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Cylindrical shock wave propagation in a self-gravitating rotational axisymmetric perfect gas under the influence of azimuthal or axial magnetic field and monochromatic radiation with variable density

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Abstract

The propagation of cylindrical shock wave generated by a moving piston in a self-gravitating perfect gas in the presence of axial or azimuthal magnetic field with monochromatic radiation in rotating medium is investigated. The gravitational effect of the gas is taken into consideration. It is considered that the radiation flux moves through electrically conducting self-gravitating perfect gas with variable density and the energy is absorbed only behind the shock which moves in the direction appositive to the radiation flux. The results are discussed by comparing self-gravitating and non-gravitating gas, rotating and non-rotating medium, with or without magnetic field. The effects of variations of Alfven–Mach number, rotational parameter, gravitational parameter, adiabatic exponent and variation of piston velocity index are discussed in detail. The increase in magnetic field strength, adiabatic exponent and gravitational parameter have decaying effect on shock wave. It is shown that the shock wave is stronger with axial magnetic field and weaker with azimuthal magnetic field.

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References

  1. L I Sedov, Similarity and dimensional methods in mechanics (Mir Publishers, Moscow, 1982)

  2. Ya B Zel’dovich and Yu P Raizer, Physics of shock waves and high temperature hydrodynamic phenomena   (Academic Press, New York, 1967) Vol. II

    Google Scholar 

  3. J F Lu and F Yuan, Mon. Not. R. Astron. Soc. 295, 66 (1998)

    Article  ADS  Google Scholar 

  4. K Fukumura and S Tsuruta, Astrophys. J. 611, 964 (2004)

    Article  ADS  Google Scholar 

  5. P Chaturani, Appl. Sci. Res. 23, 197 (1970)

    Article  Google Scholar 

  6. A Sakurai, J. Fluid Mech. 1, 436 (1956)

    Article  ADS  MathSciNet  Google Scholar 

  7. V A Levin and G A Skopina, J. Appl. Mech. Tech. Phys. 45, 457 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  8. J P Vishwakarma, A K Maurya and K K Singh, Geophys. Astrophys. Fluid Dynam. 101, 155 (2007)

    Article  ADS  Google Scholar 

  9. G Nath, Res. Astron. Astrophys. 10, 445 (2010)

    Article  ADS  Google Scholar 

  10. G Nath, Adv. Space Res. 47, 1463 (2011)

    Article  ADS  Google Scholar 

  11. G Nath, Shock Waves 24, 415 (2014)

    Article  ADS  Google Scholar 

  12. G Nath, Acta Astron. 156, 100 (2019)

    Article  Google Scholar 

  13. S Ro and C D Matzner, Astrophys. J. 841, 1 (2017)

    Article  Google Scholar 

  14. L Dessart, E Livne and R Waldman, Mon. Not. R. Astron. Soc. 405, 2113 (2010)

    ADS  Google Scholar 

  15. L D Landau and E M Lifshitz, Fluid mechanics (Pergamon, Oxford, 1959)

    Google Scholar 

  16. L Biermann, Naturwissenschaften 33, 118 (1946)

    Article  ADS  Google Scholar 

  17. L Biermann, Z. Astrophys. 25, 161 (1948)

    ADS  Google Scholar 

  18. G Nath and J P Vishwakarma, Commun. Nonlinear. Sci. Numer. Simulat. 19, 1347 (2014)

    Article  ADS  Google Scholar 

  19. E N Parker, Interplanetary dynamical processes (Interscience, New York, 1963)

    MATH  Google Scholar 

  20. M N Director and E K Dabora, AIAA J. 15, 1315 (1977)

    Article  ADS  Google Scholar 

  21. M H Rogers, J. Mech. Appl. Math. 11, 411 (1958)

    Article  Google Scholar 

  22. E K Dabora, AIAA J. 10, 1384 (1972)

    Article  ADS  Google Scholar 

  23. G Nath and J P Vishwakarma, Acta Astron. 123, 200 (2016)

    Article  Google Scholar 

  24. K P J Reddy, Pramana – J. Phys. 46, 153 (1996)

    Google Scholar 

  25. J S Shang, Prog. Aero. Sci. 21, 1 (2001)

    Article  Google Scholar 

  26. R M Lock and A J Mestel, J. Fluid Mech. 74, 531 (2008)

    Google Scholar 

  27. L Hartmann, Accretion processes in star formation (Cambridge University Press, Cambridge, 1998)

    Google Scholar 

  28. B Balick and A Frank, Annu. Rev. Astron. Astrophys. 40, 439 (2002)

    Article  ADS  Google Scholar 

  29. K S Cho, D E Gary, J Lee, Y J Moon and Y D Park, Astrophys. J. 665, 799 (2007)

    Article  ADS  Google Scholar 

  30. E P Carley et al, Nat. Phys. 9, 811 (2013)

    Article  Google Scholar 

  31. P Zucca, E P Carley, D S Bloomfield and P T Gallagher, A & A 564, A47 (2014)

    Article  ADS  Google Scholar 

  32. C A Maguire, E P Carley, J McCauley and T Gallagher, A&A 633, A56 (2020)

    Article  ADS  Google Scholar 

  33. R C I Fleck, Astrophys. J. 246, L151 (1981)

    Article  ADS  Google Scholar 

  34. J M Scalo and W A Palmer, Astrophys. J. 258, L29 (1982)

    Article  ADS  Google Scholar 

  35. P Goldreich and J Kwan, Astrophys. J. 189, 441 (1974)

    Article  ADS  Google Scholar 

  36. L Spitzer, Diffuse matter in space (Wiley, New York, 1968)

    Google Scholar 

  37. P Padoa and A Nordlund, Astrophys. J.  526, 279 (1999)

    Article  ADS  Google Scholar 

  38. T Sundberg, D Burgess, M Scholer, A Master and A H Sulaiman, Astrophys. Lett. 836, L4 (2017)

    Article  ADS  Google Scholar 

  39. A Ando, T Hagiwara and T Komagome, Plasma Fusion Res. 3, S1018-1–S1018-4 (2008)

  40. R E Marshak, Phys. Fluids 1, 24 (1958)

    Article  ADS  MathSciNet  Google Scholar 

  41. L A Elliott, Proc. Roy. Soc. London A 258, 287 (1960)

    Article  ADS  Google Scholar 

  42. K C Wang, J. Fluid Mech. 20, 447 (1964)

    Article  ADS  MathSciNet  Google Scholar 

  43. J B Helliwell, J. Fluid Mech. 37, 497 (1969)

    Article  ADS  Google Scholar 

  44. J R Nicastro, Phys. Fluids 13, 2000 (1970)

    Article  ADS  Google Scholar 

  45. G Deb-Ray and J B Bhowmick, Ind. J. Pure Appl. Math. 7, 96 (1976)

    Google Scholar 

  46. V M Khudyakov, Sov. Phys. Dokl. (Trans. AIP) 28, 853 (1983)

  47. A N Zheltukhin, J. Appl. Math. Mech. 52, 262 (1988)

    Article  Google Scholar 

  48. O Nath and H S Takhar, Astrophys. Space Sci.  166, 35 (1990)

    Article  ADS  Google Scholar 

  49. O Nath, Astrophys. Space Sci. 155, 163 (1989)

    Article  ADS  Google Scholar 

  50. J P Vishwakarma and V K Pandey, Appl. Math. 2, 28 (2012)

    Google Scholar 

  51. G Nath and P K Sahu, Ain Shams Eng. J. 9, 1151 (2018)

    Article  Google Scholar 

  52. G Nath, Chin. J. Phys. 56, 2741 (2018)

    Article  Google Scholar 

  53. P Carrus, P Fox, F Hass and Z Kopal, Astrophys. J. 113, 496 (1951)

    Article  ADS  MathSciNet  Google Scholar 

  54. M H Rogers, Astrophys. J. 152, 478 (1957)

    Article  ADS  Google Scholar 

  55. A K Turgut, T Aydemir and A Saha, Pramana – J. Phys. 90, 78 (2018)

    Google Scholar 

  56. J K Truelove, R I Klein, C F McKee, J H Holliman, L H Howell, A G Jeffrey and D T Wood, Astrophys. J. 495, 821 (1998)

    Article  ADS  Google Scholar 

  57. G Nath, J P Vishwakarma, V K Srivastava and A K Sinha, J. Theor. Appl. Phys. 7, 15 (2013), https://doi.org/10.1186/2251-7235-7-15

  58. G Nath, R P Pathak and M Dutta, Acta Astron. 142, 152 (2018)

    Article  Google Scholar 

  59. G Nath and S Singh, Int. J. Nonlin. Mech. 88, 102 (2017)

    Article  Google Scholar 

  60. G Nath, J. Astrophys. Astron. 41, 21 (2020), https://doi.org/10.1007/s12036-020-09638-7

  61. K Fujisawa, H Okawa, Yu Yamamoto and S Yamada, Ap. J. 872, 155 (2019)

    Article  ADS  Google Scholar 

  62. V A Levin, I S Manuylovich and V V Markov, Proc. Steklov Inst. Math. 300, 126 (2018)

    Article  MathSciNet  Google Scholar 

  63. G Nath, Acta Astron. 182, 599 (2021)

    Article  Google Scholar 

  64. G Nath, Z. Naturforsch. A 76(3), 265 (2021)

  65. P Gupta, R K Chaturvedi and L P Singh, Eur. Phys. Plus 135, 17 (2020)

    Article  Google Scholar 

  66. J Ridoux, N Lardjane, L Monasse and F Coulouvrat, Shock Wave 30, 503 (2020)

    Article  Google Scholar 

  67. D Summers, Astron. Astophys. 45, 151(1975)

    ADS  Google Scholar 

  68. P Rosenau, Phys. Fluids 20, 1097 (1977)

    Article  ADS  Google Scholar 

  69. P Rosenau and S Frankenthal, Phys. Fluids 19, 1889 (1976)

    Article  ADS  Google Scholar 

  70. G Nath and J P Vishwakarma, Acta Astron. 128, 377 (2016)

    Article  Google Scholar 

  71. S I Popel and A A Gisko, Nonlinear Process Geophys. 13, 223 (2006)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

The author is thankful to Dr J P Vishwakarma, Professor and former Head, Department of Mathematics and Statistics, DDU Gorakhpur University, Gorakhpur, India for technical discussion during the revision of the manuscript. The author is also thankful to the anonymous reviewers for valuable comments to improve the manuscript.

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  1. Department of Mathematics, Motilal Nehru National Institute of Technology, Allahabad,  211 004, India

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Nath, G. Cylindrical shock wave propagation in a self-gravitating rotational axisymmetric perfect gas under the influence of azimuthal or axial magnetic field and monochromatic radiation with variable density. Pramana - J Phys 95, 149 (2021). https://doi.org/10.1007/s12043-021-02160-7

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