Interaction of a thin shock with turbulence. I. Effect on shock structure: Analytic model

Physics of Fluids

Volumn 20, Issue 12, 2008, Pages

  Ao, Xianzhi ^a,b   Zank, Gary P ^a,b   Pogorelov, Nikolai V ^a,b   Shaikh, Dastgeer ^a,b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UNIVERSITY OF ALABAMA IN HUNTSVILLE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

MAGNETOHYDRODYNAMICS; NUMERICAL MODELS; SHOCK WAVES; TURBULENCE;

ANALYTIC MODELING; BURGERS' EQUATIONS; HUGONIOT STATE; MAGNETIC FIELD PERTURBATIONS; NONLINEAR STEEPENING; PERTURBATION ANALYSIS; PHYSICAL QUANTITIES; SHOCK STRUCTURE;

WAVE PLASMA INTERACTIONS;

EID: 58249088922     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.3041706     Document Type: Article

References (41)

1. F. K. Moore, "Unsteady oblique interaction of a shock wave with a plane disturbance," NACA Report No. 1165, 1954.
2. H. S. Ribner, "Convection of a pattern of vorticity through a shock wave," NACA Report No. 1164, 1954.
3. J. E. Ffowcs Williams and M. S. Howe, "On the possibility of turbulent thickening of weak shock waves," J. Fluid Mech. JFLSA70022-112010.1017/S0022112073002272 58, 461 (1973).
4. H. S. Ribner, "Spectra of noise and amplified turbulence emanating from shock-turbulence interaction," AIAA J.AIAJAH0001-145210.2514/ 3.9642 25, 436 (1987).
5. T. E. Giddings, Z. Rusak, and J. Fish, "A transonic small-disturbance model for the propagation of weak shock waves in heterogeneous gases," J. Fluid Mech. JFLSA70022-112010.1017/ S0022112000002779 429, 255 (2001).
6. S. C. Crow, "Distortion of sonic bangs by atmosphere turbulence," J. Fluid Mech. JFLSA70022-112010.1017/ S0022112069000711 37, 529 (1969).
7. K. J. Plotkin and A. R. George, "Propagation of weak shock waves through turbulence," J. Fluid Mech. JFLSA70022-112010.1017/ S0022112072000795 54, 449 (1972).
8. H. S. Ribner, "Shock-turbulence interaction and the generation of noise," NACA Report No. 1233, 1955.
9. H. S. Ribner, "Acoustic energy flux from shock-turbulence interaction," J. Fluid Mech. JFLSA70022-112010.1017/ S0022112069001121 35, 299 (1969).
10. A. R. George and K. J. Plotkin, "Propagation of sonic booms and other weak nonlinear waves through turbulence," Phys. Fluids PFLDAS0031-917110.1063/1.1693471 14, 548 (1971).
11. A. D. Pierce and D. J. Maglieri, "Effects of atmospheric irregularities on sonic-boom propagation," J. Acoust. Soc. Am.JASMAN0001-496610.1121/1.1912904 51, 702 (1972).
12. S. Lee, S. K. Lele, and P. Moin, "Direct numerical simulation of isotropic turbulence interacting with a weak shock wave," J. Fluid Mech. JFLSA70022-112010.1017/S0022112093003519 251, 533 (1993).
13. Z. Rusak, T. E. Giddings, and J. D. Cole, "Interaction of a weak shock with free stream disturbances," AIAA J. AIAJAH0001-145210.2514/3.12517 33, 977 (1995).
14. J. F. McKenzie and K. O. Westphal, "Interaction of linear waves with oblique shock waves," Phys. Fluids PFLDAS0031-917110.1063/ 1.1691825 11, 2350 (1968).
15. G. P. Zank, I. Kryukov, D. Shaikh, S. Borovikov, X. Ao, and N. V. Pogorelov, "The interaction of turbulence with gas dynamic shocks," AIP Conf. Proc. APCPCS0094-243X10.1063/1.2778970 932, 233 (2007).
16. G. P. Zank, Y. Zhou, W. Matthaeus, and W. Rice, "The interaction of turbulence with shock waves: A basic model," Phys. FluidsPHFLE61070-663110.1063/1.1507772 14, 3766 (2002).
17. X. Ao and G. P. Zank, "Interaction of turbulence with shock waves: mean-field theory and a weak-linearization analysis," AIP Conf. Proc. APCPCS0094-243X10.1063/1.2778963 932, 191 (2007).
18. X. Ao, G. P. Zank, N. V. Pogorelov, and D. Shaikh, "Application of perturbation method in investigating the interaction of thin shock with turbulence," AIP Conf. Proc.APCPCS0094-243X10.1063/1.2359345 858, 321 (2006).
19. G. P. Zank, "Interaction of the solar wind with the local interstellar medium: A theoretical perspective," Space Sci. Rev. SPSRA40038-630810.1023/A:1005155601277 89, 413 (1999).
20. T. R. Story and G. P. Zank, "The response of a gasdynamic interplanetary disturbances," J. Geophys. Res. JGREA20148-022710.1029/94JA03359 100, 9489, DOI: 10.1029/94JA03359 (1995).
21. V. Florinski and G. P. Zank, "Dynamical evolution of the termination shock: Consequences for charged particle acceleration," AIP Conf. Proc.APCPCS0094-243X10.1063/1.2359321 858, 159 (2006).
22. G. P. Zank, D. Shaikh, and X. Ao, "The interaction of turbulence with the heliospheric termination shock," AIP Conf. Proc.APCPCS0094-243X10.1063/1.2359343 858, 308 (2006).
23. L. F. Burlaga, N. F. Ness, and M. H. Acuña, "Magnetic fields in the heliosheath: Voyager 1 observations," Astrophys. J. ASJOAB0004-637X10.1086/500826 642, 584 (2006).
24. T. Taniuti and C. Wei, "Reductive perturbation method in nonlinear wave propagation," J. Phys. Soc. Jpn.JUPSAU0031-9015 24, 94 (1968).
25. C. H. Su and C. S. Gardner, "Korteweg-de Vries equation and generalizations. III: Derivation of the Korteweg-de Vries equation and Burgers equation," J. Math. Phys.JMAPAQ0022-248810.1063/1.1664873 10, 536 (1969).
26. C. L. Frenzen and J. Kevorkian, "A review of the multiple scale and reductive perturbation methods for deriving uncoupled nonlinear evolution equations," Wave MotionWAMOD90165-212510.1016/ 0165-2125(85)90025-3 7, 25 (1985).
27. G. P. Zank and G. M. Webb, "Weakly multi-dimensional cosmic-ray-modified MHD shocks," J. Plasma Phys.JPLPBZ0022-3778 44, 91 (1990).
28. J. D. Cole, "Modern developments in transonic flow," J. Appl. Math.ZZZZZZ1110-757X 29, 763 (1975).
29. G. P. Zank, W. H. Matthaeus, J. W. Bieber, and H. Moraal, "The radial and latitudinal dependence of the cosmic ray diffusion tensor in the heliosphere," J. Geophys. Res. JGREA20148-022710.1029/97JA03013 103, 2085, DOI: 10.1029/97JA03013 (1998).
30. R. Courant, E. Isaacson, and M. Rees, "On the solution of nonlinear hyperbolic differential equations by finite differences," Commun. Pure Appl. Math.CPMAMV0010-364010.1002/cpa.3160050303 5, 243 (1952).
31. S. K. Godunov, "A finite difference method for the computation of discontinuous solutions of the equations of fluid dynamics," Mat. Sb.MATSAB0368-8666 47, 271 (1959).
32. P. D. Lax and B. Wendroff, "Difference schemes for hyperbolic equations with high order of accuracy," Commun. Pure Appl. Math. CPMAMV0010-364010.1002/cpa.3160170311 17, 381 (1964).
33. A. S. Kholodov, "On construction of difference schemes with positive approximation for hyperbolic equations," Comput. Math. Math. Phys. ZZZZZZ0965-5425 18, 1476 (1978).
34. A. G. Kulikovskii, N. V. Pogorelov, and A. Y. Semenov, Mathematical Aspects of Numerical Solution of Hyperbolic Systems (Chapman and Hall, London/CRC, Boca Raton, 2001), Vol. 118.
35. P. L. Roe, "Approximate Riemann problem solver, parameter vectors and difference scheme," J. Comput. Phys. JCTPAH0021-999110.1016/ 0021-9991(81)90128-5 43, 357 (1981).
36. T. Hanawa, Y. Nakajima, and K. Kobuta, "Extensions of Roe's approximate Riemann solver for general equation of state and magnetohydrodynamics," Nagoya University Preprint No. DPNU 94-34 (1994).
37. N. V. Pogorelov and A. Y. Semenov, "A family of approximate solutions to the MHD Riemann problem retaining the shock relations," Comput. Math. Math. Phys. ZZZZZZ0965-5425 37, 320 (1997).
38. G. Webb, G. Zank, and J. McKenzie, "Relativistic oblique magnetohydrodynamic shocks," J. Plasma Phys.JPLPBZ0022-3778 37, 117 (1987).
39. C. Kennel, R. Blandford, and C. Wu, "Structure and evolution of small-amplitude intermediate shock waves," Phys. Fluids B PFBPEI0899-822110.1063/1.859235 2, 253 (1990).
40. G. B. Whitham, Linear and Nonlinear Waves (Wiley, New York, 1974).
41. G. P. Zank, G. M. Webb, and J. F. McKenzie, "Modified non-linear Burgers equations and cosmic-ray shocks," Astron. Astrophys.AAEJAF0004-6361 189, 338 (1988).