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 τm [0 < τm < 10]. For the system size considered, using a linear stability analysis, similar to Navier Stokes fluid (τm = 0), it is found that for Reynolds number beyond a critical R, say Rc, the Kolmogorov flow becomes unstable. Importantly, it is found that Rc is strongly reduced for increasing values of τm. A critical is found above which Kolmogorov flow is unconditionally unstable and becomes independent of Reynolds number. For R < Rc, the neutral stability regime found in Navier Stokes fluid (τm = 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.
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July 2014
Research Article|
July 17 2014
Kolmogorov flow in two dimensional strongly coupled dusty plasma
Akanksha Gupta;
Akanksha Gupta
Institute for Plasma Research
, Bhat Gandhinagar, Gujarat 382 428, India
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R. Ganesh;
R. Ganesh
a)
Institute for Plasma Research
, Bhat Gandhinagar, Gujarat 382 428, India
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Ashwin Joy
Ashwin Joy
Institute for Plasma Research
, Bhat Gandhinagar, Gujarat 382 428, India
Search for other works by this author on:
Akanksha Gupta
R. Ganesh
a)
Ashwin Joy
Institute for Plasma Research
, Bhat Gandhinagar, Gujarat 382 428, India
a)
Electronic mail: [email protected]
Phys. Plasmas 21, 073707 (2014)
Article history
Received:
May 07 2014
Accepted:
July 07 2014
Citation
Akanksha Gupta, R. Ganesh, Ashwin Joy; Kolmogorov flow in two dimensional strongly coupled dusty plasma. Phys. Plasmas 1 July 2014; 21 (7): 073707. https://doi.org/10.1063/1.4890488
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