Kolmogorov scales in a driven cavity flow

Abstract

Turbulent flow in a three-dimensional driven cavity has been simulated directly by solving the Navier–Stokes equations. The results at Re=3200 and 10 000 compare well with the experimental data. Viscous dissipation rate has been calculated without making the assumption of isotropy. Near the top moving wall, the instantaneous dissipation rate is very high and also has high amplitude. Its frequency increases but amplitude decreases as one moves away from the wall and it becomes intermittent in the vortex core. The high Reynolds number assumption that dissipation is mainly due to the fluctuating velocity components is seen to be true in the present case except near the wall. The Kolmogorov length scale attains higher values in the core of the primary vortex due to low dissipation rate there. A value of 0.01 times the size of the cubic cavity is a good representative value at Re=10 000. Even though the present (84×84×84) grid cannot resolve this scale very well, it can resolve all the scales dynamically significant in the flow as seen from the velocity and dissipation spectra.