Mixing Analysis in a Lid-Driven Cavity Flow at Finite Reynolds Numbers

Abstract

The influence of inertial effects on chaotic advection and mixing is investigated for a two-dimensional, time-dependent lid-driven cavity flow. Previous work shows that this flow exhibits exponential stretching and folding of material lines due to the presence of figure-eight stirring patterns in the creeping flow regime. The high sensitivity to initial conditions and the exponential growth of errors in chaotic flows necessitate an accurate solution of the flow in order to calculate metrics based on Lagrangian particle tracking. The streamfunction-vorticity formulation of the Navier-Stokes equations is solved using a Fourier-Chebyshev spectral method, providing the necessary exponential convergence and machine-precision accuracy. Poincaré sections and mixing measures are used to analyze chaotic advection and quantify the mixing efficiency. The calculated mixing characteristics are almost identical for Re ≤ 1. For the time range investigated, the best mixing in this system is observed for Re = 10. Interestingly, increasing the Reynolds number to the range 10 < Re ≤ 100 results in an observed decrease in mixing efficacy.