Dynamic Similarity and Instability in Porous Flows

Abstract:

Kelvin-Helmholtz type instabilities are often observed in coupled viscous flows through and over permeable media. The onset of instability is generally attributed to an inflection point in the mean velocity profile, as stated by Rayleigh's theorem for inviscid flows. Additionally, turbulent flows over porous media exhibit dynamic similarity across systems and scales, as evidenced by recent finding of empirical universal scaling laws correlating relevant length and velocity scales. In this work, we analytically derive a universal scaling law for the turbulence intensity, which is in agreement with experimental findings. Also, through an instability analysis, we identify key parameters that render the flow through the permeable layer unstable and show that no strict causality exists between inflection points in the mean velocity profile and flow instability. Instead, we show that a complex interplay between instability, inflection points and flow self-similarity exists.