In this paper, we employ Lagrangian coherent structures (LCSs) theory for the three dimensional vortex eduction and investigate the effect of large-scale vortical structures on the turbulent/non-turbulent interface (TNTI) and entrainment of a gravity current. The gravity current is realized experimentally and different levels of stratification are examined. For flow measurements, we use a multivolume three-dimensional particle tracking velocimetry technique. To identify vortical LCSs (VLCSs), a fully automated 3D extraction algorithm for multiple flow structures based on the so-called Lagrangian-Averaged Vorticity Deviation method is implemented. The size, the orientation and the shape of the VLCSs are analyzed and the results show that these characteristics depend only weakly on the strength of the stratification. Through conditional analysis, we provide evidence that VLCSs modulate the average TNTI height, affecting consequently the entrainment process. Furthermore, VLCSs influence the local entrainment velocity and organize the flow field on both the turbulent and non-turbulent sides of the gravity current boundary.
We analyse the flow organization of turbulent fountains in stratified media under different conditions, using three-dimensional finite-time Lyapunov exponents. The dominant Lagrangian coherent structures responsible for the transport barriers in three different configurations suggest a self-similarity behaviour. After proposing a criterion for delimiting the boundary surface of the uprising fountain, we quantify the entrainment and re-entrainment rates under fully developed flow conditions using the proper coefficients. Finally, our analysis was applied to the Selective Inverted Sink, a techno…
Understanding and modeling turbulent fluxes and entrainment in a gravity current
本文对重力流在斜面上的混合过程进行了实验研究。动量和密度的湍流输运可以用一个非常直接和紧凑的形式来描述，由普朗特混合长度模型：湍流的动量和密度的垂直通量被发现与速度和密度的垂直平均梯度成二次比例。比例系数，混合长度的平方，是近似恒定的混合区的分层剪切层。我们展示了在不同的流动构型中，这个长度如何与流动的剪切长度（$ε$ / $\partial$ z u ^3）^[1/2]相关。我们还研究了动量和密度湍流通量的波动，展示了它们如何与混合和夹带/分离平衡。我们提出了一个定量的措施，来自所观察到的密度通量和密度或垂直速度波动的条件相关性的本地夹带和detrainment。
The effect of freestream turbulence on the spreading of the near wake of a circular cylinder is investigated through particle image velocimetry (PIV) data. Different ``flavours'' of freestream turbulence, in which the turbulence intensity and integral length scale are independently varied, are subjected to the cylinder. The time-averaged spreading of the near wake is decoupled into the growth through entrainment and the envelope of the spatial extent of the instantaneous wake due to wake ``meandering'', induced by the presence of large-scale coherent structures, i.e. the von Karman vortex stre…
We use laboratory experiments to investigate the entrainment of ambient fluid into an axisymmetric turbulent plume that contains dense particles with a settling velocity that is considerably smaller than the plume velocity. We consider the effect of particle size, particle concentration, and the orientation of the plume buoyancy flux - either in the same or opposite direction to the particle buoyancy flux. When the plume buoyancy flux is in the opposite direction to the particle buoyancy flux, entrainment into the plume increases by up to 40%. The rate of entrainment increases linearly with th…
An experimental Lagrangian study based on particle tracking velocimetry has been completed in an incompressible turbulent round water jet freely spreading into water. The jet is seeded with tracers only through the nozzle: inhomogeneous seeding called nozzle seeding. The Lagrangian flow tagged by these tracers therefore does not contain any contribution from particles entrained into the jet from the quiescent surrounding fluid. The mean velocity field of the nozzle seeded flow, $\langle \boldsymbol{U_φ} \rangle$, is found to be essentially indistinguishable from the global mean velocity field …
We present a mathematical description of turbulent entrainment that is applicable to free shear problems that evolve in space, time or both. Defining the global entrainment velocity $\overline V_g$ to be the fluid motion across an isosurface of an averaged scalar, we find that for a slender flow, $\overline V_g=\overline u_ζ- \overline{D}h_t/\overline{D}t$, where $\overline D/\overline D t$ is the material derivative of the average flowfield and $\overline u_ζ$ is the average velocity perpendicular to the flow direction across the interface located at $ζ=h_t$. The description is shown to repro…
This investigation is based on a DNS of a steady self-preserving incompressible axisymmetric turbulent jet at a Reynolds number of 2400. The DNS data enable accurate maps of the outer irrotational flow field, and also the vorticity field in the turbulent core of the jet. It is found necessary to define two separate boundaries of the jet. The first is an inner boundary (turbulent/nonturbulent, T/NT), from where vorticity rises steeply towards to the core. The second is an outer rotational/irrotational boundary, beyond which the flow may be considered irrotational. The velocity field beyond the …
We analyse the entrainment and energetics of equal and opposite axisymmetric turbulent air plumes in a vertically confined space at a Rayleigh number of $1.24\times 10^{7}$ using theory and direct numerical simulation. On domains of sufficiently large aspect ratio, the steady state consists of turbulent plumes penetrating an interface between two layers of approximately uniform buoyancy. As described by Baines and Turner (J. Fluid Mech. vol. 37, 1969, pp. 51-80), upon penetrating the interface the flow in each plume becomes forced and behaves like a constant-momentum jet, due to a reduction in…
We investigate ambient fluid entrainment and near-field flow characteristics of a free surface plunging jet for five Reynolds numbers ranging from 3000 to 10000 using time-resolved stereo particle image velocimetry (SPIV). We present time-averaged velocities, RMS velocity fluctuations, mean entrainment and unsteady flow features and compare them with previous studies on free jets. We find that plunging jets have a smaller potential core length, and earlier decay of the mean centerline velocity. The peak RMS velocity fluctuations occur at a location significantly upstream compared to the free j…
The air entrainment due to the turbulence in a free surface boundary layer shear flow created by a horizontally moving vertical surface-piercing wall is studied through experiments and direct numerical simulations. In the experiments, a laboratory-scale device was built that utilizes a surface-piercing stainless steel belt that travels in a loop around two vertical rollers, with one length of the belt between the rollers acting as a horizontally-moving flat wall. To complement the experiments, Direct Numerical Simulations (DNS) of the two-phase boundary layer problem were carried out with the …
We explore the dynamics of inclined temporal gravity currents using direct numerical simulation, and find that the current creates an environment in which the flux Richardson number $Ri_f$, gradient Richardson number $Ri_g$, and turbulent flux coefficient $Γ$ are constant across a large portion of the depth. Changing the slope angle $α$ modifies these mixing parameters, and the flow approaches a maximum Richardson number $Ri_\textrm{max}\approx 0.15$ as $α\rightarrow 0$ at which the entrainment coefficient $E \rightarrow 0$. The turbulent Prandtl number remains $O(1)$ for all slope angles, dem…
Entrainment in cumulus convection remains ill-understood and difficult to quantify. For instance, entrainment is widely believed to be a fundamentally turbulent process, even though Turner (1957) pointed out that dry thermals entrain primarily because of buoyancy (via a dynamical constraint requiring an increase in radius $r$), rather than turbulence. Furthermore, entrainment has been postulated to obey a $1/r$ scaling, but this scaling has not been firmly established. Here, we study the classic case of dry, turbulent thermals in a neutrally stratified environment using fully resolved direct n…
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 experimentally investigate the effects on scaling of separating/reattaching flows of the ratio $δ_e/h$, where $δ_e$ is the thickness at separation of the incoming boundary layer and $h$ the characteristic cross-stream scale of the flow. In the present study, we propose an original approach based on mean mass entrainment, which is the driving mechanism accounting for the growth of the separated shear layer. The focus is on mass transfer at the Turbulent/Non-Turbulent Interface (TNTI). In particular, the scaling of the TNTI, which is well documented in turbulent boundary layers, is used to tr…
\citet{turner1957} proposed that dry thermals entrain because of buoyancy (via a constraint which requires an increase in the radius $a$). This however, runs counter to the scaling arguments commonly used to derive the entrainment rate, which rely on either the self-similarity of \citet{scorer1957} or the turbulent entrainment hypothesis of \citet{morton1956}. The assumption of turbulence-driven entrainment was investigated by \citet{lecoanet2018}, who found that the entrainment efficiency $e$ varies by less than $20\%$ between laminar (Re = 630) and turbulent (Re = 6300) thermals. This motiva…
Passive scalar mixing, produced by Lagrangian chaos generated a) by quasi-periodic (integrable) motion of three quasi-point vortices and b) by chaotic motion of three and six quasi-point vortices, has been studied and compared with turbulent mixing of passive scalar in 2D and 3D steady isotropic homogeneous turbulence and in turbulent wakes behind grid and behind cylinder. Results of numerical and laboratory experiments have been used and effective diffusivity approximation as well as distributed chaos approach have been applied to this problem.
A closure theory is developed for inhomogeneous turbulent flow, which enables a systematic derivation of the turbulence constitutive relations without relying on any empirical parameters. Renormalized-perturbation approximation is performed in the convective coordinate frame based on the mean flow, successfully incorporating the convective integration in generally covariant manner.
A temporal complex network-based approach is proposed as a novel formulation to investigate turbulent mixing from a Lagrangian viewpoint. By exploiting a spatial proximity criterion, the dynamics of a set of fluid particles is geometrized into a time-varying weighted network. Specifically, a numerically solved turbulent channel flow is employed as an exemplifying case. We show that the time-varying network is able to clearly describe the particle swarm dynamics, in a parametrically robust and computationally inexpensive way. The network formalism enables to straightforwardly identify transient…
We investigate the Lagrangian statistics of three-dimensional rotating turbulent flows through direct numerical simulations. We find that the emergence of coherent vortical structures because of the Coriolis force leads to a suppression of the "flight-crash" events reported by Xu, et al. [Proc. Natl. Acad. Sci. (U.S.A) 111, 7558 (2014)]. We perform systematic studies to trace the origins of this suppression in the emergent geometry of the flow and show why such a Lagrangian measure of irreversibility may fail in the presence of rotation.
The mechanism of turbulent viscosity is the central question in investigations of turbulence. This is also the case in the accretion disk theory, where turbulence is considered to be responsible for the outward transport of angular momentum in the accretion disk. In turbulent flows, vortices transport momentum over their length scales providing the mechanism of viscosity that is controlled by mass entrainment. We have earlier proposed an entrainment model for the particular case of the relativistic jets in the radio galaxy 3C31. In this paper, we further constrain the model parameters. The mod…
A Lagrangian experimental study of an axisymmetric turbulent water jet is performed to investigate the highly anisotropic and inhomogeneous flow field. The measurements were conducted within a Lagrangian exploration module, an icosahedron apparatus, to facilitate optical access of three cameras. The stereoscopic particle tracking velocimetry results in three component tracks of position, velocity and acceleration of the tracer particles within the vertically-oriented jet with a Taylor-based Reynolds number $\mathcal R_λ\simeq 230$. Analysis is performed at seven locations from 15 diameters up …
Spatial regions that do not mix effectively with their surroundings and thus contribute less to the heat transport in fully turbulent three-dimensional Rayleigh-Bénard flows are identified by Lagrangian trajectories that stay together for a longer time. These trajectories probe Lagrangian coherent sets (CS) which we investigate here in direct numerical simulations in convection cells with square cross section of aspect ratio $Γ= 16$, Rayleigh number $Ra = 10^{5}$, and Prandtl numbers $Pr = 0.1, 0.7$ and $7$. The analysis is based on $N=524,288$ Lagrangian tracer particles which are advected in…
We analyze large-scale patterns in three-dimensional turbulent convection in a horizontally extended square convection cell by Lagrangian particle trajectories calculated in direct numerical simulations. A simulation run at a Prandtl number Pr $=0.7$, a Rayleigh number Ra $=10^5$, and an aspect ratio $Γ=16$ is therefore considered. These large-scale structures, which are denoted as turbulent superstructures of convection, are detected by the spectrum of the graph Laplacian matrix. Our investigation, which follows Hadjighasem {\it et al.}, Phys. Rev. E {\bf 93}, 063107 (2016), builds a weighted…
The Lagrangian approach is natural to study issues of turbulent dispersion and mixing. We propose in this work a general Lagrangian stochastic model including velocity and acceleration as dynamical variables for inhomogeneous turbulent flows. The model takes the form of a diffusion process and the coefficients of the model are determined via Kolmogorov theory and the requirement of consistency with the velocity-based models. It is shown that the present model generalises both the acceleration-based models for homogeneous flows and the generalised Langevin models for the velocity. The resulting…
We investigate the ability of 4D Particle Tracking Velocimetry measurements at high particle density to explore intermittency and irreversibility in a turbulent swirling flow at various Reynolds numbers. For this, we devise suitable tools to remove the experimental noise, and compute the statistics of both Lagrangian velocity increments and wavelet coefficients of the Lagrangian power (the time derivative of the kinetic energy along a trajectory). We show that the signature of noise is strongest on short trajectories, and results in deviations from the regularity condition at small time scales…
Due to large scale flow inhomogeneities and the effects of temperature, turbulence small-scale structure in thermal convection is still an active field of investigation, especially considering sophisticated Lagrangian statistics. Here we experimentally study Lagrangian pair dispersion (one of the canonical problems of Lagrangian turbulence) in a Rayleigh-Bénard convection cell. A sufficiently high temperature difference is imposed on a horizontal layer of fluid to observe a turbulent flow. We perform Lagrangian tracking of sub-millimetric particles on a large measurement volume including part …
