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Uniform momentum zone scaling arguments from direct numerical simulation of inertia-dominated channel turbulence. (English) Zbl 1460.76528
Summary: 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.

##### MSC:
 76F65 Direct numerical and large eddy simulation of turbulence 76F40 Turbulent boundary layers 76F25 Turbulent transport, mixing
##### Keywords:
turbulent mixing; turbulence theory
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##### References:
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