Formulation of the Problem of Sonic Boom by a Maneuvering Aerofoil as a One-Parameter Family of Cauchy Problems

Proceedings Mathematical Sciences

S Baskar²  Phoolan Prasad¹ 

[1] $$;Department of Mathematics, Indian Institute of Science, Bangalore 0 0, India$$

关键词: Sonic boom;    shock propagation;    ray theory;    elliptic equation;    conservation laws;    Cauchy problem.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

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].

【 授权许可】

Unknown