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Experimental assessment of mixing layer scaling laws in Rayleigh-Taylor instability

Marco De Paoli1,2,*, Diego Perissutti3, Cristian Marchioli3, and Alfredo Soldati1,3

  • 1Institute of Fluid Mechanics and Heat Transfer, TU Wien, 1060 Vienna, Austria
  • 2Physics of Fluids Group, University of Twente, 7500AE Enschede, The Netherlands
  • 3Polytechnic Department, University of Udine, 33100 Udine, Italy

  • *Corresponding author: marco.de.paoli@tuwien.ac.at
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Phys. Rev. Fluids 7, 093503 – Published 30 September, 2022

DOI: https://doi.org/10.1103/PhysRevFluids.7.093503

Abstract

We assess experimentally the scaling laws that characterize the mixing region produced by the Rayleigh-Taylor instability in a confined porous medium. In particular, we wish to assess experimentally the existence of a superlinear scaling for the growth of the mixing region, which was observed in recent two-dimensional simulations. To this purpose, we use a Hele-Shaw cell. The flow configuration consists of a heavy fluid layer overlying a lighter fluid layer, initially separated by a horizontal, flat interface. When small perturbations of concentration and velocity fields occur at the interface, convective mixing is eventually produced: Perturbations grow and evolve into large finger-like convective structures that control the transition from the initial diffusion-dominated phase of the flow to the subsequent convection-dominated phase. As the flow evolves, diffusion acts to reduce local concentration gradients across the interface of the fingers. When the gradients become sufficiently small, the system attains a stablystratified state and diffusion is again the dominant mixing mechanisms. We employ an optical method to obtain high-resolution measurements of the density fields, and we perform experiments for values of the Rayleigh-Darcy number (i.e., the ratio between convection and diffusion) sufficiently large to exhibit all the flow phases just described, which we characterize via the mixing length, a measure of the extension of the mixing region. We are able to confirm that the growth of the mixing length during the convection-dominated phase follows the superlinear scaling predicted by previous simulations.

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Phys. Rev. Fluids 7, 093503– Published 30 September, 2022
  • Received 28 June 2022
  • Accepted 15 September 2022
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