2 results
Shared dynamical features of smooth- and rough-wall boundary-layer turbulence
- R. L. Ebner, Faraz Mehdi, J. C. Klewicki
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- Journal:
- Journal of Fluid Mechanics / Volume 792 / 10 April 2016
- Published online by Cambridge University Press:
- 03 March 2016, pp. 435-469
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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.
Mean force structure and its scaling in rough-wall turbulent boundary layers
- Faraz Mehdi, J. C. Klewicki, C. M. White
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- Journal:
- Journal of Fluid Mechanics / Volume 731 / 25 September 2013
- Published online by Cambridge University Press:
- 28 August 2013, pp. 682-712
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The combined roughness/Reynolds number problem is explored. Existing and newly acquired data from zero pressure gradient rough-wall turbulent boundary layers are used to clarify the leading order balances of terms in the mean dynamical equation. For the variety of roughnesses examined, it is revealed that the mean viscous force retains dominant order above (and often well above) the roughness crests. Mean force balance data are shown to be usefully organized relative to the characteristic length scale, which is equal or proportional to the width of the region from the wall to where the leading order mean dynamics become described by a balance between the mean and turbulent inertia. This is equivalently the width of the region from the wall to where the mean viscous force loses leading order. For both smooth-wall and rough-wall flows, the wall-normal extent of this region consistently ends just beyond the zero-crossing of the turbulent inertia term. In smooth-wall flow this characteristic length is a known function of Reynolds number. The present analyses indicate that for rough-wall flows the wall-normal position where the mean dynamics become inertial is an irreducible function of roughness and Reynolds number, as it is an inherent function of the relative scale separations between the inner, roughness, and outer lengths. These findings indicate that, for any given roughness, new dynamical regimes will typically emerge as the Reynolds number increases. For the present range of parameters, there appear to be three identifiable regimes. These correspond to the ratio of the equivalent sand grain roughness to the characteristic length being less than, equal to, or greater than $O(1)$. The relative influences of the inner, outer, and roughness length scales on the characteristic length are explored empirically. A prediction for the decay rate of the mean vorticity is developed via extension of the smooth-wall theory. Existing data are shown to exhibit good agreement with this extension. Overall, the present results appear to expose unifying connections between the structure of smooth- and rough-wall flows. Among other findings, the present analyses show promise toward providing a self-consistent and dynamically meaningful way of identifying the domain where the wall similarity hypothesis, if operative, should hold.