Shared dynamical features of smooth- and rough-wall boundary-layer turbulence

Abstract

The structure of smooth-and rough-wall turbulent boundary layers is investigated using existing data and newly acquired measurements derived from a four element spanwise vorticity sensor. Scaling behaviours and structural features are interpreted using the mean momentum equation based framework described for smooth-wall flows by Klewicki (J. Fluid Mech., vol. 718, 2013, pp. 596-621), and its extension to rough-wall flows by Mehdi et al. (J. Fluid Mech., vol. 731, 2013, pp. 682-712). This framework holds potential relative to identifying and characterizing universal attributes shared by smooth-and rough-wall flows. As prescribed by the theory, the present analyses show that a number of statistical features evidence invariance when normalized using the characteristic length associated with the wall-normal transition to inertial leading-order mean dynamics. On the inertial domain, the spatial size of the advective transport contributions to the mean momentum balance attain approximate proportionality with this length over significant ranges of roughness and Reynolds number. The present results support the hypothesis of Mehdi et al., that outer-layer similarity is, in general, only approximately satisfied in rough-wall flows. This is because roughness almost invariably leaves some imprint on the vorticity field; stemming from the process by which roughness influences (generally augments) the near-wall three-dimensionalization of the vorticity field. The present results further indicate that the violation of outer similarity over regularly spaced spanwise oriented bar roughness correlates with the absence of scale separation between the motions associated with the wall-normal velocity and spanwise vorticity on the inertial domain.

The Atmospheric Boundary Layer Over Urban-Like Terrain: Influence of the Plan Density on Roughness Sublayer Dynamics

“…Addressing this question therefore calls for new experiments performed at high Reynolds number δ + with similar δ/h ratio in the range 10 to 20, which are representative of typical flow over urban terrain, as in the present study or in Cheng and Castro (2002) and Placidi and Ganapathisubramani (2017). This question of the relative importance of the viscous scale ν/u τ , roughness length z 0 (or the equivalent sand-grain roughness k s ) and outer scale δ on the structure of the near-wall region for rough-wall boundary layers has recently been investigated by Mehdi et al (2013), with experimental support by Ebner et al (2016) and Squire et al (2016). These authors focussed their analysis on the combined influence of the wall roughness and the Reynolds number on the wall-normal onset z I of the region where "the leading order mean dynamics becomes described by a balance between the mean and turbulent inertia" and where Townsend's attached eddy phenomenology should apply (i.e where the wall-normal profiles of the mean and the variance of the streamwise velocity component follow a logarithmic law).…”

“…Therefore, they introduced a modified form of the scaling using the mean streamwise velocity component deficit (or roughness parameter) ∆U + normalized by U e that enables all the data, from smooth or rough walls, to be fitted empirically. There is still no clear physical foundation for the linear relationship between the streamwise turbulence intensity and the mean streamwise velocity component (Castro et al, 2015), but this peculiar behaviour is tied to the structure of the flow in the outer-layer region (Castro et al, 2015;Ebner et al, 2016). Therefore, the agreement with the diagnostic plot must be viewed rather as a necessary condition than a sufficient one to validate the characteristics of the flow.…”

Smooth- and rough-wall boundary layer structure from high spatial range particle image velocimetry

“…Hong et al [41] note, however, that for randomly distributed and/or closely packed rough surfaces, the characteristics and interaction frequency of the roughness-induced vortices may differ from their case of a regular roughness, resulting in less obvious, or nonexistent, outer layer roughness-scale influences. There is also evidence that the vorticity structure in rough-wall boundary layer flows is influenced by the relative magnitude of the roughness scale and the wall-normal location of the peak in the Reynolds shear stress; see Mehdi et al [42] and Ebner et al [43].…”

Turbulence Production in the Low Polymer Drag Reduction Regime

“…Here it is noted that the action of roughness is to generally augment drag. A symptom of this is that the layer II three-dimensionalization of the vorticity field is also augmented, and accordingly, there is a more rapid development of inertial mean dynamics with distance from the wall (Ebner et al 2016). As just noted, these effects are opposite those associated with polymer DR.…”

“…Under such cases, however, the characteristic scale (analogous to ǫ) must generally be determined empirically. In this regard, y + m provides a convenient and physically equivalent surrogate scale, and rough-wall experiments provide clear evidence that y + m effectively recovers the invariant scaling for |Ω z | described above (Mehdi et al 2013;Ebner et al 2016;Squire et al 2016).…”