Velocity profile in a two-layer Kolmogorov-like flow

Balachandra Suri, Jeffrey Tithof, Radford Mitchell, Roman O. Grigoriev, Michael F. Schatz

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29 Scopus citations


In this article, we discuss flows in shallow, stratified horizontal layers of two immiscible fluids. The top layer is an electrolyte which is electromagnetically driven and the bottom layer is a dielectric fluid. Using a quasi-two-dimensional approximation, which assumes a horizontal flow whose direction is independent of the vertical coordinate, we derive a generalized two-dimensional vorticity equation describing the evolution of the horizontal flow. Also, we derive an expression for the vertical profile of the horizontal velocity field. Measuring the horizontal velocity fields at the electrolyte-air and electrolyte-dielectric interfaces using particle image velocimetry, we validate the theoretical predictions of the horizontal velocity and its vertical profile for steady as well as for freely decaying Kolmogorov-like flows. Our analysis shows that by increasing the viscosity of the electrolyte relative to that of the dielectric, one may significantly improve the uniformity of the flow in the electrolyte, yielding excellent agreement between the analytical predictions and the experimental measurements.

Original languageEnglish (US)
Article number053601
JournalPhysics of Fluids
Issue number5
StatePublished - May 2 2014
Externally publishedYes


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