Three-dimensionality of one- and two-layer electromagnetically driven thin-layer flows

We measure and compare the out-of-plane motion in three experimental configurations for approximating two-dimensional flow with electromagnetically driven thin fluid layers. A prior study found that out-of-plane motion grows suddenly when the Reynolds number Re exceeds a critical value Rec in a two-layer miscible configuration [Kelley and Ouellette, Phys. Fluids 23, 045103 (2011)PHFLE61070-663110.1063/1.3570685]. Here, we confirm that observation; however, we find that a similar onset does not occur in either a single-layer or two-layer immiscible configuration for the ranges Re<520 and Re<740, respectively. Below the critical Reynolds number, the three configurations have out-of-plane motion with similar magnitude. We confirm that two different normalized measures of out-of-plane motion show similar trends among the three configurations as Re varies. Finally, we compute the vertical velocity profiles using an analytical model of each of the three configurations and provide further evidence suggesting the transition observed in the miscible configuration is due to a shear instability. Our results lead to suggestions for future experimentalists: The single-layer and immiscible configurations most closely approximate two-dimensional flow over a wide range of Re, though the miscible configuration minimizes clumping of tracer particles.