Direct measurement of the stream-function in a quasi-two-dimensional liquid metal flow

Abstract

Flows of electrically conducting fluids become quasi-two-dimensional (2D) under the influence of a homogeneous magnetic field. In this regime the electrical potential induced in the flow is directly proportional to the 2D stream function. We utilize this property in order to perform simultaneous multi-channel measurements of the stream function in an electromagnetically driven annular liquid metal flow in the weakly nonlinear regime. Spatio-temporal maps of the stream functions of a quasi-periodic unstable flow are observed and used as a basis for a systematic decomposition of the flow into spatial modes belonging to different frequencies. The approach can be generalized to flows with complex time-dependence.