Fine Scale Structure of High Reynolds Number Taylor-Couette Flow

Abstract

Direct numerical simulation (DNS) has been conducted to investigate turbulence transition process and fine scale structures in Taylor-Couette flow. Fourier-Chebyshev spectral methods have been used for spatial discretization and DNS are conducted up to Re = 12000. With the increase of Reynolds number, fine scale eddies are formed in a stepwise fashion. In relatively weak turbulent Taylor-Couette flow, fine scale eddies elongated in the azimuthal direction appear near the outflow and inflow boundaries between Taylor vortices. These fine scale eddies in the outflow and inflow boundaries are inclined at about −45/135 degree with respect to the azimuthal direction. With the increase of Reynolds number, the number of fine scale eddies increases and fine scale eddies appear in whole flow fields. The Taylor vortices in high Reynolds number organize lots of fine scale eddies. In high Reynolds number Taylor-Couette flow, fine scale eddies parallel to the axial direction are formed in sweep regions between large scale Taylor vortices. The most expected diameter and maximum azimuthal velocity of coherent fine scale eddies are 8 times of Kolmogorov scale and 1.7 times of Kolmogorov velocity respectively for high Reynolds Taylor-Couette flow. This scaling law coincides with that in other turbulent flow fields.