Evolution of the Orszag-Tang vortex system in a compressible medium. I: Initial average subsonic flow

In this paper the results of fully compressible, Fourier collocation, numerical simulations of the Orszag–Tang vortex system are presented. The initial conditions for this system consist of a nonrandom, periodic field in which the magnetic and velocity field contain X points but differ in modal structure along one spatial direction. The velocity field is initially solenoidal, with the total initial pressure field consisting of the superposition of the appropriate incompressible pressure distribution upon a flat pressure field corresponding to the initial, average Mach number of the flow. In these numerical simulations, this initial Mach number is varied from 0.2–0.6. These values correspond to average plasma beta values ranging from 30.0 to 3.3, respectively. It is found that compressible effects develop within one or two Alfven transit times, as manifested in the spectra of compressible quantities such as the mass density and the nonsolenoidal flow field. These effects include (1) a retardation of growth...

[1]  D. M. Bushnell,et al.  Numerical computations of turbulence amplification in shock wave interactions , 1984 .

[2]  A. Soward,et al.  Stellar and planetary magnetism , 1983 .

[3]  L. Ting.  Transmission of singularities through a shock wave and the sound generation , 1974 .

[4]  M. Lighthill.  On sound generated aerodynamically I. General theory , 1952, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[5]  Jay P. Boris,et al.  Vorticity Generation by Asymmetric Energy Deposition in a Gaseous Medium. , 1983 .

[6]  W. Matthaeus,et al.  Density Fluctuation Spectra in Magnetohydrodynamic Turbulence a Recurrent but Theoretically Unexplained Observation Has a Poisson Equation for P* Results from Taking the Diver- Gence of (la) and Using (lb): V2(p*/po)----v. [¾-v¾-b' Vb/4r@bulletpo ] (2) , 2022 .

[7]  Jay P. Boris,et al.  Convective Cooling of Lightning Channels , 1981 .

[8]  J. Hawley,et al.  Simulation of magnetohydrodynamic flows: A Constrained transport method , 1988 .

[9]  J. P. Boris,et al.  Vorticity generation by shock propagation through bubbles in a gas , 1988, Journal of Fluid Mechanics.

[10]  Frisch,et al.  Growth of correlations in magnetohydrodynamic turbulence. , 1986, Physical review. A, General physics.

[11]  S. S. Moiseev,et al.  THE INFLUENCE OF COMPRESSIBILITY ON THE SELFSIMILAR SPECTRUM OF SUBSONIC TURBULENCE , 1981 .

[12]  Tetsuya Sato,et al.  Self‐organization process in three‐dimensional compressible magnetohydrodynamics , 1986 .

[13]  W. Matthaeus.  Reconnection in two dimensions: Localization of vorticity and current near magnetic X‐points , 1982 .

[14]  A. Bondeson,et al.  Relaxation toward states of minimum energy in a compact torus , 1982 .

[15]  P. Sulem,et al.  Influence of velocity‐magnetic field correlations on decaying magnetohydrodynamic turbulence with neutral X points , 1988 .

[16]  Roger E. A. Arndt,et al.  Advances in Turbulence , 1988, Lecture Notes in Mechanical Engineering.

[17]  E. Marsch,et al.  Ideal MHD equations in terms of compressive Elsässer variables , 1987 .

[18]  Elaine S. Oran,et al.  A barely implicit correction for flux-corrected transport , 1987 .

[19]  Richard Courant,et al.  Supersonic Flow And Shock Waves , 1948 .

[20]  Dalton D. Schnack,et al.  Dynamical evolution of a solar coronal magnetic field arcade , 1988 .

[21]  R. Dahlburg,et al.  Unstable transition properties of the driven magnetohydrodynamic sheet pinch , 1986, Journal of Fluid Mechanics.

[22]  W. Matthaeus,et al.  Turbulent generation of outward-traveling interplanetary Alfvenic fluctuations , 1983 .

[23]  A. Hasegawa,et al.  Self-organization processes in continuous media , 1985 .

[24]  T. Taylor,et al.  Computational methods for fluid flow , 1982 .

[25]  S. Orszag,et al.  Small-scale structure of two-dimensional magnetohydrodynamic turbulence , 1979, Journal of Fluid Mechanics.

[26]  Louis J. Lanzerotti,et al.  Solar system plasma physics , 1979 .

[27]  J. Picone,et al.  Growth of correlation in compressible two-dimensional magnetofluid turbulence , 1988 .

[28]  R B Dahlburg,et al.  Viscous, resistive magnetohydrodynamic stability computed by spectral techniques. , 1983, Proceedings of the National Academy of Sciences of the United States of America.

[29]  Dissipative, forced turbulence in two-dimensional magnetohydrodynamics , 1977 .

[30]  D. Fyfe,et al.  High-beta turbulence in two-dimensional magnetohydrodynamics , 1975, Journal of Plasma Physics.

[31]  T. A. Zang,et al.  Spectral methods for fluid dynamics , 1987 .

[32]  J. Dahlburg,et al.  Helical magnetohydrodynamic turbulence and the coronal heating problem , 1988 .

[33]  Dalton D. Schnack,et al.  Numerical simulation of Reversed-Field Pinch dynamics , 1986 .

[34]  Turbulent magnetohydrodynamic density fluctuations , 1988 .

[35]  H. S. Ribner,et al.  Spectra of noise and amplified turbulence emanating from shock-turbulence interaction: Two scenarios , 1986 .

[36]  M. Lighthill.  On sound generated aerodynamically II. Turbulence as a source of sound , 1954, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[37]  David Montgomery,et al.  Two-Dimensional Turbulence , 2012 .

[38]  T. Passot,et al.  Numerical simulation of compressible homogeneous flows in the turbulent regime , 1987, Journal of Fluid Mechanics.

[39]  R. Grappin.  Onset and decay of two‐dimensional magnetohydrodynamic turbulence with velocity–magnetic field correlation , 1986 .

[40]  Tetsuya Sato,et al.  Self-organization in three-dimensional compressible magnetohydrodynamic flow , 1988 .

[41]  Phillips,et al.  Minimum dissipation rates in magnetohydrodynamics. , 1988, Physical review. A, General physics.

[42]  W. Matthaeus,et al.  Nonlinear evolution of the sheet pinch , 1981, Journal of Plasma Physics.

[43]  Brian Launder,et al.  Numerical methods in laminar and turbulent flow , 1983 .

[44]  W. Matthaeus,et al.  SELECTIVE DECAY HYPOTHESIS AT HIGH MECHANICAL AND MAGNETIC REYNOLDS NUMBERS * , 1980 .

[45]  C. H. Finan,et al.  Solution of the time-dependent, three-dimensional resistive magnetohydrodynamic equations , 1981 .