Surface-wave Doppler velocimetry in a liquid metal: inferring the bifurcations of the subsurface flow

We introduce a velocimetry technique based on the Doppler-shift of surface waves propagating between an emitter and a receiver. In the limit of scale separation between the wavelength and the scale of the flow, we derive the direct connection between the subsurface flow and the measured phase shift between emitter and receiver. Because of its ease of implementation and high sensitivity, this method is useful to detect small velocities in liquid metal flows, where acoustical and optical methods remain challenging. As an example, we study the Hopf bifurcation of a Kolmogorov flow of Galinstan.