Comparing free surface and interface motion in electromagnetically driven thin-layer flows

Two-dimensional fluid dynamics is often approximated via laboratory experiments that drive a thin layer of fluid electromagnetically. That approximation would be most accurate if both the direction and magnitude of the flow were uniform over the depth of the layer. In practice, boundary conditions require the flow magnitude to drop to zero at the no-slip floor, but put no strong constraint on flow direction. We measure the velocity magnitude and direction simultaneously at the free surface and lower interface of a thin, two-layer vortex flow. We find that the flow direction is almost entirely independent of depth, though its slight misalignment grows as the Reynolds number (Re) increases. Similarly, we find that the ratio of speeds at the free surface and interface nearly matches an analytically derived profile based on idealized assumptions, even for complex flows, but deviates systematically as Re increases. We find that flows with thinner fluid layers are better aligned and more nearly match the predicted speed ratio than flows with thicker layers. Finally, we observe that in time-dependent flows, flow structures at the interface tend to follow flow structures at the free surface via complicated dynamics, moving along similar paths with a short time delay. Our results suggest that the depth-averaged equation of motion recently developed for thin-layer flows [Suri, Phys. Fluids 26, 053601 (2014)PHFLE61070-663110.1063/1.4873417], which relies on flow alignment and idealized profiles and was previously tested for Kolmogorov flows with Re up to 30, is reasonably accurate for vortex flows with Re up to 470.