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Growth and decay of weak shock waves in magnetogasdynamics

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Abstract

The purpose of the present study is to investigate the problem of the propagation of weak shock waves in an inviscid, electrically conducting fluid under the influence of a magnetic field. The analysis assumes the following two cases: (1) a planar flow with a uniform transverse magnetic field and (2) cylindrically symmetric flow with a uniform axial or varying azimuthal magnetic field. A system of two coupled nonlinear transport equations, governing the strength of a shock wave and the first-order discontinuity induced behind it, are derived that admit a solution that agrees with the classical decay laws for a weak shock. An analytic expression for the determination of the shock formation distance is obtained. How the magnetic field strength, whether axial or azimuthal, influences the shock formation is also assessed.

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Acknowledgments

The second and third authors, respectively, acknowledge the financial support from the CSIR and UGC, India, under the SRF scheme.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Indian Institute of Technology, Banaras Hindu University, Varanasi, 221005, India

    L. P. Singh, D. B. Singh & S. D. Ram

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  1. L. P. Singh
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  2. D. B. Singh
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  3. S. D. Ram
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Correspondence to D. B. Singh.

Additional information

Communicated by A. Merlen and A. Higgins.

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Singh, L.P., Singh, D.B. & Ram, S.D. Growth and decay of weak shock waves in magnetogasdynamics. Shock Waves 26, 709–716 (2016). https://doi.org/10.1007/s00193-015-0607-y

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  • DOI: https://doi.org/10.1007/s00193-015-0607-y

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