Very Large Anisotropic Scales in Turbulent Wall-Bounded Flows

Abstract

It has long been realized that turbulent flows contain a wide range of scales, from small viscous ones responsible for the viscous dissipation, to large ones which carry the turbulent energy and the Reynolds stresses. The former are believed to be roughly universal among different flows, while the latter vary with the geometry and with the flow conditions. Evidence has accumulated for some time that in an intermediate layer of wall-bounded shear flows, including the logarithmic region and part of the outer layer, these large scales are very anisotropic and very large, with streamwise lengths that may be of the order of 100 times their distance to the wall [2,4,8]. At their longest, somewhat above the top of the logarithmic layer, this amounts to 20–30 times the boundary layer thickness. The earliest detailed study of these structures was done by Perry [9,10], who identified them as an E _uu ~ k ^-1, long-wavelength, spectral range. Since the turbulent energy is proportional to ∫ k E _uu d (log k), a k ^-1 spectral range essentially contains most of the fluctuating energy in the flow (see figure 1). Moreover, because the size of these structures requires either very large computational boxes or very long experiments, relatively little was known about them until recently. There is for example very little information on their spanwise dimensions, or on the relation of the different velocity components. The goal of the simulations discussed here is to study the large anisotropic scales in turbulent channels, their origin and structure, and their possible influence on other flow properties.