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Kelvin–Helmholtz instability in strongly coupled dusty plasma with rotational shear flows and tracer transport

Published online by Cambridge University Press:  18 January 2022

Vikram S. Dharodi Open the ORCID record for Vikram S. Dharodi [Opens in a new window] ,
Bhavesh Patel  and
Amita Das
Vikram S. Dharodi*
Affiliation:
Institute for Plasma Research, HBNI, Bhat, Gandhinagar382428, India
Bhavesh Patel
Affiliation:
Institute for Plasma Research, HBNI, Bhat, Gandhinagar382428, India
Amita Das
Affiliation:
Department of Physics, Indian Institute of Technology, New Delhi110016, Delhi, India
*
†Email address for correspondence: dharodiv@msu.edu
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Abstract

Kelvin–Helmholtz (KH) instability plays a significant role in transport and mixing in various media such as hydrodynamic fluids, plasmas, geophysical flows and astrophysical situations. In this paper, we numerically explore this instability for a two-dimensional strongly coupled dusty plasma medium with rotational shear flows. We study this medium using a generalized hydrodynamic fluid model which treats it as a viscoelastic fluid. We consider the specific cases of rotating vorticity with abrupt radial profiles of rotation. In particular, single-circulation and multi-circulation vorticity shell profiles have been chosen. We observe the KH vortices at each circular interface between two relative rotating flows along with a pair of ingoing and outgoing wavefronts of transverse shear waves. Our studies show that due to the interplay between KH vortices and shear waves in the strongly coupled medium, the mixing and transport behaviour are much better than those of standard inviscid hydrodynamic fluids. In the interest of substantiating the mixing and transport behaviour, the generalized hydrodynamic fluid model is extended to include Lagrangian tracer particles. The numerical dispersion of these tracer particles in a flow provides an estimate of the diffusion in such a medium. We present the preliminary observations of tracer distribution (cluster formation) and diffusion (mean square displacement) across the medium.

Keywords

dusty plasmasstrongly coupled plasmascomplex plasmas
Type
Research Article
Information
Journal of Plasma Physics , Volume 88 , Issue 1 , February 2022 , 905880103
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Copyright
Copyright © The Author(s), 2022. Published by Cambridge University Press

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References

REFERENCES

Ashwin, J. & Ganesh, R. 2010 Kelvin–Helmholtz instability in strongly coupled Yukawa liquids. Phys. Rev. Lett. 104 (21), 215003.Google Scholar
Avinash, K. & Sen, A. 2015 Rayleigh–Taylor instability in dusty plasma experiment. Phys. Plasmas 22 (8), 083707.CrossRefGoogle Scholar
Balkovsky, E., Falkovich, G. & Fouxon, A. 2001 Intermittent distribution of inertial particles in turbulent flows. Phys. Rev. Lett. 86 (13), 2790.CrossRefGoogle ScholarPubMed
Banerjee, D., Janaki, M.S. & Chakrabarti, N. 2012 Shear flow instability in a strongly coupled dusty plasma. Phys. Rev. E 85 (6), 066408.CrossRefGoogle Scholar
Bec, J., Biferale, L., Boffetta, G., Celani, A., Cencini, M., Lanotte, A., Musacchio, S. & Toschi, F. 2006 Acceleration statistics of heavy particles in turbulence. J. Fluid Mech. 550, 349–358.CrossRefGoogle Scholar
Biferale, L., Boffetta, G., Celani, A., Devenish, B.J., Lanotte, A. & Toschi, F. 2004 Multifractal statistics of lagrangian velocity and acceleration in turbulence. Phys. Rev. Lett. 93 (6), 064502.CrossRefGoogle ScholarPubMed
Biferale, L., Boffetta, G., Celani, A., Lanotte, A. & Toschi, F. 2005 Particle trapping in three-dimensional fully developed turbulence. Phys. Fluids 17 (2), 021701.CrossRefGoogle Scholar
Boivin, M., Simonin, O. & Squires, K.D. 1998 Direct numerical simulation of turbulence modulation by particles in isotropic turbulence. J. Fluid Mech. 375, 235–263.CrossRefGoogle Scholar
Boris, J.P., Landsberg, A.M., Oran, E.S. & Gardner, J.H. 1993LCPFCT A flux-corrected transport algorithm for solving generalized continuity equations. Tech. Rep. NRL Memorandum Report 93-7192. Naval Research Laboratory.CrossRefGoogle Scholar
Cencini, M., Bec, J., Biferale, L., Boffetta, G., Celani, A., Lanotte, A.S., Musacchio, S. & Toschi, F. 2006 Dynamics and statistics of heavy particles in turbulent flows. J. Turbul 7 (36), 1–16.CrossRefGoogle Scholar
Chandrasekhar, S. 1981 Hydrodynamic and Hydromagnetic Stability. Dover, 1981.Google Scholar
Choudhary, M., Bergert, R., Mitic, S. & Thoma, M.H. 2020 Three-dimensional dusty plasma in a strong magnetic field: Observation of rotating dust tori. Phys. Plasmas 27 (6), 063701.CrossRefGoogle Scholar
Chun, J., Koch, D.L., Rani, S.L., Ahluwalia, A. & Collins, L.R. 2005 Clustering of aerosol particles in isotropic turbulence. J. Fluid Mech. 536, 219.CrossRefGoogle Scholar
Collins, L.R. & Keswani, A. 2004 Reynolds number scaling of particle clustering in turbulent aerosols. New J. Phys. 6 (1), 119.CrossRefGoogle Scholar
d'Angelo, N. & Song, B. 1990 The Kelvin–Helmholtz instability in dusty plasmas. Planet. Space Sci. 38 (12), 1577–1579.CrossRefGoogle Scholar
Danielson, J.R. & Surko, C.M. 2006 Radial compression and torque-balanced steady states of single-component plasmas in Penning-Malmberg traps. Phys. Plasmas 13 (5), 055706.CrossRefGoogle Scholar
Das, A., Dharodi, V. & Tiwari, S. 2014 Collective dynamics in strongly coupled dusty plasma medium. J. Plasma Phys. 80 (6), 855–861.CrossRefGoogle Scholar
Das, A. & Kaw, P. 2014 Suppression of Rayleigh Taylor instability in strongly coupled plasmas. Phys. Plasmas 21 (6), 062102.CrossRefGoogle Scholar
Dharodi, V., Das, A., Patel, B. & Kaw, P. 2016 Sub-and super-luminar propagation of structures satisfying poynting-like theorem for incompressible generalized hydrodynamic fluid model depicting strongly coupled dusty plasma medium. Phys. Plasmas 23 (1), 013707.CrossRefGoogle Scholar
Dharodi, V., Kumar Tiwari, S. & Das, A. 2014 Visco-elastic fluid simulations of coherent structures in strongly coupled dusty plasma medium. Phys. Plasmas 21 (7), 073705.CrossRefGoogle Scholar
Dharodi, V.S. 2020 Rotating vortices in two-dimensional inhomogeneous strongly coupled dusty plasmas: shear and spiral density waves. Phys. Rev. E 102 (4), 043216.CrossRefGoogle ScholarPubMed
Diaw, A. & Murillo, M.S. 2015 Generalized hydrodynamics model for strongly coupled plasmas. Phys. Rev. E 92 (1), 013107.CrossRefGoogle ScholarPubMed
Dolai, B., Prajapati, R.P. & Chhajlani, R.K. 2016 Effect of different dust flow velocities on combined Kelvin–Helmholtz and Rayleigh–Taylor instabilities in magnetized incompressible dusty fluids. Phys. Plasmas 23 (11), 113704.CrossRefGoogle Scholar
Douady, S., Couder, Y. & Brachet, M.E. 1991 Direct observation of the intermittency of intense vorticity filaments in turbulence. Phys. Rev. Lett. 67 (8), 983.CrossRefGoogle ScholarPubMed
Drazin, P.G. 1970 Kelvin–Helmholtz instability of finite amplitude. J. Fluid Mech. 42 (2), 321–335.CrossRefGoogle Scholar
Drótos, G., Monroy, P., Hernández-García, E. & López, C. 2019 Inhomogeneities and caustics in the sedimentation of noninertial particles in incompressible flows. Chaos 29 (1), 013115.CrossRefGoogle ScholarPubMed
Falkovich, G., Fouxon, A. & Stepanov, M.G. 2002 Acceleration of rain initiation by cloud turbulence. Nature 419 (6903), 151–154.CrossRefGoogle ScholarPubMed
Falkovich, G., Gawedzki, K. & Vergassola, M. 2001 Particles and fields in fluid turbulence. Rev. Mod. Phys. 73 (4), 913.CrossRefGoogle Scholar
Falkovich, G. & Pumir, A. 2004 Intermittent distribution of heavy particles in a turbulent flow. Phys. Fluids 16 (7), L47–L50.CrossRefGoogle Scholar
Fessler, J.R., Kulick, J.D. & Eaton, J.K. 1994 Preferential concentration of heavy particles in a turbulent channel flow. Phys. Fluids 6 (11), 3742–3749.CrossRefGoogle Scholar
Foullon, C., Verwichte, E., Nakariakov, V.M., Nykyri, K. & Farrugia, C.J. 2011 Magnetic Kelvin–Helmholtz instability at the sun. Astrophys. J. Lett. 729 (1), L8.CrossRefGoogle Scholar
Goto, S. & Vassilicos, J.C. 2006 Self-similar clustering of inertial particles and zero-acceleration points in fully developed two-dimensional turbulence. Phys. Fluids 18 (11), 115103.CrossRefGoogle Scholar
Guha, A. 2008 Transport and deposition of particles in turbulent and laminar flow. Annu. Rev. Fluid Mech. 40, 311–341.CrossRefGoogle Scholar
van Haren, H. & Gostiaux, L. 2010 A deep-ocean Kelvin–Helmholtz billow train. Geophys. Res. Lett. 37 (3), L03605.CrossRefGoogle Scholar
Horton, W., Tajima, T. & Kamimura, T. 1987 Kelvin–Helmholtz instability and vortices in magnetized plasma. Phys. Fluids 30 (11), 3485–3495.CrossRefGoogle Scholar
Ikezi, H. 1986 Coulomb solid of small particles in plasmas. Phys. Fluids 29 (6), 1764–1766.CrossRefGoogle Scholar
Ishihara, T. & Kaneda, Y. 2002 Relative diffusion of a pair of fluid particles in the inertial subrange of turbulence. Phys. Fluids 14 (11), L69–L72.CrossRefGoogle Scholar
Jeon, J.-H., Leijnse, N., Oddershede, L.B. & Metzler, R. 2013 Anomalous diffusion and power-law relaxation of the time averaged mean squared displacement in worm-like micellar solutions. New J. Phys. 15 (4), 045011.CrossRefGoogle Scholar
Karasev, V., Dzlieva, E., Pavlov, S., Novikov, L. & Maiorov, S. 2017 The rotation of complex plasmas in a stratified glow discharge in the strong magnetic field. IEEE Trans. Plasma Sci. 46 (4), 727–730.CrossRefGoogle Scholar
Kaw, P.K. & Sen, A. 1998 Low frequency modes in strongly coupled dusty plasmas. Phys. Plasmas 5 (10), 3552–3559.CrossRefGoogle Scholar
Klindworth, M., Melzer, A., Piel, A. & Schweigert, V.A. 2000 Laser-excited intershell rotation of finite coulomb clusters in a dusty plasma. Phys. Rev. B 61 (12), 8404.CrossRefGoogle Scholar
Konopka, U., Samsonov, D., Ivlev, A.V., Goree, J., Steinberg, V. & Morfill, G.E. 2000 Rigid and differential plasma crystal rotation induced by magnetic fields. Phys. Rev. E 61 (2), 1890.CrossRefGoogle ScholarPubMed
La Porta, A., Voth, G.A., Crawford, A.M., Alexander, J. & Bodenschatz, E. 2001 Fluid particle accelerations in fully developed turbulence. Nature 409 (6823), 1017–1019.CrossRefGoogle ScholarPubMed
Luo, Q.Z., D'Angelo, N. & Merlino, R.L. 2001 The Kelvin–Helmholtz instability in a plasma with negatively charged dust. Phys. Plasmas 8 (1), 31–35.CrossRefGoogle Scholar
Mason, T.G., Ganesan, K., van Zanten, J.H., Wirtz, D. & Kuo, S.C. 1997 Particle tracking microrheology of complex fluids. Phys. Rev. Lett. 79 (17), 3282.CrossRefGoogle Scholar
Maxey, M.R. 1987 The gravitational settling of aerosol particles in homogeneous turbulence and random flow fields. J. Fluid Mech. 174, 441–465.CrossRefGoogle Scholar
Maxey, M.R. & Riley, J.J. 1983 Equation of motion for a small rigid sphere in a nonuniform flow. Phys. Fluids 26 (4), 883–889.CrossRefGoogle Scholar
McLaughlin, J.B. 1989 Aerosol particle deposition in numerically simulated channel flow. Phys. Fluids A 1 (7), 1211–1224.CrossRefGoogle Scholar
Mordant, N., Metz, P., Michel, O. & Pinton, J.-F. 2001 Measurement of Lagrangian velocity in fully developed turbulence. Phys. Rev. Lett. 87 (21), 214501.CrossRefGoogle ScholarPubMed
Nosenko, V., Ivlev, A.V., Zhdanov, S.K., Fink, M. & Morfill, G.E. 2009 Rotating electric fields in complex (dusty) plasmas. Phys. Plasmas 16 (8), 083708.CrossRefGoogle Scholar
Oka, S. & Goto, S. 2021 Generalized sweep-stick mechanism of inertial-particle clustering in turbulence. Phys. Rev. Fluids 6 (4), 044605.CrossRefGoogle Scholar
Ott, S. & Mann, J. 2000 An experimental investigation of the relative diffusion of particle pairs in three-dimensional turbulent flow. J. Fluid Mech. 422, 207–223.CrossRefGoogle Scholar
Pandey, B.P., Vladimirov, S.V. & Samarian, A. 2012 Shear driven instabilities in dusty plasmas. In Europhysics Conference on the Atomic and Molecular Physics of Ionized Gases (21st: 2012), pp. 1–2. European Physical Society.Google Scholar
Petersen, A.J., Baker, L. & Coletti, F. 2019 Experimental study of inertial particles clustering and settling in homogeneous turbulence. J. Fluid Mech. 864, 925–970.CrossRefGoogle Scholar
Prajapati, R.P. & Boro, P. 2021 Suppression of the Kelvin–Helmholtz instability due to polarization force in nonuniform magnetized sheared dusty plasmas. AIP Adv. 11 (9), 095202.CrossRefGoogle Scholar
Ravichandran, S., Deepu, P. & Govindarajan, R. 2017 Clustering of heavy particles in vortical flows: a selective review. Sadhana 42 (4), 597–605.CrossRefGoogle Scholar
Rawat, S.P.S. & Rao, N.N. 1993 Kelvin–Helmholtz instability driven by sheared dust flow. Planet. Space Sci. 41 (2), 137–140.CrossRefGoogle Scholar
Reade, W.C. & Collins, L.R. 2000 A numerical study of the particle size distribution of an aerosol undergoing turbulent coagulation. J. Fluid Mech. 415, 45–64.CrossRefGoogle Scholar
Riley, J.J. & Patterson, G.S. Jr. 1974 Diffusion experiments with numerically integrated isotropic turbulence. Phys. Fluids 17 (2), 292–297.CrossRefGoogle Scholar
Sapsis, T. & Haller, G. 2010 Clustering criterion for inertial particles in two-dimensional time-periodic and three-dimensional steady flows. Chaos 20 (1), 017515.CrossRefGoogle ScholarPubMed
Sawford, B.L., Yeung, P.K., Borgas, M.S., Vedula, P., La Porta, A., Crawford, A.M. & Bodenschatz, E. 2003 Conditional and unconditional acceleration statistics in turbulence. Phys. Fluids 15 (11), 3478–3489.CrossRefGoogle Scholar
Schablinski, J., Block, D., Carstensen, J., Greiner, F. & Piel, A. 2014 Sheared and unsheared rotation of driven dust clusters. Phys. Plasmas 21 (7), 073701.CrossRefGoogle Scholar
Schwabe, M., Zhdanov, S., Räth, C., Graves, D.B., Thomas, H.M. & Morfill, G.E. 2014 Collective effects in vortex movements in complex plasmas. Phys. Rev. Lett. 112 (11), 115002.CrossRefGoogle ScholarPubMed
Smyth, W.D. & Moum, J.N. 2012 Ocean mixing by Kelvin–Helmholtz instability. Oceanography 25 (2), 140–149.CrossRefGoogle Scholar
Squires, K.D. & Eaton, J.K. 1991 Preferential concentration of particles by turbulence. Phys. Fluids A 3 (5), 1169–1178.CrossRefGoogle Scholar
Swarztrauber, P., Sweet, R. & Adams, J.C. 1999 Fishpack: efficient fortran subprograms for the solution of elliptic partial differential equations. UCAR Publication, July.Google Scholar
Tiwari, S., Dharodi, V., Das, A., Kaw, P. & Sen, A. 2014 a Kelvin–Helmholtz instability in dusty plasma medium: fluid and particle approach. J. Plasma Phys. 80 (6), 817–823.CrossRefGoogle Scholar
Tiwari, S.K., Das, A., Angom, D., Patel, B.G. & Kaw, P. 2012 a Kelvin–Helmholtz instability in a strongly coupled dusty plasma medium. Phys. Plasmas 19 (7), 073703.CrossRefGoogle Scholar
Tiwari, S.K., Das, A., Kaw, P. & Sen, A. 2012 b Kelvin–Helmholtz instability in a weakly coupled dust fluid. Phys. Plasmas 19 (2), 023703.CrossRefGoogle Scholar
Tiwari, S.K., Das, A., Kaw, P. & Sen, A. 2012 c Longitudinal singular response of dusty plasma medium in weak and strong coupling limits. Phys. Plasmas 19 (1), 013706.CrossRefGoogle Scholar
Tiwari, S.K., Dharodi, V.S., Das, A., Patel, B.G. & Kaw, P. 2014 b Evolution of sheared flow structure in visco-elastic fluids. In AIP Conference Proceedings, vol. 1582, pp. 55–65. American Institute of Physics.CrossRefGoogle Scholar
Voth, G.A., La Porta, A., Crawford, A.M., Alexander, J. & Bodenschatz, E. 2002 Measurement of particle accelerations in fully developed turbulence. J. Fluid Mech. 469, 121–160.CrossRefGoogle Scholar
Waigh, T.A. 2005 Microrheology of complex fluids. Rep. Prog. Phys. 68 (3), 685.CrossRefGoogle Scholar
Wörner, L., Nosenko, V., Ivlev, A.V., Zhdanov, S.K., Thomas, H.M., Morfill, G.E., Kroll, M., Schablinski, J. & Block, D. 2011 Effect of rotating electric field on 3D complex (dusty) plasma. Phys. Plasmas 18 (6), 063706.CrossRefGoogle Scholar
Yeung, P.K. 2001 Lagrangian characteristics of turbulence and scalar transport in direct numerical simulations. J. Fluid Mech. 427, 241.CrossRefGoogle Scholar
Yeung, P.K. 2002 Lagrangian investigations of turbulence. Annu. Rev. Fluid. Mech. 34 (1), 115–142.CrossRefGoogle Scholar
Zaichik, L.I., Simonin, O. & Alipchenkov, V.M. 2003 Two statistical models for predicting collision rates of inertial particles in homogeneous isotropic turbulence. Phys. Fluids 15 (10), 2995–3005.CrossRefGoogle Scholar
Zhou, Y., Wexler, A.S. & Wang, L.-P. 2001 Modelling turbulent collision of bidisperse inertial particles. J. Fluid Mech. 433, 77.CrossRefGoogle Scholar