The autonomous cycle of near-wall turbulence

1999 ◽  
Vol 389 ◽  
pp. 335-359 ◽  
Author(s):  
JAVIER JIMÉNEZ ◽  
ALFREDO PINELLI
Keyword(s):  
Reynolds Numbers ◽  
Wall Turbulence ◽  
Wall Region ◽  
Streamwise Vortices ◽  
Outer Flow ◽  
Turbulent Fluctuations ◽  
The Mean ◽  
Turbulence Generation ◽  
Near Wall Turbulence ◽  
Near Wall

Numerical experiments on modified turbulent channels at moderate Reynolds numbers are used to differentiate between several possible regeneration cycles for the turbulent fluctuations in wall-bounded flows. It is shown that a cycle exists which is local to the near-wall region and does not depend on the outer flow. It involves the formation of velocity streaks from the advection of the mean profile by streamwise vortices, and the generation of the vortices from the instability of the streaks. Interrupting any of those processes leads to laminarization. The presence of the wall seems to be only necessary to maintain the mean shear. The generation of secondary vorticity at the wall is shown to be of little importance in turbulence generation under natural circumstances. Inhibiting its production increases turbulence intensity and drag.

Some insights for the prediction of near-wall turbulence

2013 ◽  
Vol 723 ◽  
pp. 126-139 ◽  
Author(s):  
Farid Karimpour ◽  
Subhas K. Venayagamoorthy
Keyword(s):  
Turbulent Flows ◽  
Time Scales ◽  
Time Scale ◽  
Eddy Viscosity ◽  
Wall Turbulence ◽  
Wall Region ◽  
Velocity Scale ◽  
The Mean ◽  
Near Wall Turbulence ◽  
Near Wall

AbstractIn this paper, we revisit the eddy viscosity formulation to highlight a number of important issues that have direct implications for the prediction of near-wall turbulence. For steady wall-bounded turbulent flows, we make the equilibrium assumption between rates of production ($P$) and dissipation ($\epsilon $) of turbulent kinetic energy ($k$) in the near-wall region to propose that the eddy viscosity should be given by ${\nu }_{t} \approx \epsilon / {S}^{2} $, where $S$ is the mean shear rate. We then argue that the appropriate velocity scale is given by $\mathop{(S{T}_{L} )}\nolimits ^{- 1/ 2} {k}^{1/ 2} $ where ${T}_{L} = k/ \epsilon $ is the turbulence (decay) time scale. The difference between this velocity scale and the commonly assumed velocity scale of ${k}^{1/ 2} $ is subtle but the consequences are significant for near-wall effects. We then extend our discussion to show that the fundamental length and time scales that capture the near-wall behaviour in wall-bounded shear flows are the shear mixing length scale ${L}_{S} = \mathop{(\epsilon / {S}^{3} )}\nolimits ^{1/ 2} $ and the mean shear time scale $1/ S$, respectively. With these appropriate length and time scales (or equivalently velocity and time scales), the eddy viscosity can be rewritten in the familiar form of the $k$–$\epsilon $ model as ${\nu }_{t} = \mathop{(1/ S{T}_{L} )}\nolimits ^{2} {k}^{2} / \epsilon $. We use the direct numerical simulation (DNS) data of turbulent channel flow of Hoyas & Jiménez (Phys. Fluids, vol. 18, 2006, 011702) and the turbulent boundary layer flow of Jiménez et al. (J. Fluid Mech. vol. 657, 2010, pp. 335–360) to perform ‘a priori’ tests to check the validity of the revised eddy viscosity formulation. The comparisons with the exact computations from the DNS data are remarkable and highlight how well the equilibrium assumption holds in the near-wall region. These findings could prove to be useful in near-wall modelling of turbulent flows.

A revisit of the equilibrium assumption for predicting near-wall turbulence

2014 ◽  
Vol 760 ◽  
pp. 304-312 ◽  
Author(s):  
Farid Karimpour ◽  
Subhas K. Venayagamoorthy
Keyword(s):  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Reynolds Stress ◽  
Turbulent Viscosity ◽  
Wall Turbulence ◽  
Wall Region ◽  
Turbulence Decay ◽  
Prime 2 ◽  
Near Wall Turbulence ◽  
Near Wall

AbstractIn this study, we revisit the consequence of assuming equilibrium between the rates of production ($P$) and dissipation $({\it\epsilon})$ of the turbulent kinetic energy $(k)$ in the highly anisotropic and inhomogeneous near-wall region. Analytical and dimensional arguments are made to determine the relevant scales inherent in the turbulent viscosity (${\it\nu}_{t}$) formulation of the standard $k{-}{\it\epsilon}$ model, which is one of the most widely used turbulence closure schemes. This turbulent viscosity formulation is developed by assuming equilibrium and use of the turbulent kinetic energy $(k)$ to infer the relevant velocity scale. We show that such turbulent viscosity formulations are not suitable for modelling near-wall turbulence. Furthermore, we use the turbulent viscosity $({\it\nu}_{t})$ formulation suggested by Durbin (Theor. Comput. Fluid Dyn., vol. 3, 1991, pp. 1–13) to highlight the appropriate scales that correctly capture the characteristic scales and behaviour of $P/{\it\epsilon}$ in the near-wall region. We also show that the anisotropic Reynolds stress ($\overline{u^{\prime }v^{\prime }}$) is correlated with the wall-normal, isotropic Reynolds stress ($\overline{v^{\prime 2}}$) as $-\overline{u^{\prime }v^{\prime }}=c_{{\it\mu}}^{\prime }(ST_{L})(\overline{v^{\prime 2}})$, where $S$ is the mean shear rate, $T_{L}=k/{\it\epsilon}$ is the turbulence (decay) time scale and $c_{{\it\mu}}^{\prime }$ is a universal constant. ‘A priori’ tests are performed to assess the validity of the propositions using the direct numerical simulation (DNS) data of unstratified channel flow of Hoyas & Jiménez (Phys. Fluids, vol. 18, 2006, 011702). The comparisons with the data are excellent and confirm our findings.

Regeneration mechanisms of near-wall turbulence structures

1995 ◽  
Vol 287 ◽  
pp. 317-348 ◽  
Author(s):  
James M. Hamilton ◽  
John Kim ◽  
Fabian Waleffe
Keyword(s):  
Turbulent Flows ◽  
Wall Turbulence ◽  
Direct Result ◽  
Wall Region ◽  
Computational Domain ◽  
Streamwise Vortices ◽  
Turbulence Structures ◽  
Wall Structures ◽  
Fully Developed Turbulent Flow ◽  
Near Wall

Direct numerical simulations of a highly constrained plane Couette flow are employed to study the dynamics of the structures found in the near-wall region of turbulent flows. Starting from a fully developed turbulent flow, the dimensions of the computational domain are reduced to near the minimum values which will sustain turbulence. A remarkably well-defined, quasi-cyclic and spatially organized process of regeneration of near-wall structures is observed. This process is composed of three distinct phases: formation of streaks by streamwise vortices, breakdown of the streaks, and regeneration of the streamwise vortices. Each phase sets the stage for the next, and these processes are analysed in detail. The most novel results concern vortex regeneration, which is found to be a direct result of the breakdown of streaks that were originally formed by the vortices, and particular emphasis is placed on this process. The spanwise width of the computational domain corresponds closely to the typically observed spanwise spacing of near-wall streaks. When the width of the domain is further reduced, turbulence is no longer sustained. It is suggested that the observed spacing arises because the time scales of streak formation, breakdown and vortex regeneration become mismatched when the streak spacing is too small, and the regeneration cycle at that scale is broken.

On unified boundary conditions for improved predictions of near-wall turbulence

2010 ◽  
Vol 656 ◽  
pp. 530-539 ◽  
Author(s):  
S. JAKIRLIĆ ◽  
J. JOVANOVIĆ
Keyword(s):  
Boundary Conditions ◽  
Viscous Sublayer ◽  
Wall Turbulence ◽  
Wall Region ◽  
Homogeneous Part ◽  
Wall Distance ◽  
Wall Boundary Conditions ◽  
Close Proximity ◽  
Near Wall Turbulence ◽  
Near Wall

A novel formulation of the wall boundary conditions relying on the asymptotic behaviour of the Taylor microscale λ and its relationship to the homogeneous part of the viscous dissipation rate of the kinetic energy of turbulence εh=5νq2/λ2, applicable to near-wall turbulence, is examined. The linear dependence of λ on the wall distance in close proximity to the solid surface enables the wall-closest grid node to be positioned immediately below the edge of the viscous sublayer, leading to a substantial coarsening of the grid resolution. This approach provides bridging of a major portion of the viscous sublayer, higher grid flexibility and weaker sensitivity against the grid non-uniformities in the near-wall region. The performance of the proposed formulation was checked against available direct numerical simulation databases of complex wall-bounded flows featured by swirl and separation.

Shear stress-driven flow: the state space of near-wall turbulence as

2019 ◽  
Vol 874 ◽  
pp. 606-638 ◽  
Author(s):  
Patrick Doohan ◽  
Ashley P. Willis ◽  
Yongyun Hwang
Keyword(s):  
Reynolds Number ◽  
Shear Stress ◽  
Couette Flow ◽  
Poiseuille Flow ◽  
Wall Turbulence ◽  
Phase Portraits ◽  
Wall Region ◽  
Velocity Statistics ◽  
Near Wall Turbulence ◽  
Near Wall

An inner-scaled, shear stress-driven flow is considered as a model of independent near-wall turbulence as the friction Reynolds number $Re_{\unicode[STIX]{x1D70F}}\rightarrow \infty$. In this limit, the model is applicable to the near-wall region and the lower part of the logarithmic layer of various parallel shear flows, including turbulent Couette flow, Poiseuille flow and Hagen–Poiseuille flow. The model is validated against damped Couette flow and there is excellent agreement between the velocity statistics and spectra for the wall-normal height $y^{+}<40$. A near-wall flow domain of similar size to the minimal unit is analysed from a dynamical systems perspective. The edge and fifteen invariant solutions are computed, the first discovered for this flow configuration. Through continuation in the spanwise width $L_{z}^{+}$, the bifurcation behaviour of the solutions over the domain size is investigated. The physical properties of the solutions are explored through phase portraits, including the energy input and dissipation plane, and streak, roll and wave energy space. Finally, a Reynolds number is defined in outer units and the high-$Re$ asymptotic behaviour of the equilibria is studied. Three lower branch solutions are found to scale consistently with vortex–wave interaction (VWI) theory, with wave forcing localising around the critical layer.

scholarly journals Analysis of Clusterization of Quasi-Streamwise Vortices in Near-Wall Turbulence.

1998 ◽  
Vol 64 (622) ◽  
pp. 1659-1666
Author(s):  
Koichi TSUJIMOTO ◽  
Yutaka MIYAKE ◽  
Takeshi YOSHIKAWA ◽  
Takeshi MORIKAWA
Keyword(s):  
Wall Turbulence ◽  
Streamwise Vortices ◽  
Near Wall Turbulence ◽  
Near Wall

scholarly journals Coherent structure generation in near-wall turbulence

2002 ◽  
Vol 453 ◽  
pp. 57-108 ◽  
Author(s):  
W. SCHOPPA ◽  
F. HUSSAIN
Keyword(s):  
Normal Mode ◽  
Base Flow ◽  
Wall Turbulence ◽  
Linear Perturbation ◽  
Transient Growth ◽  
Streamwise Vortices ◽  
Mean Velocity ◽  
Structure Generation ◽  
Near Wall Turbulence ◽  
Near Wall

We present a new mechanism for generation of near-wall streamwise vortices – which dominate turbulence phenomena in boundary layers – using linear perturbation analysis and direct numerical simulations of turbulent channel flow. The base flow, consisting of the mean velocity profile and low-speed streaks (free from any initial vortices), is shown to be linearly unstable to sinuous normal modes only for relatively strong streaks, i.e. for wall inclination angles of streak vortex lines exceeding 50°. Analysis of streaks extracted from fully developed near-wall turbulence indicates that about 20% of streak regions in the buffer layer exceed the strength threshold for instability. More importantly, these unstable streaks exhibit only moderate (twofold) normal-mode amplification, the growth being arrested by self-annihilation of streak-flank normal vorticity due to viscous cross-diffusion. We present here an alternative, streak transient growth (STG) mechanism, capable of producing much larger (tenfold) linear ampliflcation of x-dependent disturbances. Note the distinction of STG – responsible for perturbation growth on a streak velocity distribution U(y, z) – from prior transient growth analyses of the (streakless) mean velocity U(y). We reveal that streamwise vortices are generated from the more numerous normal-mode-stable streaks, via a new STG-based scenario: (i) transient growth of perturbations leading to formation of a sheet of streamwise vorticity ωx (by a ‘shearing’ mechanism of vorticity generation), (ii) growth of sinuous streak waviness and hence ∂u/∂x as STG reaches nonlinear amplitude, and (iii) the ωx sheet’s collapse via stretching by ∂u/∂x (rather than rollup) into streamwise vortices. Significantly, the three-dimensional features of the (instantaneous) streamwise vortices of x-alternating sign generated by STG agree well with the (ensemble-averaged) coherent structures educed from fully turbulent flow. The STG-induced formation of internal shear layers, along with quadrant Reynolds stresses and other turbulence measures, also agree well with fully developed turbulence. Results indicate the prominent – possibly dominant – role of this new, transient-growth-based vortex generation scenario, and suggest interesting possibilities for robust control of drag and heat transfer.

Sign in / Sign up

Export Citation Format

Share Document