Ultrasound scattering by a vortical flow

We report a theoretical and experimental study of the scattering of an ultrasonic wave by a vortical flow. The flow consists of a completely filled cylinder driven by the constant rotation of the two end walls. The angular momentum generated by the disk rotation is concentrated in a strong axial vortex. The scattering of an incident ultrasonic wave allow us to obtain information about the flow. The frequency of the incident wave is assumed to be high in comparison with typical frequencies of the flow. An integro-differential equation is obtained from the full Navier–Stokes equations describing the interaction of the flow and the ultrasonic wave. Using the Born approximation we obtain a wave equation with source which can be numerically integrated or, in some particular cases, be analytically solved. We numerically identify the regions of the vortical flow that contribute most to the scattered wave. The dependence of the scattered pressure on the scattering angle is also studied. Finally, we compare the numerical results with experimental data.