
month = {Tue Jul 15 00:00:00 EDT 2014}
}