Structure function tensor scaling in the logarithmic region derived from the attached eddy model of wall-bounded turbulent flows

Abstract

We investigate the scaling of the velocity structure function tensor Dij(r,z) in high Reynolds number wall-bounded turbulent flows, within the framework provided by the Townsend attached eddy hypothesis. Here i,j=1,2,3 denote velocity components in the three Cartesian directions, and r is a general spatial displacement vector. We consider spatial homogeneous conditions in wall-parallel planes and dependence on wall-normal distance is denoted by z. At small scales (r=|r|z) where turbulence approaches local isotropy, Dij(r,z) can be fully characterized as a function of r and the height-dependent dissipation rate ϵ(z), using the classical Kolmogorov scalings. At larger distances in the logarith..