A.O.Borisyuk The Green's functions of wave equation and the Helmholtz equation for an infinite straight rigid channel of circular cross-section with a mean flow

Acoustic bulletin, Vol. 14 № 4, (2011) p. 9-17

The Green's functions of three-dimensional wave and Helmholtz equations for an infinite straight rigid-walled channel of circular cross-section with a mean flow are constructed. These functions are written in terms of the corresponding series of the channel acoustic modes. They are periodic in azimuthal coordinate and symmetric about the axial section of the point source location. In the Green's function of the wave equation, each term of the series is a sum of the direct and reverse waves propagating on the corresponding channel mode downstream and upstream of the source. In the obtained Green's functions, the mean flow effects are directly reflected, that become more significant as the flow Mach number increases., In particular, this leads to occurrence and further growth of the functions' asymmetry about the cross-section of the source location. In the case of absence ща mean flow, the obtained Green's functions are symmetric about source cross-section and coincide with known Green's functions for the considered channel.

KEY WORDS: flow in the channel, average characteristics, the Mach number, the Green's function, source

TEXT LANGUAGE: Ukrainian