Abstract

The goal of this study is to investigate the interactions between turbulent kinetic, internal, and magnetic energies in planar magnetohydrodynamic (MHD) jets at different regimes of Mach and Alfvén Mach numbers. Toward this end, temporal simulations of planar MHD jets are performed, using two types of initial fluctuating velocity field: (i) single velocity perturbation mode with a streamwise wavevector and (ii) random, isotropic perturbations over a band of wavevectors. At low Mach numbers, magnetic tension work results in a reversible exchange of energy between fluctuating velocity and magnetic fields. At high Alfvén Mach numbers, this exchange results in the equipartition of turbulent kinetic and magnetic energies. At higher Mach numbers, dilatational kinetic energy is (reversibly) exchanged with internal and magnetic energies, by means of pressure-dilatation and magnetic-pressure-dilatation, respectively. Therefore, at high Mach and Alfvén Mach numbers, dilatational kinetic energy is seen to be in equipartition with the sum of turbulent internal and magnetic energies. In each of the regimes, the consequent effect of the interactions on the background Kelvin–Helmholtz vortex evolution is also identified.

References

References
1.
Diaz
,
F. R. C.
,
2000
, “
The VASIMR Rocket
,”
Sci. Am.
,
283
(
5
), pp.
90
97
.10.1038/scientificamerican1100-90
2.
Corke
,
T. C.
,
Enloe
,
C. L.
, and
Wilkinson
,
S. P.
,
2010
, “
Dielectric Barrier Discharge Plasma Actuators for Flow Control
,”
Annu. Rev, Fluid Mech.
,
42
(
1
), pp.
505
529
.10.1146/annurev-fluid-121108-145550
3.
Doeleman
,
S. S.
,
Fish
,
V. L.
,
Schenck
,
D. E.
,
Beaudoin
,
C.
,
Blundell
,
R.
,
Bower
,
G. C.
,
Broderick
,
A. E.
,
Chamberlin
,
R.
,
Freund
,
R.
,
Friberg
,
P.
,
Gurwell
,
M. A.
,
Ho
,
P. T. P.
,
Honma
,
M.
,
Inoue
,
M.
,
Krichbaum
,
T. P.
,
Lamb
,
J.
,
Loeb
,
A.
,
Lonsdale
,
C.
,
Marrone
,
D. P.
,
Moran
,
J. M.
,
Oyama
,
T.
,
Plambeck
,
R.
,
Primiani
,
R. A.
,
Rogers
,
A. E. E.
,
Smythe
,
D. L.
,
SooHoo
,
J.
,
Strittmatter
,
P.
,
Tilanus
,
R. P. J.
,
Titus
,
M.
,
Weintroub
,
J.
,
Wright
,
M.
,
Young
,
K. H.
, and
Ziurys
,
L. M.
,
2012
, “
Jet-Launching Structure Resolved Near the Supermassive Black Hole in M87
,”
Science
,
338
(
6105
), pp.
355
358
.10.1126/science.1224768
4.
Innes
,
D.
,
Inhester
,
B.
,
Axford
,
W.
, and
Wilhelm
,
K.
,
1997
, “
Bi-Directional Plasma Jets Produced by Magnetic Reconnection on the Sun
,”
Nature
,
386
(
6627
), pp.
811
813
.10.1038/386811a0
5.
Chandrasekhar
,
S.
,
1961
,
Hydrodynamic and Hydromagnetic Stability
,
Oxford University Press
,
Oxford, UK
.
6.
Sen
,
A. K.
,
1964
, “
Effect of Compressibility on Kelvin-Helmholtz Instability in a Plasma
,”
Phys. Fluids
,
7
(
8
), pp.
1293
1298
.10.1063/1.1711374
7.
Miura
,
A.
, and
Pritchett
,
P. L.
,
1982
, “
Nonlocal Stability Analysis of the MHD Kelvin-Helmholtz Instability in a Compressible Plasma
,”
J. Geophys. Res.
,
87
(
A9
), pp.
7431
7444
.10.1029/JA087iA09p07431
8.
Blumen
,
W.
,
1970
, “
Shear Layer Instability of an Inviscid Compressible Fluid
,”
J. Fluid Mech.
,
40
(
04
), pp.
769
781
.10.1017/S0022112070000435
9.
Blumen
,
W.
,
Drazin
,
P. G.
, and
Billings
,
D. F.
,
1975
, “
Shear Layer Instability of an Inviscid Compressible Fluid. Part 2
,”
J. Fluid Mech.
,
71
(
2
), pp.
305
316
.10.1017/S0022112075002595
10.
Karimi
,
M.
, and
Girimaji
,
S. S.
,
2016
, “
Suppression Mechanism of Kelvin-Helmholtz Instability in Compressible Fluid Flows
,”
Phys. Rev. E
,
93
(
4
), p.
041102
.10.1103/PhysRevE.93.041102
11.
Frank
,
A.
,
Jones
,
T. W.
,
Ryu
,
D.
, and
Gaalaas
,
J. B.
,
1996
, “
The MHD Kelvin-Helmholtz Instability: A Two-Dimensional Numerical Study
,”
Astrophys. J.
,
460
, pp.
777
793
.10.1086/177009
12.
Malagoli
,
A.
,
Bodo
,
G.
, and
Rosner
,
R.
,
1996
, “
On the Nonlinear Evolution of Magnetohydrodynamic Kelvin-Helmholtz Instabilities
,”
Astrophys. J.
,
456
, p.
708
.10.1086/176691
13.
Min
,
K.
,
1997
, “
Simulation of the Kelvin-Helmholtz Instability in the Magnetized Slab Jet
,”
Astrophys. J.
,
482
(
2
), pp.
733
746
.10.1086/304195
14.
Baty
,
H.
, and
Keppens
,
R.
,
2006
, “
Kelvin-Helmholtz Disruptions in Extended Magnetized Jet Flows
,”
Astron. Astrophys.
,
447
(
1
), pp.
9
22
.10.1051/0004-6361:20053969
15.
Palotti
,
M. L.
,
Heitsch
,
F.
,
Zweibel
,
E. G.
, and
Huang
,
Y.-M.
,
2008
, “
Evolution of Unmagnetized and Magnetized Shear Layers
,”
Astrophys. J.
,
678
(
1
), pp.
234
244
.10.1086/529066
16.
Obergaulinger
,
M.
,
Aloy
,
M.
, and
Müller
,
E.
,
2010
, “
Local Simulations of the Magnetized Kelvin-Helmholtz Instability in Neutron-Star Mergers
,”
Astron. Astrophys.
,
515
, p.
A30
.10.1051/0004-6361/200913386
17.
Ouyed
,
R.
,
Clarke
,
D. A.
, and
Pudritz
,
R. E.
,
2003
, “
Three-Dimensional Simulations of Jets From Keplerian Disks: Self-Regulatory Stability
,”
Astrophys. J.
,
582
(
1
), pp.
292
319
.10.1086/344507
18.
Fendt
,
C.
,
2006
, “
Collimation of Astrophysical Jets: The Role of the Accretion Disk Magnetic Field Distribution
,”
Astrophys. J.
,
651
(
1
), pp.
272
287
.10.1086/507976
19.
White
,
T. G.
,
Oliver
,
M. T.
,
Mabey
,
P.
,
Kühn-Kauffeldt
,
M.
,
Bott
,
A. F. A.
,
Döhl
,
L. N. K.
,
Bell
,
A. R.
,
Bingham
,
R.
,
Clarke
,
R.
,
Foster
,
J.
,
Giacinti
,
G.
,
Graham
,
P.
,
Heathcote
,
R.
,
Koenig
,
M.
,
Kuramitsu
,
Y.
,
Lamb
,
D. Q.
,
Meinecke
,
J.
,
Michel
,
T.
,
Miniati
,
F.
,
Notley
,
M.
,
Reville
,
B.
,
Ryu
,
D.
,
Sarkar
,
S.
,
Sakawa
,
Y.
,
Selwood
,
M. P.
,
Squire
,
J.
,
Scott
,
R. H. H.
,
Tzeferacos
,
P.
,
Woolsey
,
N.
,
Schekochihin
,
A. A.
, and
Gregori
,
G.
,
2019
, “
Supersonic Plasma Turbulence in the Laboratory
,”
Nat. Commun.
,
10
(
1
), pp.
1
6
.10.1038/s41467-019-09498-y
20.
Chang Díaz
,
F.
,
Squire
,
J.
,
Bering
,
E.
,
Baitty
,
F. W.
,
Goulding
,
R.
, and
Bengtson
,
R.
,
2004
, “
The Vasimr Engine: Project Status and Recent Accomplishments
,”
AIAA Paper No. 2004-0149
.10.2514/6.2004-149
21.
Kumar
,
G.
,
Bertsch
,
R. L.
, and
Girimaji
,
S. S.
,
2014
, “
Stabilizing Action of Pressure in Homogeneous Compressible Shear Flows: Effect of Mach Number and Perturbation Obliqueness
,”
J. Fluid Mech.
,
760
, pp.
540
566
.10.1017/jfm.2014.604
22.
Karimi
,
M.
, and
Girimaji
,
S. S.
,
2017
, “
Influence of Orientation on the Evolution of Small Perturbations in Compressible Shear Layers With Inflection Points
,”
Phys. Rev. E
,
95
(
3
), p.
033112
.10.1103/PhysRevE.95.033112
23.
Praturi
,
D. S.
,
Collard
,
D.
, and
Girimaji
,
S. S.
,
2019
, “
The Effect of Magnetic Field on Perturbation Evolution in Homogeneously Sheared Flows
,”
J. Fluid Mech.
,
858
, pp.
852
880
.10.1017/jfm.2018.765
24.
Zhou
,
Y.
,
2017
, “
Rayleigh-Taylor and Richtmyer-Meshkov Instability Induced Flow, Turbulence, and Mixing. I
,”
Phys. Rep.
,
720–722
, pp.
1
136
.10.1016/j.physrep.2017.07.005
25.
Zhou
,
Y.
,
2017
, “
Rayleigh–Taylor and Richtmyer–Meshkov Instability Induced Flow, Turbulence, and Mixing. II
,”
Phys. Rep.
,
723-725
, pp.
1
160
.10.1016/j.physrep.2017.07.008
26.
Zhou
,
Y.
,
Clark
,
T. T.
,
Clark
,
D. S.
,
Gail Glendinning
,
S.
,
Aaron Skinner
,
M.
,
Huntington
,
C. M.
,
Hurricane
,
O. A.
,
Dimits
,
A. M.
, and
Remington
,
B. A.
,
2019
, “
Turbulent Mixing and Transition Criteria of Flows Induced by Hydrodynamic Instabilities
,”
Phys. Plasmas
,
26
(
8
), p.
080901
.10.1063/1.5088745
27.
Elmegreen
,
B. G.
, and
Scalo
,
J.
,
2004
, “
Interstellar Turbulence I: Observations and Processes
,”
Annu. Rev. Astron. Astrophys.
,
42
(
1
), pp.
211
273
.10.1146/annurev.astro.41.011802.094859
28.
Scalo
,
J.
, and
Elmegreen
,
B. G.
,
2004
, “
Interstellar Turbulence ii: Implications and Effects
,”
Annu. Rev. Astron. Astrophys.
,
42
(
1
), pp.
275
316
.10.1146/annurev.astro.42.120403.143327
29.
Zhou
,
Y.
,
Matthaeus
,
W.
, and
Dmitruk
,
P.
,
2004
, “
Colloquium: Magnetohydrodynamic Turbulence and Time Scales in Astrophysical and Space Plasmas
,”
Rev. Mod. Phys.
,
76
(
4
), pp.
1015
1035
.10.1103/RevModPhys.76.1015
30.
Sato
,
T.
,
1985
, “
Global Energy Regulation in the Solar Wind-Magnetosphere-Ionosphere System
,”
Space Plasma Simulations
,
Springer
,
Dordrecht, The Netherlands
, pp.
485
498
.
31.
Sarkar
,
S.
,
Erlebacher
,
G.
,
Hussaini
,
M. Y.
, and
Kreiss
,
H. O.
,
1991
, “
The Analysis and Modelling of Dilatational Terms in Compressible Turbulence
,”
J. Fluid Mech.
,
227
, pp.
473
493
.10.1017/S0022112091000204
32.
Bertsch
,
R. L.
,
Suman
,
S.
, and
Girimaji
,
S. S.
,
2012
, “
Rapid Distortion Analysis of High Mach Number Homogeneous Shear Flows: Characterization of Flow-Thermodynamics Interaction Regimes
,”
Phys. Fluids
,
24
(
12
), p.
125106
.10.1063/1.4772193
33.
Praturi
,
D. S.
, and
Girimaji
,
S. S.
,
2019
, “
Effect of Pressure-Dilatation on Energy Spectrum Evolution in Compressible Turbulence
,”
Phys. Fluids
,
31
(
5
), p.
055114
.10.1063/1.5093929
34.
Praturi
,
D. S.
, and
Girimaji
,
S. S.
,
2019
, “
Mechanisms of Canonical Kelvin-Helmholtz Instability Suppression in Magnetohydrodynamic Flows
,”
Phys. Fluids
,
31
(
2
), p.
024108
.10.1063/1.5083857
35.
Araya
,
D. B.
,
Ebersohn
,
F. H.
,
Anderson
,
S. E.
, and
Girimaji
,
S. S.
,
2015
, “
Magneto-Gas Kinetic Method for Nonideal Magnetohydrodynamic Flows: Verification Protocol and Plasma Jet Simulations
,”
ASME J. Fluids Eng.
,
137
(
8
), p.
081302
.10.1115/1.4030067
36.
da Silva
,
C. B.
, and
Métais
,
O.
,
2002
, “
Vortex Control of Bifurcating Jets: A Numerical Study
,”
Phys. Fluids
,
14
(
11
), pp.
3798
3819
.10.1063/1.1506922
37.
da Silva
,
C. B.
, and
Pereira
,
J. C.
,
2008
, “
Invariants of the Velocity-Gradient, Rate-of-Strain, and Rate-of-Rotation Tensors Across the Turbulent/Nonturbulent Interface in Jets
,”
Phys. Fluids
,
20
(
5
), p.
055101
.10.1063/1.2912513
38.
Kerimo
,
J.
, and
Girimaji
,
S. S.
,
2007
, “
Boltzmann–BGK Approach to Simulating Weakly Compressible 3D Turbulence: Comparison Between Lattice Boltzmann and Gas Kinetic Methods
,”
J. Turbul.
,
8
, p.
N46
.10.1080/14685240701528551
39.
Kumar
,
G.
,
Girimaji
,
S. S.
, and
Kerimo
,
J.
,
2013
, “
WENO-Enhanced Gas-Kinetic Scheme for Direct Simulations of Compressible Transition and Turbulence
,”
J. Comput. Phys.
,
234
, pp.
499
523
.10.1016/j.jcp.2012.10.005
40.
Xie
,
Z.
, and
Girimaji
,
S. S.
,
2014
, “
Instability of Poiseuille Flow ar Extreme Mach Numbers: Linear Analysis and Simulations
,”
Phys. Rev. E
,
89
(
4
), p.
043001
.10.1103/PhysRevE.89.043001
41.
Praturi
,
D. S.
, and
Girimaji
,
S. S.
,
2020
, “
High-Speed Magnetohydrodynamic Jets: Contrasting Turbulence Suppression Mechanisms Due to Compressibility and Magnetic Field
,”
Int. J. Heat Fluid Flow
,
85
, p.
108625
.10.1016/j.ijheatfluidflow.2020.108625
42.
Gutmark
,
E.
, and
Wygnanski
,
I.
,
1976
, “
The Planar Turbulent Jet
,”
J. Fluid Mech.
,
73
(
3
), pp.
465
495
.10.1017/S0022112076001468
43.
Ramaprian
,
B.
, and
Chandrasekhara
,
M.
,
1985
, “
LDA Measurements in Plane Turbulent Jets
,”
ASME J. Fluids Eng.
,
107
(
2
), pp.
264
271
.10.1115/1.3242472
44.
Stanley
,
S.
,
Sarkar
,
S.
, and
Mellado
,
J.
,
2002
, “
A Study of the Flow-Field Evolution and Mixing in a Planar Turbulent Jet Using Direct Numerical Simulation
,”
J. Fluid Mech.
,
450
, pp.
377
407
.10.1017/S0022112001006644
You do not currently have access to this content.