Uniform momentum zone scaling arguments from direct numerical simulation of inertia-dominated channel turbulence

Abstract

Inertia-dominated wall-sheared turbulent flows are composed of an inner and outer layer, where the former is occupied by the well-known autonomous inner cycle while the latter is composed of coherent structures with spatial extent comparable to the flow depth. In arbitrary streamwise–wall-normal planes, outer-layer structures instantaneously manifest as regions of quasi-uniform momentum – relative excesses and deficits about the Reynolds average – and for this reason are termed uniform momentum zones (UMZs). By virtue of this attribute, the interfacial zones between successive UMZs exhibit abrupt wall-normal gradients in streamwise momentum; these interfacial gradients cannot be explained by the notion of attached eddies, for which the vertical gradient goes as $(x_3^+)^{-1}$ in the outer layer, where $x_3^+$ is inner-normalized wall-normal position. Using data from direct numerical simulation (DNS) of channel turbulence across inertial regimes, we recover vertical profiles of Kolmogorov length a posteriori and show that $\eta ^+ \sim (x_3^+)^{1/4}$, thereby requiring that ambient wall-normal gradients in streamwise velocity must scale as $(x_3^+)^{-1/2}$. The data reveal that UMZ interfaces are responsible for these relatively larger wall-normal gradients. The DNS data afford a unique opportunity to interpret inner- and outer-layer structures simultaneously: we propose that UMZs – and the associated outer-layer dynamics – can be explained as the product of inner-layer bluff-body-like interactions, wherein wakes of quasi-uniform momentum emanate from the inner layer; wake-scaling arguments agree with observations from DNS.