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 the fluid layer thickness. Using a multicamera 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 ($\mathrm{Re}$) in layers with three different mean thicknesses. Across experiments, we show that deformations and undulations remain small for $\mathrm{Re}\lesssim 400$ but become sizable for $\mathrm{Re}\gtrsim 800$, showcasing a strong (approximately quadratic) dependence on Reynolds number and a weak (sublinear) dependence on fluid layer thickness. Consequently, surface deformations and undulations—measured as percentages of the mean fluid layer thickness—repeatedly approach $\pm 20\%$ and $30\%$, respectively, at the highest Reynolds number ($\mathrm{Re}\approx 1190$) 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.

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• Geophysical fluid dynamics
• Thin fluid films
• Transition to turbulence
• Turbulence
• Waves and free surface flows