The structure of homogeneous turbulent shear flow is studied using data generated by Direct Numerical Simulations (DNS) and a linear analysis for both compressible and incompressible cases. At large values of the mean shear rate, the Rapid Distortion Theory (RDT) limit is approached. Analytical solutions are found for the inviscid compressible RDT equations at long times. The RDT equations are also solved numerically for both inviscid and viscous cases. The RDT solutions, confirmed by the DNS results, show that the even order transverse derivative moments of the dilatational and solenoidal velocity fields are anisotropic, with the dilatational motions more anisotropic than their solenoidal counterparts. The results obtained for the incompressible case are similar to those obtained for the solenoidal motions in the compressible case. The DNS results also indicate an increase in the anisotropy of the even order transverse derivative moments with the order of the moment, in agreement with the RDT predictions. Although the anisotropy decreases with Reynolds number, it is likely that for higher even order moments it will persist at large values of the Reynolds number, in contrast with the postulate of local isotropy. The RDT solutions also predict that the normalized odd order transverse derivative moments of the solenoidal velocity for the compressible case and of the velocity for the incompressible case should approach a constant different than zero at large times. This prediction is supported by the DNS data. For higher odd order normalized moments, the RDT analysis suggests that the anisotropy may persist at large values of the Reynolds number, in agreement with the existent experimental data.
We study the physics of turbulent/non-turbulent interface of an isolated turbulent region in dilute polymer solutions and Newtonian fluid. The performance of a FENE-P model with a localized homogeneous forcing is verified using the specially designed experimental setup of a turbulent patch growing in water/dilute polymer solution, without mean shear and far from the walls. The results of the small scale dynamics of vorticity and strain help to reveal the key mechanism of polymer action in turbulent flows without mean shear. Modified degrees of alignment between vorticity, the polymer conformat…
Turbulent-laminar intermittency, typically in the form of bands and spots, is a ubiquitous feature of the route to turbulence in wall-bounded shear flows. Here we study the idealised shear between stress-free boundaries driven by a sinusoidal body force and demonstrate quantitative agreement between turbulence in this flow and that found in the interior of plane Couette flow -- the region excluding the boundary layers. Exploiting the absence of boundary layers, we construct a model flow that uses only four Fourier modes in the shear direction and yet robustly captures the range of spatiotempor…
The expected universality of small-scale properties of turbulent flows implies isotropic properties of the velocity gradient tensor in the very large Reynolds number limit. Using direct numerical simulations, we determine the tensors formed by n = 2 and 3 velocity gradients at a single point in turbulent homogeneous shear flows, and in the log-layer of a turbulent channel flow, and we characterize the departure of these tensors from the corresponding isotropic prediction. Specifically, we separate the even components of the tensors, invariant under reflexion with respect to all axes, from the …
Localised turbulent structures such as puffs or oblique stripes are building blocks of the intermittency regimes in subcritical wall-bounded shear flows. These turbulent structures are investigated in incompressible pressure-driven annular pipe flow using direct numerical simulations in long domains. For low enough radius ratio $η$, these coherent structures have a dynamics comparable to that of puffs in cylindrical pipe flow. For $η$ larger than 0.5, they take the shape of helical stripes inclined with respect to the axial direction. The transition from puffs to stripes is analysed statistica…
We study the morphology of Eulerian vortical structures and their interaction with density interfaces in increasingly turbulent stably-stratified shear layers. We analyse the three-dimensional, simultaneous velocity and density fields obtained in the stratified inclined duct laboratory experiment. We track, across 15 datasets, the evolution of coherent structures from pre-turbulent Holmboe waves, through intermittent turbulence, to full turbulence and mixing. We use the Rortex--Shear decomposition of the vorticity field into a pure rotational part (the rortex vector), and a non-rotational part…
We present a simple model for the development of shear layers between parallel flows in confining channels. Such flows are important across a wide range of topics from diffusers, nozzles and ducts to urban air flow and geophysical fluid dynamics. The model approximates the flow in the shear layer as a linear profile separating uniform-velocity streams. Both the channel geometry and wall drag affect the development of the flow. The model shows good agreement with both particle-image-velocimetry experiments and computational turbulence modelling. The low computational cost of the model allows it…
We present a new physically-motivated parameterization, based on the ratio of Thorpe and Ozmidov scales, for the irreversible turbulent flux coefficient $Γ_{\mathcal M}= {\mathcal M}/ε$, i.e. the ratio of the irreversible rate ${\mathcal M}$ at which the background potential energy increases in a stratified flow due to macroscopic motions to the dissipation rate of turbulent kinetic energy. Our parameterization covers all three key phases (crucially, in time) of a shear-induced stratified turbulence life cycle: the initial, `hot' growing phase, the intermediate energetically forced phase, and …
Data-driven methods for modelling purposes in fluid mechanics are a promising alternative given the continuous increase of both computational power and data-storage capabilities. Highly non-linear flows including turbulence and reaction are challenging to model, and accurate closures for the unresolved terms in large eddy simulations of such flows are difficult to obtain. In this study, we investigate the use of artificial neural networks for modelling an important unclosed term namely the unresolved stress tensor, in a highly demanding turbulent and reacting flow, which additionally includes …
The rupture of a liquid film due to co-flowing turbulent shear flows in the gas phase is studied using a volume-of-fluid method. To simulate this multiphase problem, we use a simplified numerical setup where the liquid film is 'sandwiched' between two fully developed boundary layers from a turbulent channel simulation. The film deforms and eventually ruptures within the shear zone created by the co-flows. This efficient setup allows systematic variation of physical parameters to gauge their role in the aerodynamically-driven deformation and rupture of a liquid film under fully developed sheare…
In turbulent wall sheared thermal convection, there are three different flow regimes, depending on the relative relevance of thermal forcing and wall shear. In this paper we report the results of direct numerical simulations of such sheared Rayleigh-Bénard convection, at fixed Rayleigh number $Ra=10^6$, varying the wall Reynolds number in the range $0 \leq Re_w \leq 4000$ and Prandtl number $0.22 \leq Pr \leq 4.6$, extending our prior work by Blass et al. (2020), where $Pr$ was kept constant at unity and the thermal forcing ($Ra$) varied. We cover a wide span of bulk Richardson numbers $0.014 …
Measurements of wall shear-stress fluctuations on very long timescales ($\ge$ 1900 free-fall time units) are reported for turbulent Rayleigh-Benard (RB) convection in air at the heated bottom plate of a RB cell, 2.5 m in diameter and 2.5 m in height. The novel sensor simultaneously captures the fluctuations of the magnitude and the direction of the wall shear stress vector $\boldsymbolτ(t)$ with high resolution in the slow air currents. The results show the persistence of a tumble-type structure, which is in a bi-stable state as it oscillates regularly about a mean orientation at a timescale t…
We study the bifurcations of the large scale jets in the turbulent regime of a forced shear flow using direct numerical simulations of the Navier-Stokes equations. The bifurcations are seen in the probability density function (PDF) of the largest scale mode with the control parameter being the Reynolds number based on the friction coefficient denoted as $Rh$. As one increases $Rh$ in the turbulent regime, the PDF of the large scale mode first bifurcates from a Gaussian to a bimodal behaviour, signifying the emergence of reversals of the large scale flow where the flow fluctuates between two di…
In wall-bounded shear flow the primary coherent structure is the streamwise roll and streak (R-S). Absent of an associated instability the R-S has been ascribed to non-normality mediated interaction between the mean flow and perturbations. This interaction may occur either directly due to excitation of a transiently growing perturbation or indirectly due to destabilization of the R-S by turbulent Reynolds stresses. A fundamental distinction between the direct and the indirect mechanisms, which is central to understanding the physics of turbulence, is that in the direct mechanism the R-S is its…
There are more than 300,000 heart valves implanted annually worldwide with about 50% of them being mechanical valves. The heart valve replacement is often a common treatment for severe valvular disease. However, valves may dysfunction leading to adverse hemodynamic conditions. The current computational study investigated the flow around a bileaflet mechanical heart valve at different leaflet dysfunction levels of 0%, 50%, and 100%, and documented the relevant flow characteristics such as vortical structures and turbulent shear stresses. Studying the flow characteristics through these valves du…
The aim of this paper is to substantiate the importance of non-normality of shear flow linear operators and its consequence -- the non-modal dynamics of the perturbations -- in the formation of acoustic wave output of time-developing free shear/mixing layers. Initially, the linear transient dynamics of spatial Fourier harmonics is considered in a 3D homentropic parallel unbounded inviscid constant shear flow which can model the central/body part of the shear layer. The non-modal approach allows to capture the only linear mechanism of the acoustic wave generation -- \textit{the linear vortex-wa…
A model for the development of turbulent shear flows, created by non-uniform parallel flows in a confining channel, is used to identify the diffuser shape that maximises pressure recovery when the inflow is non-uniform. Wide diffuser angles tend to accentuate the non- uniform flow, causing poor pressure recovery. On the other hand, shallow diffuser angles create longer regions with large wall drag, which is also detrimental to pressure recovery. Thus, optimal diffuser shapes strike a balance between the two effects. We use a simple model which describes the evolution of an approximate flow pro…
Turbulent mixing layers in nature are often characterized by the presence of a mean shear and an unstable buoyancy gradient between two streams of different velocity. Depending on the relative strength of shear versus buoyancy, either the former or the latter may dominate the turbulence and mixing between the two streams. In this paper, we present a phenomenological theory that leads to the identification of two distinct turbulent regimes: an early regime, dominated by the mean shear, and a later regime dominated by the buoyancy. The main theoretical result consists of the identification of a …
The Lagrangian (LA) and Eulerian Acceleration (EA) properties of fluid particles in homogeneous turbulence with uniform shear and uniform stable stratification are studied using direct numerical simulations. The Richardson number is varied from $Ri=0$, corresponding to unstratified shear flow, to $Ri=1$, corresponding to strongly stratified shear flow. The probability density functions (pdfs) of both LA and EA have a stretched-exponential shape and they show a strong and similar influence on the Richardson number. The extreme values of the EA are stronger than those observed for the LA. Geomet…
We perform direct numerical simulations of wall sheared Rayleigh-Bénard (RB) convection for Rayleigh numbers up to $Ra=10^8$, Prandtl number unity, and wall shear Reynolds numbers up to $Re_w=10000$. Using the Monin-Obukhov length $L_{MO}$ we identify three different flow states, a buoyancy dominated regime ($L_{MO} \lesssim λ_θ$; with $λ_θ$ the thermal boundary layer thickness), a transitional regime ($0.5H \gtrsim L_{MO} \gtrsim λ_θ$; with $H$ the height of the domain), and a shear dominated regime ($L_{MO} \gtrsim 0.5H$). In the buoyancy dominated regime the flow dynamics are similar to tha…
The inner-outer interaction model (Marusic, Mathis & Hutchins, Science, vol. 329, 2010, 193-196) and the attached-eddy model (Townsend, Cambridge University Press, 1976) are two fundamental models describing the multi-scale turbulence interactions and the organization of energy-containing motions in the logarithmic region of high-Reynolds number wall-bounded turbulence, respectively. In this paper, by coupling the additive description with the attached-eddy model, the generation process of streamwise wall-shear fluctuations, resulting from wall-attached eddies, is portrayed. Then, by resorting…
We study the experimental properties of exchange flows in a stratified inclined duct (SID), which are simultaneously turbulent, strongly stratified by a mean vertical density gradient, driven by a mean vertical shear, and continuously forced by gravity. We focus on the core shear layer away from the duct walls, where these flows are excellent experimentally-realisable approximations of canonical hyperbolic-tangent stratified shear layers, whose forcing allows mean and turbulent properties to reach quasi steady states. We analyse state-of-the-art data sets of the time-resolved density and veloc…
Relation between shear parameter and Reynolds number in statistically stationary turbulent shear flows
本文研究了近似均匀的统计定常剪切湍流的剪切参数S^* 与雷诺数Re之间的关系。参数研究与最近概述的关于剪切流中局部各向同性的回归的广义观点一致[Schumacher，Sreenivasan and Yeung，Phys. Fluids，vol.15，84（2003）]。因此，系统地改变两个参数，即恒定剪切速率S和由能量注入速率epsilon_{in}规定的初始湍流波动水平。研究表明，剪切参数的水平为更大的雷诺数，这是由尺寸参数支持。结果发现，偏度的横向导数表现出不同的衰减行为，相对于雷诺数时，模拟运行的序列遵循不同的途径在两个参数的平面。该研究可以为高雷诺数实验中奇阶矩衰减的不同解释提供新的思路。
For the gas near a solid planar wall, we propose a scaling formula for the mean free path of a molecule as a function of the distance from the wall, under the assumption of a uniform distribution of the incident directions of the molecular free flight. We subsequently impose the same scaling onto the viscosity of the gas near the wall, and compute the Navier-Stokes solution of the velocity of a shear flow parallel to the wall. This solution exhibits the Knudsen velocity boundary layer in agreement with the corresponding Direct Simulation Monte Carlo computations for argon and nitrogen. We also…
The prediction of turbulent boundary layer (TBL) flow over a convex surface as in aircraft wings or gas turbine blades is a challenging problem. Finding a universal scaling law of turbulence statistics of TBLs over a wide range of adverse pressure gradients (APG) remains unresolved. Here, we introduce characteristic length and velocity scales for APG-TBLs and nondimensionalise the turbulence statistics of the recent canonical self-similar APG-TBLs by Kitsios {\it et al.} ({\it J. Fluid Mech.}, vol.829, 2018, pp. 392--419). The characteristic length scale, which is termed the `shear thickness',…
ENS de Lyon（里昂高等师范学院）；CNRS（法国国家科学研究中心）；LPENSL（理论物理实验室）；Université Paris-Saclay（巴黎萨克雷大学）；CEA（法国原子能和替代能源委员会）；SPEC（物质与环境研究科学与技术中心）；Laboratoire des Sciences du Climat et de l’Environnement（气候与环境科学实验室）；IPSL（地球物理学研究所）
We simulate the flow of two immiscible and incompressible fluids separated by an interface in a homogeneous turbulent shear flow at a shear Reynolds number equal to 15200. The viscosity and density of the two fluids are equal, and various surface tensions and initial droplet diameters are considered in the present study. We show that the two-phase flow reaches a statistically stationary turbulent state sustained by a non-zero mean turbulent production rate due to the presence of the mean shear. Compared to single-phase flow, we find that the resulting steady state conditions exhibit reduced Ta…
Direct numerical simulations (DNS) are performed to study the turbulent shear flow of an electrically conducting fluid in a cylindrical container. The flow is driven by the interaction between the radial electric currents ($I$) injected through a large number of small electrodes at the bottom wall and an axial magnetic field. All the numerical parameters, including the geometry of the container, the total injcected currents and the magnetic field, are in line with the experiment performed in J. Fluid Mech. 456, 137-159. First, witth laminar Hartmann layers, three dimensional simulations recove…
In this Part 2 we study further experimental properties of two-layer exchange flows in a stratified inclined duct (SID), which are turbulent, strongly-stratified, shear-driven, and continuously-forced. We analyse the same state-of-the-art data sets using the same core shear layer methodology as in Part 1, but we focus here on turbulent energetics and mixing statistics. The detailed analysis of kinetic and scalar energy budgets reveals the specificity and scalings of SID turbulence, while energy spectra provide insight into the current strengths and limitations of our experimental data. The ani…
Turbulent emulsions are complex physical systems characterized by a strong and dynamical coupling between small-scale droplets and large-scale rheology. By using a specifically designed Taylor-Couette (TC) shear flow system, we are able to characterize the statistical properties of a turbulent emulsion made of oil droplets dispersed in an ethanol-water continuous solution, at the oil volume fraction up to 40%. We find that the dependence of the droplet size on the Reynolds number of the flow at the volume fraction of 1% can be well described by Hinze's criterion. The distribution of droplet si…
We study the effect of droplet coalescence on turbulent wall-bounded flows, by means of direct numerical simulations. In particular, the volume-of-fluid and front-tracking methods are used to simulate turbulent channel flows containing coalescing and non-coalescing droplets, respectively. We find that coalescing droplets have a negligible effect on the drag, whereas the non-coalescing ones steadily increase drag as the volume fraction of the dispersed phase increases: indeed, at 10\% volume fraction, the non-coalescing droplets show a 30\% increase in drag, whereas the coalescing droplets show…
Small-scale dynamos are ubiquitous in a broad range of turbulent flows with large-scale shear, ranging from solar and galactic magnetism to accretion disks, cosmology and structure formation. Using high-resolution direct numerical simulations we show that in non-helically forced turbulence with zero mean magnetic field, large-scale shear supports small-scale dynamo action, i.e., the dynamo growth rate increases with shear and shear enhances or even produces turbulence, which, in turn, further increases the dynamo growth rate. When the production rates of turbulent kinetic energy due to shear a…
