Low Mach Number Flow and Acoustics Equations

Abstract

Low Mach number flow theory is a singular asymptotic theory. A typical example is that considered in Sect. 4.7.2 relative to the degeneracy of the unsteady-state Steichen, hyperbolic equation (4.181a), in an elliptical Laplace equation (4.182). As a matter of fact, this degeneracy is a consequence of filtering acoustics waves that are present in (4.181a) but absent in (4.182). In this chapter, we derive, first, the incompressible Euler equations as an outer approximation (see Sect. 6.1) and then, in the case of the external aerodynamics, the linear acoustics equations — as associated inner equations valid near time zero (see the Sect. 6.2.1). In Sect. 6.2.2, we also give some brief information concerning the very interesting case of a slightly compressible inviscid fluid flow in a bounded deformable (in time) container (internal aerodynamics). Finally, in Sect. 6.2.3, the singular nature of the far field is investigated.