Abstract
Numerical simulations are used here to analyze the Rayleigh-Taylor instability in confined and isotropic porous media. The Rayleigh-Taylor instability phenomena arise when a layer of heavy fluid sits on top of a layer of a lighter fluid. Small fluctuations of the interface separating the two fluid layers produce larger structures that eventually drive the flow into a nonlinear convective stage. The flow is initially controlled by diffusion, but rather quickly the action of gravity produces efficient fluid mixing in the entire domain. The single parameter controlling the flow is the Rayleigh number, which is the dimensionless ratio of diffusive to convective timescales. The flow evolution is often parametrized by the mixing length (a suitably defined extension of the mixing region), which, according to Gopalakrishnan et al. [Phys. Rev. Fluids 2, 012501(R) (2017)], has a linear growth. From the analysis of a broad range of simulations spanning three orders of magnitude of the Rayleigh number, we could observe a superlinear asymptotic growth of the mixing length. The present results, which are in line with previous simulations, allow us to evaluate precisely the superlinear evolution coefficient. We further provide simple scaling arguments to justify the observed superlinear growth.
1 More- Received 30 October 2018
DOI:https://doi.org/10.1103/PhysRevFluids.4.023502
©2019 American Physical Society