• Formulation of the problem of sonic boom by a maneuvering aerofoil as a one-parameter family of Cauchy problems

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      https://www.ias.ac.in/article/fulltext/pmsc/116/01/0097-0119

    • Keywords

       

      Sonic boom; shock propagation; ray theory; elliptic equation; conservation laws; Cauchy problem

    • Abstract

       

      For the structure of a sonic boom produced by a simple aerofoil at a large distance from its source we take a physical model which consists of a leading shock (LS), a trailing shock (TS) and a one-parameter family of nonlinear wavefronts in between the two shocks. Then we develop a mathematical model and show that according to this model the LS is governed by a hyperbolic system of equations in conservation form and the system of equations governing the TS has a pair of complex eigenvalues. Similarly, we show that a nonlinear wavefront originating from a point on the front part of the aerofoil is governed by a hyperbolic system of conservation laws and that originating from a point on the rear part is governed by a system of conservation laws, which is elliptic. Consequently, we expect the geometry of the TS to be kink-free and topologically different from the geometry of the LS. In the last section we point out an evidence of kinks on the LS and kink-free TS from the numerical solution of the Euler’s equations by Inoue, Sakai and Nishida [5].

    • Author Affiliations

       

      S Baskar1 Phoolan Prasad1

      1. Department of Mathematics, Indian Institute of Science, Bangalore - 560 012, India
    • Dates

       
  • Proceedings – Mathematical Sciences | News

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