We introduce an elementary model of a turbulent boundary layer over a flat surface, given as a vertical random distribution of spanwise Lamb-Oseen vortex configurations placed over a non-slip boundary condition line. We are able to reproduce several important features of realistic flows, such as the viscous and logarithmic boundary sublayers, and the general behavior of the first statistical moments (turbulent intensity, skewness and flatness) of the streamwise velocity fluctuations. As an application, we advance some heuristic considerations on the boundary layer underlying kinematics that could be associated with the phenomenon of drag reduction by polymers, finding a suggestive support from its experimental signatures.
This video shows three-dimensional contours at two different values of enstrophy for a turbulent boundary layer up to $Re_θ\simeq 2500$. Its intention is to show how, what can be be considered the turbulent/nonturbulent interface for a turbulent boundary layer, evolves in time. Keyword: fluid dynamics video
One of the most enigmatic science question concerning inertial particle transport by a turbulent boundary layer flow is the value of the turbulent Schmidt number as the ratio of particle diffusivity and turbulent eddy viscosity. Using direct acoustic measurement of turbulent particle flux profile, and two-phase flow turbulence-resolving numerical simulation, it is demonstrated that turbulent dispersion of particles is reduced rather than enhanced when predicted with existing literature model. The explanation lies in the misleading assumption of settling velocity in quiescent water to estimate …
We study a boundary layer problem for the Navier-Stokes-alpha model obtaining a generalization of the Prandtl equations conjectured to represent the averaged flow in a turbulent boundary layer. We solve the equations for the semi-infinite plate, both theoretically and numerically. The latter solutions agree with some experimental data in the turbulent boundary layer.
We present a fluid dynamics video which illustrates the dynamics of the velocity field in the boundary layer in a turbulent Rayleigh-Benard convection flow. The data are obtained from direct numerical simulation.
Here we show the hairpin vortices point the upstream direction of flow instead of downstream, and this characteristic is found intrinsic behavior for turbulent buoyancy-driven boundary layer. We uncover the coherent vortices straddle high-speed streak instead of low-speed streak; moreover, the quadrant of the tangential Reynolds shear stresses dominates the first and third quadrant instead of the second and fourth one. These findings may help to improve our understanding of buoyancy-driven flow and buoyancy effects in turbulent models.
The turbulence statistics of the intermittent region in a supersonic turbulent boundary layer are studied by direct numerical simulation. Recently, Kwon et al. (2016) have shown that this intermittent behavior, consisting of the coexistence of turbulent and non-turbulent flows separated by an interface, could result in perils when the traditional Reynolds decomposition is used to analyze data. Here, we extend the study of turbulent/non-turbulent interfaces to the supersonic regime and report turbulence statistics conditioned to the interface. We show that the mathematical artefact of the tradi…
A composite representation of the turbulent boundary-layer velocity profile is proposed, which combines a recently determined accurate interpolation of the universal law of the wall with a simple analytical expression of the smooth transition of velocity to a constant value in the outer stream. Several examples are given of application of this representation to DNS and experimental data from the literature, and a conjecture is offered for the asymptotic approach of the velocity to its constant inviscid value.
The power laws in the overlap region of two layer theory of turbulent boundary layer have been obtained by Izakson-Millikan-Kolmogorov hypothesis. The solution of the open functional equation is not unique. The power laws for velocity \& skin friction have equivalence with log laws for velocity \& skin friction, for large Reynolds numbers.
We present the results of a Direct Numerical Simulation of a particle-laden spatially developing turbulent boundary layer up to Reθ = 2500. Two main features differentiate the behavior of inertial particles in a zero- pressure-gradient turbulent boundary layer from the more commonly studied case of a parallel channel flow. The first is the variation along the streamwise direction of the local dimensionless parameters defining the fluid-particle in- teractions. The second is the coexistence of an irrotational free-stream and a near-wall rotational turbulent flow. As concerns the first issue, an…
We report a new thermal boundary layer equation for turbulent Rayleigh-Benard convection for Prandtl number Pr>1 that takes into account the effect of turbulent fluctuations. These fluctuations are neglected in existing equations, which are based on steady-state and laminar assumptions. Using this new equation, we derive analytically the mean temperature profiles in two limits: (a) Pr>1, Pr~1 and (b) Pr>>1. These two theoretical predictions are in excellent agreement with the results of our direct numerical simulations for Pr=4.38 (water) and Pr=2547.9 (glycerol) respectively.
The turbulent boundary layer over a flat plate is computed by direct numerical simulation (DNS) of the incompressible Navier-Stokes equations as a test bed for a synthetic turbulence generator (STG) inflow boundary condition. The inlet momentum thickness Reynolds number is approximately 1,000. The study provides validation of the ability of the STG to develop accurate turbulence in 5 to 7 boundary layer thicknesses downstream of the boundary condition. Also tested was the effect of changes in the stabilization scheme on the development of the boundary layer. Moreover, the grid resolution requi…
In the first part of this study, we compared the performances of two categories of no-slip boundary treatments, i.e., the interpolated bounce-back schemes and the immersed boundary methods in a series of laminar flow simulations within the lattice Boltzmann method. In this second part, these boundary treatments are further compared in the simulations of turbulent flows with complex geometry to provide a next-level assessment of these schemes. Two non-trivial turbulent flow problems, a fully developed turbulent pipe flow at a low Reynolds number, and a decaying homogeneous isotropic turbulent f…
The boundary layer flow in a Rayleigh-Bénard convection cell of rectangular shape has been visualized in this fluid dynamics video. The experiment has been undertaken in air at a Rayleigh number $Ra=1.3\times 10^{10}$ and a Prandtl number $Pr=0.7$. Various sequences captured at selected positions of the heating plate show that the boundary layer is a very transient flow region characterized by coherent structures that permanently evolve. It becomes fully turbulent in the areas where the large-scale circulation impinge or leave the bottom plate.
Using the flow governing equation approach to similarity, Weyburne (D. Weyburne, arXiv:1701.02364, 2016) recently showed that for 2-D turbulent boundary layer flows, the Prandtl Plus scalings are NOT, in general, the proper similarity scaling parameters. Based on that failure, Weyburne proposed alternative length and velocity scaling parameters that satisfy the flow governing approach to similarity for external turbulent boundary layer flows. Herein, we show that both the proposed new scalings and the Prandtl Plus scalings have a theoretical underpinning which requires that the boundary layer …
A turbulent boundary layer is an essential flow case of fundamental and applied fluid mechanics. However, accurate measurements of turbulent boundary layer parameters (e.g., friction velocity $u_τ$ and wall shear $τ_w$), are challenging, especially for high speed flows (Smits et al., 2011). Many direct and/or indirect diagnostic techniques have been developed to measure wall shear stress (Vinuesa et al., 2017). However, based on different principles, these techniques usually give different results with different uncertainties. The current study introduces a nonlinear data assimilation framewor…
Boundary layers in turbulent flows require fine grid spacings near the walls which depend on the choice of turbulence model. To satisfy these requirements a semi-structured mesh is generally used in this area with orthogonal and layered elements. Adaptation of such a mesh needs to take into account the flow physics along with the standard error indicator approach. In this paper a novel methodology which combines Hessian based error indicators with flow physics to drive mesh adaptation is illustrated. Particular focus is on the thickness adaptation of the layered mesh. The technique is applied …
Wang and Castillo have developed empirical parameters for scaling the temperature profile of the turbulent boundary layer flowing over a heated wall in the paper X. Wang and L. Castillo, J. Turbul., 4, 1(2003). They presented experimental data plots that showed similarity type behavior when scaled with their new scaling parameters. However, what was actually plotted, and what actually showed similarity type behavior, was not the temperature profile but the defect profile formed by subtracting the temperature in the boundary layer from the temperature in the bulk flow. We show that if the same …
This paper describes an experimental investigation, by means of hot-wire anemometry, of the characteristics of velocity and temperature in a rotating turbulent boundary layer under isothermal and non-isothermal conditions. The ranges of experimental parameters are: Reynolds number from 10000 to 25000, rotational speed from 0 to 150 rpm, and y+ from 1.8 to 100. The relative temperature difference is held constant at 0.1. Detailed velocity and temperature distributions in the boundary layer are measured in the rotating state, and a new criterion for boundary layer segmentation under rotation is …
The shape of velocity and temperature profiles near the horizontal conducting plates in turbulent Rayleigh-Bénard convection are studied numerically and experimentally over the Rayleigh number range $10^8\lesssim Ra\lesssim3\times10^{11}$ and the Prandtl number range $0.7\lesssim Pr\lesssim5.4$. The results show that both the temperature and velocity profiles well agree with the classical Prandtl-Blasius laminar boundary-layer profiles, if they are re-sampled in the respective dynamical reference frames that fluctuate with the instantaneous thermal and velocity boundary-layer thicknesses.
Large scale coherent streaks are artificially forced in a well developed turbulent boundary layer at $\Redstar \approx 1000$ using an array of cylindrical roughness elements. Measures of the velocity field with particle image velocimetry reveal the presence of well reproducible, streamwise oriented, steady coherent streaks. We show that the amplitude of these coherent streaks transiently grows in space. The position of the maximum amplitude is proportional to the spanwise wavelength of the streaks and the most amplified spanwise wavelength is of very large scale $\lz \approx 6 \dblo$. These re…
In this short review it is suggested that the relationship between third- and fourth-order moments of turbulence in the atmospheric boundary layer depends on stability. This can explain some differences among datasets, and provides a key point for modelling improvement.
Analytic predictions of mean velocity profile (MVP) and streamwise ($x$) development of related integral quantities are presented for flows in channel and turbulent boundary layer (TBL), based on a symmetry analysis of eddy length and total stress. Specific predictions are the friction velocity $u_τ$: ${ U_e/u_τ}\approx 2.22\ln Re_x+2.86-3.83\ln(\ln Re_x)$; the boundary layer thickness $δ_e$: $x/δ_e \approx 7.27\ln Re_x-5.18-12.52\ln(\ln Re_x)$; the momentum thickness Reynolds number: $Re_x/Re_θ=4.94[{(\ln {{\mathop{\rm Re}\nolimits} _θ } + 1.88)^2} + 1]$, all in good agreement with empirical …
Time-dependent visualisations of large-scale direct and large-eddy simulations (DNS and LES) of a turbulent boundary layer reaching up to $Re_θ=4300$ are presented. The focus of the present fluid dynamics video is on analysing the coherent vortical structures in the boundary layer: It is clearly shown that hairpin vortices are indeed present in the simulation data, however they are characteristic remainders of the laminar-turbulent transition at lower Reynolds numbers. At higher $Re$ (say $Re_θ>2000$), these structures are no longer seen as being dominant; the coherence is clearly lost, both i…
By tailoring the geometry of the upper boundary in turbulent Rayleigh-Bénard convection we manipulate the boundary layer -- interior flow interaction, and examine the heat transport using the Lattice Boltzmann method. For fixed amplitude and varying boundary wavelength $λ$, we find that the exponent $β$ in the Nusselt-Rayleigh scaling relation, $Nu-1 \propto Ra^β$, is maximized at $λ\equiv λ_{\text{max}} \approx (2 π)^{-1}$, but decays to the planar value in both the large ($λ\gg λ_{\text{max}}$) and small ($λ\ll λ_{\text{max}}$) wavelength limits. The changes in the exponent originate in the …
This fluid dynamics video submitted to the Gallery of Fluid motion shows a turbulent boundary layer developing under a 5 metre-long flat plate towed through water. A stationary imaging system provides a unique view of the developing boundary layer as it would form over the hull of a ship or fuselage of an aircraft. The towed plate permits visualisation of the zero-pressure-gradient turbulent boundary layer as it develops from the trip to a high Reynolds number state ($Re_τ\approx 3000$). An evolving large-scale coherent structure will appear almost stationary in this frame of reference. The vi…
Experiments in an extraordinary turbulent boundary layer called the sink flow, displaying a perfect streamwise invariance, show a wide extent of logarithmic scaling for moments of streamwise velocity up to order 12, even at moderate Reynolds numbers. This is in striking contrast to canonical constant-pressure turbulent boundary layers that show such comprehensive log scaling only at ultra-high Reynolds numbers. This demonstrates that ultra-high Reynolds number is not necessary for comprehensive log scaling to occur; while specific details of the sink flow are special, the relevance to general …
The turbulent/non-turbulent interface is analysed in a direct numerical simulation of a boundary layer in the range $Re_θ=2800-6600$, with emphasis on the behaviour of the relatively large-scale fractal intermittent region. This requires the introduction of a new definition of the distance between a point and a general surface, which is compared with the more usual vertical distance to the top of the layer. Interfaces are obtained by thresholding the enstrophy field and the magnitude of the rate-of-strain tensor, and it is concluded that, while the former are physically relevant features, the …
The resolvent formulation of McKeon & Sharma (2010) is applied to supersonic turbulent boundary layers to study the validity of Morkovin's hypothesis, which postulates that high-speed turbulence structures in zero pressure-gradient turbulent boundary layers remain largely the same as its incompressible counterpart. Supersonic zero-pressure-gradient turbulent boundary layers with adiabatic wall boundary conditions at Mach numbers ranging from 2 to 4 are considered. Resolvent analysis highlights two distinct regions of the supersonic turbulent boundary layer in the wave parameter space: the rela…
Heat transport in turbulent thermal convection increases with the thermal forcing, but in almost all studies the rate of this increase is slower than it would be if transport became independent of the molecular diffusivities -- the heat transport scaling is slower than the mixing-length (or `ultimate') scaling. In configurations driven by either thermal boundary conditions or internal heating, thermal boundary layers instead lead to a boundary-limited (or `classical') scaling. With net-zero internal heating and cooling in different regions, mixing-length scaling can occur because heat need not…
Turbulent boundary layers exhibit a universal structure which nevertheless is rather complex, being composed of a viscous sub-layer, a buffer zone, and a turbulent log-law region. In this letter we present a simple analytic model of turbulent boundary layers which culminates in explicit formulae for the profiles of the mean velocity, the kinetic energy and the Reynolds stress as a function of the distance from the wall. The resulting profiles are in close quantitative agreement with measurements over the entire structure of the boundary layer, without any need of re-fitting in the different zo…
We apply the iterated edge state tracking algorithm to study the boundary between laminar and turbulent dynamics in plane Couette flow at Re=400. Perturbations that are not strong enough to become fully turbulent nor weak enough to relaminarize tend towards a hyperbolic coherent structure in state space, termed the edge state, which seems to be unique up to obvious continuous shift symmetries. The results reported here show that in cases where a fixed point has only one unstable direction, as for the lower branch solution in in plane Couette flow, the iterated edge tracking algorithm converges…
For rapidly rotating turbulent Rayleigh--Bénard convection in a slender cylindrical cell, experiments and direct numerical simulations reveal a boundary zonal flow (BZF) that replaces the classical large-scale circulation. The BZF is located near the vertical side wall and enables enhanced heat transport there. Although the azimuthal velocity of the BZF is cyclonic (in the rotating frame), the temperature is an anticyclonic traveling wave of mode one whose signature is a bimodal temperature distribution near the radial boundary. The BZF width is found to scale like $Ra^{1/4}Ek^{2/3}$ where the…
Recent theoretical results together with established theory have identified the displacement thickness and the velocity at the boundary layer edge as similarity scaling parameter candidates for the wall-bounded turbulent boundary layer. In the work described herein, we examine these scaling parameters along with the Prandtl Plus scaling's and the Zagarola and Smits scaling's to search for similarity in the outer region of experimental turbulent boundary layer velocity profile datasets. A new integral area method combined with the traditional chi-by-eye method is used to search for similar velo…
We perform direct numerical simulations of rotating Rayleigh--Bénard convection of fluids with low ($Pr=0.1$) and high ($Pr=5$) Prandtl numbers in a horizontally periodic layer with no-slip top and bottom boundaries. At both Prandtl numbers, we demonstrate the presence of an upscale transfer of kinetic energy that leads to the development of domain-filling vortical structures. Sufficiently strong buoyant forcing and rotation foster the quasi-two-dimensional turbulent state of the flow, despite the formation of plume-like vertical disturbances promoted by so-called Ekman pumping from the viscou…
Two-dimensional simulations of Rayleigh-Bénard convection at $Ra = 5\times10^{10}$ show that vertical logarithmic mean temperature profiles can be observed in regions of the boundary layer where thermal plumes are emitted. The profile is logarithmic only in these regions and not in the rest of the boundary layer where it is sheared by the large scale wind and impacted by plumes. In addition, the logarithmic behavior is not visible in the horizontal average. The findings reveal that the temperature profiles are strongly connected to thermal plume emission and support a perception that parts of …
A study of large-scale motions from a new direct numerical simulation database of the turbulent boundary layer up to Reθ ~ 2500 is presented. The statistics of large-scale streamwise structures have been investigated using two-dimensional and three-dimensional extraction procedures. The large-scale structures are abstracted using a robust skeletonization method usually applied to other research domains to simplify complex 3D objects. Different structure parameters such as the length, shape or angle are investigated. The features of the detected structures are compared to their mean counterpart…
The entrainment of ambient fluid into a turbulent shear flow has been a topic of wide interest for several decades. To estimate the entrainment of ambient fluid into turbulent jet, it is essential to define the boundary of the jet. The question arises as to what should be the appropriate criterion to determine the edge of the turbulent jet. From the present DNS simulations, we observe that there is a need to define two boundaries for the turbulent jet, namely, the Rotational/Irrotational (R/IR) interface termed here as "Outer boundary" and the Turbulent/Non-Turbulent (T/NT) interface as "Inner…
We use momentum transfer arguments to predict the friction factor $f$ in two-dimensional turbulent soap-film flows with rough boundaries (an analogue of three-dimensional pipe flow) as a function of Reynolds number Re and roughness $r$, considering separately the inverse energy cascade and the forward enstrophy cascade. At intermediate Re, we predict a Blasius-like friction factor scaling of $f\propto\textrm{Re}^{-1/2}$ in flows dominated by the enstrophy cascade, distinct from the energy cascade scaling of $\textrm{Re}^{-1/4}$. For large Re, $f \sim r$ in the enstrophy-dominated case. We use …
A new set of three-dimensional visualisations of a large-scale direct numerical simulations (DNS) of a turbulent boundary layer is presented. The Reynolds number ranges from $Re_θ=180$ to 4300, based on the momentum-loss thickness $θ$ and the free-stream velocity $U_\infty$. The focus of the present fluid dynamics video is on analysing the coherent vortical structures in the boundary layer: It is clearly shown that the initial phases are dominated by coherent so-called hairpin vortices which are characteristic remainders of the laminar-turbulent transition at lower Reynolds numbers. At higher …
We perform direct numerical simulations of shock-wave/boundary-layer interactions (SBLI) at Mach number M = 1.7 to investigate the influence of the state of the incoming boundary layer on the interaction properties. We reproduce and extend the flow conditions of the experiments performed by Giepman et al., in which a spatially evolving laminar boundary layer over a flat plate is initially tripped by an array of distributed roughness elements and impinged further downstream by an oblique shock wave. Four SBLI cases are considered, based on two different shock impingement locations along the str…
A hybrid RANS/LES framework is developed based on a recently proposed Improved Delayed Detached Eddy Simulation (IDDES) model combined with a variant of recycling and rescaling method of generating inflow turbulence. This framework was applied to investigate spatially developing flat plate turbulent boundary layer up to momentum thickness Reynolds number, $R_θ = 31000$ and the results are compared with the available experimental data. Good agreement was obtained for the global quantities such as mean velocity and skin friction at all momentum thickness Reynolds numbers considered. The trends o…
This paper develops a spatial input-output approach to investigate the dynamics of a turbulent boundary layer subject to a localized single frequency excitation. This method uses one-way spatial integration to reformulate the problem in terms of spatial evolution equations. The technique is used to examine the effect of localized periodic actuation at a given temporal frequency, based on an experimental set-up in which an active large-scale is introduced into the outer layer of a turbulent boundary layer. First, the large-scale structures associated with the phase-locked modal velocity field o…
Results on the Prandtl-Blasius type kinetic and thermal boundary layer thicknesses in turbulent Rayleigh-Bénard convection in a broad range of Prandtl numbers are presented. By solving the laminar Prandtl-Blasius boundary layer equations, we calculate the ratio of the thermal and kinetic boundary layer thicknesses, which depends on the Prandtl number Pr only. It is approximated as $0.588Pr^{-1/2}$ for $Pr\ll Pr^*$ and as $0.982 Pr^{-1/3}$ for $Pr^*\ll\Pr$, with $Pr^*= 0.046$. Comparison of the Prandtl--Blasius velocity boundary layer thickness with that evaluated in the direct numerical simula…
At sufficiently high Reynolds numbers, shear-flow turbulence close to a wall acquires universal properties. When length and velocity are rescaled by appropriate characteristic scales of the turbulent flow and thereby measured in \emph{inner units}, the statistical properties of the flow become independent of the Reynolds number. We demonstrate the existence of a wall-attached non-chaotic exact invariant solution of the fully nonlinear 3D Navier-Stokes equations for a parallel boundary layer that captures the characteristic self-similar scaling of near-wall turbulent structures. The branch of t…
This paper presents a study on wave cancellation in forced jets. Building on recent work on real-time control of forced turbulent jets [1,2], we here assess the effect of jet upstream conditions and nonlinearity on wave-cancellation performance. The experiments are performed in jets with laminar and turbulent boundary layers inside the nozzle. An open-loop campaign is first conducted, in which the goal is to analyse the jet response to stochastic forcing with variable bandwidth. The upstream conditions of the jet are found to have a strong influence on the jet response. For narrow forcing band…
Direct numerical simulations are performed to contrast turbulent boundary layers over a concave wall without and with free-stream turbulence. Adverse pressure gradient near the onset of curvature leads to sharp decrease in skin friction and intermittent separation. The presence of free-stream turbulence reduces the probability of reverse flow, accelerates the recovery of the boundary layer in the downstream zero-pressure gradient region, and leads to a sustained and appreciable increase in the skin friction. The forcing also promotes the amplification of coherent Görtler structures in the loga…
