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

Baskar, S. ; Prasad, Phoolan (2006) Formulation of the problem of sonic boom by a maneuvering aerofoil as a one-parameter family of Cauchy problems Proceedings of the Indian Academy of Sciences - Mathematical Sciences, 116 (1). pp. 97-119. ISSN 0253-4142

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Official URL: http://ns1.ias.ac.in/mathsci/vol116/feb2006/PM2526...

Related URL: http://dx.doi.org/10.1007/BF02829742

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.

Item Type:Article
Source:Copyright of this article belongs to Indian Academy of Sciences.
Keywords:Sonic Boom; Shock Propagation; Ray Theory; Elliptic Equation; Conservation Laws; Cauchy Problem
ID Code:37552
Deposited On:25 Apr 2011 10:20
Last Modified:17 May 2016 20:27

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