Shape and scaling of the mean-velocity profile in thermally-stratified plane-Couette flows

2021 ◽  
Author(s):  
Dongrong Zhang
Keyword(s):  
Theoretical Analysis ◽  
Velocity Profile ◽  
Turbulent Flows ◽  
Intermediate Layer ◽  
Scaling Laws ◽  
Similarity Theory ◽  
Constant Density ◽  
Mean Velocity ◽  
The Mean

Abstract It has long been known from measurements that buoyant motions cause the mean-velocity profile (MVP) in thermally-stratified, wall-bounded turbulent flows to significantly deviate from its constant-density counterpart. Theoretical analysis has restricted attention to an “intermediate layer” of the MVP, akin to the celebrated “log layer” in the constant-density case. Here, for thermally-stratified plane-Couette flows, we study the shape and scaling of the whole MVP. We elucidate the mechanisms that dictate the shape of the MVP by using the framework of the spectral link (Gioia et al.; 2010), and obtain scaling laws for the whole MVP by generalizing the Monin-Obukhov similarity theory.

Revisiting the mixing-length hypothesis in the outer part of turbulent wall layers: mean flow and wall friction

2014 ◽  
Vol 745 ◽  
pp. 378-397 ◽  
Author(s):  
Sergio Pirozzoli
Keyword(s):  
Velocity Profile ◽  
Turbulent Flows ◽  
Outer Part ◽  
Wall Layer ◽  
Wall Friction ◽  
Mixing Length ◽  
Mean Flow ◽  
Mean Velocity ◽  
The Mean ◽  
Turbulent Wall

AbstractWe reconsider foundations and implications of the mixing length theory as applied to wall-bounded turbulent flows in uniform pressure gradient. Based on recent channel-flow direct numerical simulation (DNS) data at sufficiently high Reynolds number, we find that Prandtl’s hypothesis of linear variation of the mixing length with the wall distance is rather inaccurate, hence overlap arguments are stronger in justifying the formation of a logarithmic layer in the mean velocity profile. Regarding the core region of the wall layer, we find that Clauser’s hypothesis of uniform eddy viscosity is strictly connected with the observed size of the eddy structures, and it delivers surprisingly good agreement with DNS and experiments for channels, pipes, and boundary layers. We show that the analytically derived composite mean velocity profiles can be used to accurately predict skin friction in canonical wall-bounded flows with a minimal number of adjustable parameters directly related to the mean velocity profile, and to obtain some insight into transient growth phenomena.

scholarly journals Summary-Introduction: Similarity arguments for fully developed turbulence

1960 ◽  
Vol 12 ◽  
pp. 376-384 ◽  
Author(s):  
W. V. R. Malkus
Keyword(s):  
Velocity Profile ◽  
Turbulent Flows ◽  
Mean Velocity ◽  
Shearing Flow ◽  
Fully Developed Turbulence ◽  
General Behavior ◽  
Developed Turbulence ◽  
Euler's Equations ◽  
The Mean

In the study of turbulent flows similarity arguments are used to explore the consequences of non-mechanistic assertions concerning the general behavior of the flow. For example, it is currently assumed that viscosity plays no role in the determination of the mean velocity profile of turbulent shearing flow far from a boundary. The consequences of this assumption are that the amplitude of the mean velocity will be determined by the momentum transported into such a region and that the velocity profile will be a solution to Euler's equations.

scholarly journals Effect of the Flame Dome Depth and Improvement of the Pressure Loss in the Dump Diffuser

1998 ◽  
Author(s):  
Shinji Honami ◽  
Wataru Tsuboi ◽  
Takaaki Shizawa
Keyword(s):  
Velocity Profile ◽  
Reynolds Stress ◽  
Flow Rate ◽  
Pressure Loss ◽  
Total Pressure ◽  
Flow Behavior ◽  
Sudden Expansion ◽  
Mean Velocity ◽  
The Mean ◽  
Stress Profiles

This paper presents the effect of flame dome depth on the total pressure performance and flow behavior in a sudden expansion region of the combustor diffuser without flow entering the dome head. The mean velocity and turbulent Reynolds stress profiles in the sudden expansion region were measured by a Laser Doppler Velocitmetry (LDV) system. The experiments show that total pressure loss is increased, when flame dome depth is increased. Installation of an inclined combuster wall in the sudden expansion region is suggested from the viewpoint of a control of the reattaching flow. The inclined combustor wall is found to be effective in improvement of the diffuser performance. Better characteristics of the flow rate distribution into the branched channels are obtained in the inclined wall configuration, even if the distorted velocity profile is provided at the diffuser inlet.

scholarly journals On the streamwise evolution of turbulent boundary layers in arbitrary pressure gradients

2002 ◽  
Vol 461 ◽  
pp. 61-91 ◽  
Author(s):  
A. E. PERRY ◽  
IVAN MARUSIC ◽  
M. B. JONES
Keyword(s):  
Boundary Layers ◽  
Scaling Laws ◽  
Power Spectra ◽  
Adverse Pressure Gradient ◽  
Turbulent Boundary Layers ◽  
Stream Velocity ◽  
Mean Flow ◽  
Mean Velocity ◽  
Law Of The Wall ◽  
The Mean

A new approach to the classic closure problem for turbulent boundary layers is presented. This involves, first, using the well-known mean-flow scaling laws such as the log law of the wall and the law of the wake of Coles (1956) together with the mean continuity and the mean momentum differential and integral equations. The important parameters governing the flow in the general non-equilibrium case are identified and are used for establishing a framework for closure. Initially closure is achieved here empirically and the potential for achieving closure in the future using the wall-wake attached eddy model of Perry & Marusic (1995) is outlined. Comparisons are made with experiments covering adverse-pressure-gradient flows in relaxing and developing states and flows approaching equilibrium sink flow. Mean velocity profiles, total shear stress and Reynolds stress profiles can be computed for different streamwise stations, given an initial upstream mean velocity profile and the streamwise variation of free-stream velocity. The attached eddy model of Perry & Marusic (1995) can then be utilized, with some refinement, to compute the remaining unknown quantities such as Reynolds normal stresses and associated spectra and cross-power spectra in the fully turbulent part of the flow.

scholarly journals Natural logarithms

2013 ◽  
Vol 718 ◽  
pp. 1-4 ◽  
Author(s):  
B. J. McKeon
Keyword(s):  
Turbulent Flows ◽  
Reynolds Numbers ◽  
Streamwise Velocity ◽  
Wall Turbulence ◽  
Significant Advance ◽  
Mean Velocity ◽  
Velocity Fluctuations ◽  
Logarithmic Scaling ◽  
The Mean ◽  
High Reynolds

AbstractMarusic et al. (J. Fluid Mech., vol. 716, 2013, R3) show the first clear evidence of universal logarithmic scaling emerging naturally (and simultaneously) in the mean velocity and the intensity of the streamwise velocity fluctuations about that mean in canonical turbulent flows near walls. These observations represent a significant advance in understanding of the behaviour of wall turbulence at high Reynolds number, but perhaps the most exciting implication of the experimental results lies in the agreement with the predictions of such scaling from a model introduced by Townsend (J. Fluid Mech., vol. 11, 1961, pp. 97–120), commonly termed the attached eddy hypothesis. The elegantly simple, yet powerful, study by Marusic et al. should spark further investigation of the behaviour of all fluctuating velocity components at high Reynolds numbers and the outstanding predictions of the attached eddy hypothesis.

scholarly journals Stochastic flow approach to model the mean velocity profile of wall-bounded flows

2019 ◽  
Vol 99 (6) ◽  
Author(s):  
Benoît Pinier ◽  
Etienne Mémin ◽  
Sylvain Laizet ◽  
Roger Lewandowski
Keyword(s):  
Velocity Profile ◽  
Stochastic Flow ◽  
Mean Velocity ◽  
The Mean ◽  
Wall Bounded Flows

Simplified theory of the near-wall turbulent layer of Newtonian and drag-reducing fluids

1982 ◽  
Vol 119 ◽  
pp. 423-441 ◽  
Author(s):  
M. A. Goldshtik ◽  
V. V. Zametalin ◽  
V. N. Shtern
Keyword(s):  
Velocity Profile ◽  
Turbulent Flow ◽  
Drag Reduction ◽  
Outer Boundary ◽  
Viscous Sublayer ◽  
Viscous Layer ◽  
Mean Velocity ◽  
Turbulent Layer ◽  
The Mean ◽  
Near Wall

We propose a simplified theory of a viscous layer in near-wall turbulent flow that determines the mean-velocity profile and integral characteristics of velocity fluctuations. The theory is based on the concepts resulting from the experimental data implying a relatively simple almost-ordered structure of fluctuations in close proximity to the wall. On the basis of data on the greatest contribution to transfer processes made by the part of the spectrum associated with the main size of the observed structures, the turbulent fluctuations are simulated by a three-dimensional running wave whose parameters are found from the problem solution. Mathematically the problem reduces to the solution of linearized Navier-Stokes equations. The no-slip condition is satisfied on the wall, whereas on the outer boundary of a viscous layer the conditions of smooth conjunction with the asymptotic shape of velocity and fluctuation-energy profiles resulting from the dimensional analysis are satisfied. The formulation of the problem is completed by the requirement of maximum curvature of the mean-velocity profile on the outer boundary applied from stability considerations.The solution of the problem does not require any quantitative empirical data, although the conditions of conjunction were formulated according to the well-known concepts obtained experimentally. As a result, the near-wall law for the averaged velocity has been calculated theoretically and is in good agreement with experiment, and the characteristic scales for fluctuations have also been determined. The developed theory is applied to turbulent-flow calculations in Maxwell and Oldroyd media. The elastic properties of fluids are shown to lead to near-wall region reconstruction and its associated drag reduction, as is the case in turbulent flows of dilute polymer solutions. This theory accounts for several features typical of the Toms effect, such as the threshold character of the effect and the decrease in the normal fluctuating velocity. The analysis of the near-wall Oldroyd fluid flow permits us to elucidate several new aspects of the drag-reduction effect. It has been established that the Toms effect does not always result in thickening of the viscous sublayer; on the contrary, the most intense drag reduction takes place without thickening in the viscous sublayer.

The Effects of Surface Roughness on the Mean Velocity Profile in a Turbulent Boundary Layer

2002 ◽  
Vol 124 (3) ◽  
pp. 664-670 ◽  
Author(s):  
Donald J. Bergstrom ◽  
Nathan A. Kotey ◽  
Mark F. Tachie
Keyword(s):  
Boundary Layer ◽  
Surface Roughness ◽  
Turbulent Boundary Layer ◽  
Velocity Profile ◽  
Friction Velocity ◽  
Outer Region ◽  
Stream Velocity ◽  
Mean Velocity ◽  
Outer Flow ◽  
The Mean

Experimental measurements of the mean velocity profile in a canonical turbulent boundary layer are obtained for four different surface roughness conditions, as well as a smooth wall, at moderate Reynolds numbers in a wind tunnel. The mean streamwise velocity component is fitted to a correlation which allows both the strength of the wake, Π, and friction velocity, Uτ, to vary. The results show that the type of surface roughness affects the mean defect profile in the outer region of the turbulent boundary layer, as well as determining the value of the skin friction. The defect profiles normalized by the friction velocity were approximately independent of Reynolds number, while those normalized using the free stream velocity were not. The fact that the outer flow is significantly affected by the specific roughness characteristics at the wall implies that rough wall boundary layers are more complex than the wall similarity hypothesis would allow.

Connections between the Ozmidov scale and mean velocity profile in stably stratified atmospheric surface layers

2016 ◽  
Vol 797 ◽  
Author(s):  
Dan Li ◽  
Scott T. Salesky ◽  
Tirtha Banerjee
Keyword(s):  
Velocity Profile ◽  
Atmospheric Stability ◽  
Length Scale ◽  
Surface Layers ◽  
Mean Velocity ◽  
Stable Conditions ◽  
Stringent Constraint ◽  
Ozmidov Scale ◽  
The Mean ◽  
Good Agreement

The mean velocity profile (MVP) in thermally stratified atmospheric surface layers (ASLs) deviates from the classic logarithmic form. A theoretical framework was recently proposed (Katulet al.Phys. Rev. Lett., vol. 107, 2011, 268502) to link the MVP to the spectrum of turbulence and was found to successfully predict the MVP for unstable stratification. However, the theory failed to reproduce the MVP in stable conditions (Saleskyet al.Phys. Fluids, vol. 25, 2013, 105101), especially when${\it\zeta}>0.2$(where${\it\zeta}$is the atmospheric stability parameter). In the present study, it is demonstrated that this shortcoming is due to the failure to identify the appropriate length scale that characterizes the size of momentum transporting eddies in the stable ASL. Beyond${\it\zeta}\approx 0.2$(near where the original theory fails), the Ozmidov length scale becomes smaller than the distance from the wall$z$and hence is a more stringent constraint for characterizing the size of turbulent eddies. An expression is derived to connect the Ozmidov length scale to the normalized MVP (${\it\phi}_{m}$), allowing${\it\phi}_{m}$to be solved numerically. It is found that the revised theory produces a prediction of${\it\phi}_{m}$in good agreement with the widely used empirical Businger–Dyer relation and two experimental datasets in the stable ASL. The results here demonstrate that the behaviour of${\it\phi}_{m}$in the stable ASL is closely linked to the size of momentum transporting eddies, which can be characterized by the Ozmidov scale under mildly to moderately stable conditions ($0.2<{\it\zeta}<1-2$).

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