On numerical beamforming for correlated dipole type sources

A numerical beamforming method for correlated dipole-type sources in the frequency domain is developed. The typical configuration of the location of acoustic field sources and microphones is considered to analyze the noise generated under an aircraft flying in turbulent flow regimes. Three problems of numerical beamforming are studied, allowing one to take into account a priori information about connections between the components of the dipole function at a point. They differ in the number of real functions to be found: six (no connection), four (components are in phase) and two (the direction of the dipole moment is known). The discretization parameters of source function grids and microphones are estimated to ensure stable matrix inversion in numerical beamforming algorithms. The issues of nonuniqueness of solutions for the tangent components of the dipole function in the first and second problems are identified and discussed; for the third problem such an issue does not arise.