Free-Surface Deformations in Shallow Electrolyte Flows

We present an experimental investigation of free-surface deformations and undulations in horizontally driven shallow flows within electrolyte layers—commonly employed laboratory analogs for quasi-two-dimensional flows and oceanic circulations. We characterize deformations as deviations of the free-surface height relative to its mean level and undulations as spatial variations in fluid layer thickness. Using a multi-camera imaging setup, we simultaneously track the spatiotemporal evolution of the electrolyte-air interface and the horizontal velocity fields at this free surface across a wide range of Reynolds numbers (Re) in layers with three different mean thicknesses. Across experiments with different mean thicknesses, deformations and undulations remain small for Re ≲ 400, but become sizable for Re ≳ 800, showcasing a strong (approximately quadratic) dependence on Reynolds number and a weak (sub-linear) dependence on fluid layer thickness. Consequently, surface deformations and undulations–measured as percentages of the mean fluid layer thickness–repeatedly approach ±20% and 30%, respectively, at the highest Reynolds number (Re ≈ 1360) in the shallowest (3 mm thick) layer realized in our experiments. These findings suggest that, similar to observations in soap film experiments, deviations from quasi-two-dimensionality in shallow electrolyte flows must be evaluated also in terms of free-surface deformations and thickness variations—an important refinement to current understanding.