Velocity Profile in a Two-Layer Kolmogorov-Like Flow

Abstract

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, we derive the depth-averaged two-dimensional (2D) vorticity equation which includes a prefactor to the advection term, previously unaccounted for. In addition, we study how the horizontal components of velocity vary in the vertical direction. For a Kolmogorov-like flow, we evaluate analytical expressions for the coefficients in the generalized 2D vorticity equation, uncovering their dependence on experimental parameters. To test the accuracy of these estimates, we experimentally measure the horizontal velocity fields at the free-surface and at the electrolyte-dielectric interface using particle image velocimetry (PIV). We show that there is excellent agreement between the analytical predictions and the experimental measurements. 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 along the vertical direction.

18 pages, 5 figures

Cited by in corpus (16)

• Using Noisy or Incomplete Data to Discover Models of Spatiotemporal Dynamics
• Robust learning from noisy, incomplete, high-dimensional experimental data via physically constrained symbolic regression
• Universal continuous transition to turbulence in a planar shear flow
• Analysis of Kolmogorov Flow and Rayleigh-Bénard Convection using Persistent Homology
• Forecasting Fluid Flows Using the Geometry of Turbulence
• Spatiotemporal dynamics in 2D Kolmogorov flow over large domains
• Capturing Turbulent Dynamics and Statistics in Experiments with Unstable Periodic Orbits
• Bifurcations in a Quasi-Two-Dimensional Kolmogorov-Like Flow
• Data-driven discovery of partial differential equation models with latent variables
• Closed-loop adaptive control of extreme events in a turbulent flow
• Unstable Equilibria and Invariant Manifolds in Quasi-Two-Dimensional Kolmogorov-like Flow
• Heteroclinic and Homoclinic Connections in a Kolmogorov-Like Flow
• Instability of a dusty Kolmogorov flow
• Kolmogorov flow: Linear Stability and Energy Transfers in a minimal low-dimensional model
• Predicting the Critical Number of Layers for Hierarchical Support Vector Regression
• Model for transitional turbulence in a planar shear flow