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

2016 ◽  
Vol 792 ◽  
pp. 435-469 ◽  
Author(s):  
R. L. Ebner ◽  
Faraz Mehdi ◽  
J. C. Klewicki
Keyword(s):  
Structural Features ◽  
Momentum Equation ◽  
Rough Wall ◽  
Momentum Balance ◽  
Normal Velocity ◽  
Advective Transport ◽  
Vorticity Field ◽  
Wall Flows ◽  
The Mean ◽  
Spanwise Vorticity

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 Mehdiet 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 Mehdiet 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 momentum balance in moderately favourable pressure gradient turbulent boundary layers

2008 ◽  
Vol 617 ◽  
pp. 107-140 ◽  
Author(s):  
M. METZGER ◽  
A. LYONS ◽  
P. FIFE
Keyword(s):  
Pressure Gradient ◽  
Boundary Layers ◽  
Outer Region ◽  
Present Theory ◽  
Momentum Equation ◽  
Turbulent Boundary Layers ◽  
Momentum Balance ◽  
Physical Layers ◽  
Multi Scale ◽  
The Mean

Moderately favourable pressure gradient turbulent boundary layers are investigated within a theoretical framework based on the unintegrated two-dimensional mean momentum equation. The present theory stems from an observed exchange of balance between terms in the mean momentum equation across different regions of the boundary layer. This exchange of balance leads to the identification of distinct physical layers, unambiguously defined by the predominant mean dynamics active in each layer. Scaling domains congruent with the physical layers are obtained from a multi-scale analysis of the mean momentum equation. Scaling behaviours predicted by the present theory are evaluated using direct measurements of all of the terms in the mean momentum balance for the case of a sink-flow pressure gradient generated in a wind tunnel with a long development length. Measurements also captured the evolution of the turbulent boundary layers from a non-equilibrium state near the wind tunnel entrance towards an equilibrium state further downstream. Salient features of the present multi-scale theory were reproduced in all the experimental data. Under equilibrium conditions, a universal function was found to describe the decay of the Reynolds stress profile in the outer region of the boundary layer. Non-equilibrium effects appeared to be manifest primarily in the outer region, whereas differences in the inner region were attributed solely to Reynolds number effects.

Mean force structure and its scaling in rough-wall turbulent boundary layers

2013 ◽  
Vol 731 ◽  
pp. 682-712 ◽  
Author(s):  
Faraz Mehdi ◽  
J. C. Klewicki ◽  
C. M. White
Keyword(s):  
Reynolds Number ◽  
Boundary Layers ◽  
Characteristic Length ◽  
Turbulent Boundary Layers ◽  
Rough Wall ◽  
Viscous Force ◽  
Leading Order ◽  
Smooth Wall ◽  
Wall Flows ◽  
The Mean

AbstractThe 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.

A physical model of the turbulent boundary layer consonant with mean momentum balance structure

2007 ◽  
Vol 365 (1852) ◽  
pp. 823-840 ◽  
Author(s):  
Joe Klewicki ◽  
Paul Fife ◽  
Tie Wei ◽  
Pat McMurtry
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Physical Model ◽  
Momentum Equation ◽  
Momentum Balance ◽  
Dynamical Structure ◽  
Mean Flow ◽  
Structure And Dynamics ◽  
The Mean ◽  
Balance Structure

Recent studies by the present authors have empirically and analytically explored the properties and scaling behaviours of the Reynolds averaged momentum equation as applied to wall-bounded flows. The results from these efforts have yielded new perspectives regarding mean flow structure and dynamics, and thus provide a context for describing flow physics. A physical model of the turbulent boundary layer is constructed such that it is consonant with the dynamical structure of the mean momentum balance, while embracing independent experimental results relating, for example, to the statistical properties of the vorticity field and the coherent motions known to exist. For comparison, the prevalent, well-established, physical model of the boundary layer is briefly reviewed. The differences and similarities between the present and the established models are clarified and their implications discussed.

On the diffusion of momentum and mass by internal gravity waves

1976 ◽  
Vol 77 (4) ◽  
pp. 789-823 ◽  
Author(s):  
Peter Mtfller
Keyword(s):  
Wave Field ◽  
Gravity Waves ◽  
General Circulation ◽  
Viscosity Coefficient ◽  
Internal Gravity Waves ◽  
Momentum Equation ◽  
Momentum Balance ◽  
Mean Flow ◽  
Vertical Diffusion ◽  
The Mean

The interaction between short internal gravity waves and a larger-scale mean flow in the ocean is analysed in the Wkbj approximation. The wave field determines the radiation-stress term in the momentum equation of the mean flow and a similar term in the buoyancy equation. The mean flow affects the propagation characteristics of the wave field. This cross-coupling is treated as a small perturbation. When relaxation effects within the wave field are considered, the mean flow induces a modulation of the wave field which is a linear functional of the spatial gradients of the mean current velocity. The effect that this modulation itself has on the mean flow can be reduced to the addition of diffusion terms to the equations for the mass and momentum balance of the mean flow. However, there is no vertical diffusion of mass and other passive properties. The diffusion coefficients depend on the frequency spectrum and the relaxation time of the internal-wave field and can be evaluated analytically. The vertical viscosity coefficient is found to be vv [ape ] 4 x 103cm2/s and exceeds values typically used in models of the general circulation by at least two orders of magnitude.

scholarly journals Scaling of the turbulent/non-turbulent interface in boundary layers

2014 ◽  
Vol 751 ◽  
pp. 298-328 ◽  
Author(s):  
Kapil Chauhan ◽  
Jimmy Philip ◽  
Ivan Marusic
Keyword(s):  
Boundary Layer ◽  
Outer Part ◽  
Tangential Velocity ◽  
Reynolds Numbers ◽  
Momentum Balance ◽  
Normal Velocity ◽  
Mean Velocity ◽  
Order Of Magnitude ◽  
Theoretical Reasoning ◽  
The Mean

AbstractScaling of the interface that demarcates a turbulent boundary layer from the non-turbulent free stream is sought using theoretical reasoning and experimental evidence in a zero-pressure-gradient boundary layer. The data-analysis, utilising particle image velocimetry (PIV) measurements at four different Reynolds numbers ($\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\delta u_{\tau }/\nu =1200\mbox{--}14\, 500$), indicates the presence of a viscosity dominated interface at all Reynolds numbers. It is found that the mean normal velocity across the interface and the tangential velocity jump scale with the skin-friction velocity$u_{\tau }$and are approximately$u_{\tau }/10$and$u_{\tau }$, respectively. The width of the superlayer is characterised by the local vorticity thickness$\delta _{\omega }$and scales with the viscous length scale$\nu /u_{\tau }$. An order of magnitude analysis of the tangential momentum balance within the superlayer suggests that the turbulent motions also scale with inner velocity and length scales$u_{\tau }$and$\nu /u_{\tau }$, respectively. The influence of the wall on the dynamics in the superlayer is considered via Townsend’s similarity hypothesis, which can be extended to account for the viscous influence at the turbulent/non-turbulent interface. Similar to a turbulent far-wake the turbulent motions in the superlayer are of the same order as the mean velocity deficit, which lends to a physical explanation for the emergence of the wake profile in the outer part of the boundary layer.

Properties of the mean momentum balance in polymer drag-reduced channel flow

2017 ◽  
Vol 834 ◽  
pp. 409-433 ◽  
Author(s):  
C. M. White ◽  
Y. Dubief ◽  
J. Klewicki
Keyword(s):  
Drag Reduction ◽  
Channel Flow ◽  
Layer Structure ◽  
Momentum Equation ◽  
Momentum Balance ◽  
Viscous Effects ◽  
Logarithmic Scaling ◽  
The Mean ◽  
Balance Of Forces ◽  
Altered Form

Mean momentum equation based analysis of polymer drag-reduced channel flow is performed to evaluate the redistribution of mean momentum and the mechanisms underlying the redistribution processes. Similar to channel flow of Newtonian fluids, polymer drag-reduced channel flow is shown to exhibit a four layer structure in the mean balance of forces that also connects, via the mean momentum equation, to an underlying scaling layer hierarchy. The self-similar properties of the flow related to the layer hierarchy appear to persist, but in an altered form (different from the Newtonian fluid flow), and dependent on the level of drag reduction. With increasing drag reduction, polymer stress usurps the role of the inertial mechanism, and because of this the wall-normal position where inertially dominated mean dynamics occurs moves outward, and viscous effects become increasingly important farther from the wall. For the high drag reduction flows of the present study, viscous effects become non-negligible across the entire hierarchy and an inertially dominated logarithmic scaling region ceases to exist. It follows that the state of maximum drag reduction is attained only after the inertial sublayer is eradicated. According to the present mean equation theory, this coincides with the loss of a region of logarithmic dependence in the mean profile.

On scaling pipe flows with sinusoidal transversely corrugated walls: analysis of data from the laminar to the low-Reynolds-number turbulent regime

2015 ◽  
Vol 779 ◽  
pp. 245-274 ◽  
Author(s):  
S. Saha ◽  
J. C. Klewicki ◽  
A. Ooi ◽  
H. M. Blackburn
Keyword(s):  
Reynolds Number ◽  
Pressure Drop ◽  
Flow Separation ◽  
Rough Wall ◽  
Recent Analysis ◽  
Wall Structure ◽  
Turbulent Regime ◽  
Smooth Wall ◽  
Wall Flows ◽  
The Mean

Direct numerical simulation was used to study laminar and turbulent flows in circular pipes with smoothly corrugated walls. The corrugation wavelength was kept constant at $0.419D$, where $D$ is the mean diameter of the wavy-wall pipe and the corrugation height was varied from zero to $0.08D$. Flow rates were varied in steps between low values that generate laminar flow and higher values where the flow is in the post-transitional turbulent regime. Simulations in the turbulent regime were also carried out at a constant Reynolds number, $\mathit{Re}_{{\it\tau}}=314$, for all corrugation heights. It was found that even in the laminar regime, larger-amplitude corrugations produce flow separation. This leads to the proportion of pressure drop attributable to pressure drag being approximately 50 %, and rising to approximately 85 % in transitional rough-wall flow. The near-wall structure of turbulent flow is seen to be heavily influenced by the effects of flow separation and reattachment. Farther from the wall, the statistical profiles examined exhibit behaviours characteristic of smooth-wall flows or distributed roughness rough-wall flows. These observations support Townsend’s wall-similarity hypothesis. The organized nature of the present roughness allows the mean pressure drop to be written as a function of the corrugation height. When this is exploited in an analysis of the mean dynamical equation, the scaling problem is explicitly revealed to result from the combined influences of roughness and Reynolds number. The present results support the recent analysis and observations of Mehdi et al. (J. Fluid Mech., vol. 731, 2013, pp. 682–712), indicating that the length scale given by the distance from the wall at which the mean viscous force loses leading order is important to describing these combined influences, as well as providing a dynamically self-consistent connection to the scaling structure of smooth-wall pipe flow.

scholarly journals Turbulent flow over transitionally rough surfaces with varying roughness densities

2016 ◽  
Vol 804 ◽  
pp. 130-161 ◽  
Author(s):  
M. MacDonald ◽  
L. Chan ◽  
D. Chung ◽  
N. Hutchins ◽  
A. Ooi
Keyword(s):  
Turbulent Flows ◽  
Reynolds Shear Stress ◽  
Three Dimensional ◽  
Turbulent Energy ◽  
Rough Wall ◽  
Momentum Balance ◽  
Wall Flows ◽  
Roughness Elements ◽  
The Difference ◽  
Near Wall

We investigate rough-wall turbulent flows through direct numerical simulations of flow over three-dimensional transitionally rough sinusoidal surfaces. The roughness Reynolds number is fixed at $k^{+}=10$, where $k$ is the sinusoidal semi-amplitude, and the sinusoidal wavelength is varied, resulting in the roughness solidity $\unicode[STIX]{x1D6EC}$ (frontal area divided by plan area) ranging from 0.05 to 0.54. The high cost of resolving both the flow around the dense roughness elements and the bulk flow is circumvented by the use of the minimal-span channel technique, recently demonstrated by Chung et al. (J. Fluid Mech., vol. 773, 2015, pp. 418–431) to accurately determine the Hama roughness function, $\unicode[STIX]{x0394}U^{+}$. Good agreement of the second-order statistics in the near-wall roughness-affected region between minimal- and full-span rough-wall channels is observed. In the sparse regime of roughness ($\unicode[STIX]{x1D6EC}\lesssim 0.15$) the roughness function increases with increasing solidity, while in the dense regime the roughness function decreases with increasing solidity. It was found that the dense regime begins when $\unicode[STIX]{x1D6EC}\gtrsim 0.15{-}0.18$, in agreement with the literature. A model is proposed for the limit of $\unicode[STIX]{x1D6EC}\rightarrow \infty$, which is a smooth wall located at the crest of the roughness elements. This model assists with interpreting the asymptotic behaviour of the roughness, and the rough-wall data presented in this paper show that the near-wall flow is tending towards this modelled limit. The peak streamwise turbulence intensity, which is associated with the turbulent near-wall cycle, is seen to move further away from the wall with increasing solidity. In the sparse regime, increasing $\unicode[STIX]{x1D6EC}$ reduces the streamwise turbulent energy associated with the near-wall cycle, while increasing $\unicode[STIX]{x1D6EC}$ in the dense regime increases turbulent energy. An analysis of the difference of the integrated mean momentum balance between smooth- and rough-wall flows reveals that the roughness function decreases in the dense regime due to a reduction in the Reynolds shear stress. This is predominantly due to the near-wall cycle being pushed away from the roughness elements, which leads to a reduction in turbulent energy in the region previously occupied by these events.

Dynamics of vortical structures in a homogeneous shear flow

1994 ◽  
Vol 274 ◽  
pp. 43-68 ◽  
Author(s):  
Shigeo Kida ◽  
Mitsuru Tanaka
Keyword(s):  
Longitudinal Vortex ◽  
Navier Stokes ◽  
Spanwise Direction ◽  
Vorticity Field ◽  
Navier Stokes Equation ◽  
Vortical Structures ◽  
Homogeneous Shear ◽  
The Mean ◽  
Spanwise Vorticity ◽  
Vortex Tubes

The mechanism of generation, development and interaction of vortical structures, extracted as concentrated-vorticity regions, in homogeneous shear turbulence is investigated by the use of the results of a direct numerical simulation of the Navier-Stokes equation with 1283 grid points. Among others, a few of typical vortical structures are identified as important dynamical elements, namely longitudinal and lateral vortex tubes and vortex layers. They interact strongly with each other. Longitudinal vortex tubes are generated from a random fluctuating vorticity field through stretching of fluid elements caused by the mean linear shear. They are inclined toward the streamwise direction by rotational motion due to the mean shear. There is a small (about 10°) deviation in direction between the longitudinal vortex tubes and vorticity vectors therein, which makes the vorticity vectors turn toward the spanwise direction (against the mean vorticity) until the spanwise components of the fluctuating vorticity become comparable in magnitude with the mean vorticity. These longitudinal vortex tubes induce straining flows perpendicular to themselves which generate vortex layers with spanwise vorticity in planes spanned by the tubes and the spanwise axis. These vortex layers are unstable, and roll up into lateral vortex tubes with concentrated spanwise vorticity through the Kelvin-Helmholtz instability. All of these vortical structures, through strong mutual interactions, break down into a complicated smallscale random vorticity field. Throughout the simulated period an oblique stripe structure dominates the whole flow field: initially it is inclined at about 45° to the downstream and, as the flow develops, the inclination angle decreases but eventually stays at around 10°–20°.

scholarly journals On interpreting studies of tracer transport by deep cumulus convection and its effects on atmospheric chemistry

2008 ◽  
Vol 8 (20) ◽  
pp. 6037-6050 ◽  
Author(s):  
M. G. Lawrence ◽  
M. Salzmann
Keyword(s):  
Atmospheric Chemistry ◽  
Large Scale ◽  
Deep Convection ◽  
Convective Transport ◽  
Advective Transport ◽  
Tracer Transport ◽  
Transport Models ◽  
Mass Fluxes ◽  
Split Treatment ◽  
The Mean

Abstract. Global chemistry-transport models (CTMs) and chemistry-GCMs (CGCMs) generally simulate vertical tracer transport by deep convection separately from the advective transport by the mean winds, even though a component of the mean transport, for instance in the Hadley and Walker cells, occurs in deep convective updrafts. This split treatment of vertical transport has various implications for CTM simulations. In particular, it has led to a misinterpretation of several sensitivity simulations in previous studies in which the parameterized convective transport of one or more tracers is neglected. We describe this issue in terms of simulated fluxes and fractions of these fluxes representing various physical and non-physical processes. We then show that there is a significant overlap between the convective and large-scale mean advective vertical air mass fluxes in the CTM MATCH, and discuss the implications which this has for interpreting previous and future sensitivity simulations, as well as briefly noting other related implications such as numerical diffusion.

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