Coherent interferometric imaging in a random flow

Etienne Gay, Josselin Garnier, Eric Savin

Abstract:

This paper is concerned with the development of imaging methods to localize sources
or reflectors in inhomogeneous moving media with acoustic waves that have travelled
through them. A typical example is the localization of broadband acoustic sources in a
turbulent jet flow for aeroacoustic applications. The proposed algorithms are extensions of
Kirchhoff migration (KM) and coherent interferometry (CINT) which have been considered
for smooth and randomly inhomogeneous quiescent media so far. They are constructed
starting from the linearized Euler equations for the acoustic perturbations about a sta-
tionary ambient flow. A model problem for the propagation of acoustic waves generated
by a fixed point source in an ambient flow with constant velocity is addressed. Based on
this result imaging functions are proposed to modify the existing KM and CINT functions
to account for the ambient flow velocity. They are subsequently tested and compared by
numerical simulations in various configurations, including a synthetic turbulent jet repre-
sentative of the main features encountered in actual jet flows.