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

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

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Abstract

For the structure of a sonic boom produced by a simple aerofoil at it 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 oil the LS and kink-free TS from the numerical solution of the Euler's equations by Inoue, Sakai and Nishida [5].

Item Type:	Journal Article
Publication:	Proceedings Of The Indian Academy Of Sciences-Mathematical Sciences
Publisher:	Indian Academy Sciences
Additional Information:	Copyright of this article belongs to Indian Academy Sciences.
Keywords:	Sonic boom;shock propagation;ray theory;elliptic equation; conservation laws;Cauchy problem.
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	24 Mar 2009 06:52
Last Modified:	19 Sep 2010 04:56
URI:	http://eprints.iisc.ac.in/id/eprint/17245

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