Turbulent/non-turbulent Interface Research Articles

On The Determination Of Conditional Statistics Along Gradient Trajectories At The Turbulent/Non-Turbulent Interface Of Jet Flows.

Conditional sampling and averaging are valuable techniques for discerning and quantifying notable regions within turbulent flows. These methods have been particularly prevalent in experimental and numerical investigations of turbulent shear flows. Conditional statistics effectively analyze the dynamics and characteristics of turbulent flows, offering insights into transitional behaviors and distinct features within these regimes. This approach is instrumental in studying turbulent shear flows, such as jets or mixing layers, where a well-defined zone separates the turbulent core from the non-turbulent surrounding fluid. This zone, known as the Turbulent/Non-Turbulent Interface (TNTI), plays a crucial role in various phenomenological changes, including the transfer of mass, momentum, and scalar fluxes. While statistics in jet flows are often reported along the radial direction for a given downstream position, this method can obscure the underlying physical processes. Scalar dissipation rate, transport, or turbulent kinetic energy involve velocity or concentration gradients at the flow interface. To date, the impact of sampling direction on conditional statistics within jet flows has not yet been thoroughly discussed. This study focuses on determining gradient trajectories at the interface of turbulent flows. Gradient trajectories have been used to explore structures in turbulent flows, proving effective in analyzing homogeneous shear turbulence. This study introduces a methodology for sampling conditional data by computing gradient trajectories intersecting the TNTI. The primary objective is to verify whether sampling statistics along the gradient of scalar concentration provide a more detailed understanding of the processes occurring near the TNTI. The methodology involves computing a field of gradient trajectories from concentration fields obtained through Planar Laser-Induced Fluorescence (PLIF) in a N2/N2 jet with Re = 2900. Conditional statistics at the TNTI of a jet flow along the gradient trajectory for a given downstream position are calculated and reported. The paper aims to compare conditional statistics along gradient trajectories with those obtained along radial and normal directions at the TNTI. It is expected that gradient trajectory statistics align more closely with normal direction statistics near the interface and diverge as it gets into the jet or coflow fluid.

Move With The Flow To Track The Evolving Turbulent/Non-Turbulent Interface

This study investigates the turbulent/non-turbulent interface (TNTI) in self-similar turbulent axisymmetric jet flows, focusing on a novel approach named ’move with the flow’ where the image acquisition is space-based rather than time-based. Experiments were conducted at three different Reynolds numbers (9000, 12000, and 31000), utilizing particle image velocimetry (PIV) and laser-induced fluorescence (LIF) techniques. The core of this research was developing a traverse system specifically designed to follow the evolving flow structures at the TNTI synchronously. We succeeded in tracking large-scale events in TNTI from creation to dissolution.

Generalized scaling laws for the irrotational motions bordering a turbulent region.

In turbulent free shear flows such as jets and wakes, and also in turbulent boundary layers, the turbulent region is bounded by a region of irrotational flow where the magnitude of the potential velocity fluctuations can be very high. This is particularly true close to the turbulent-nonturbulent interface layer (TNTI) that separates the regions of turbulent (rotational) and nonturbulent (irrotational) fluid motion in these flows. Previous works have shown that for distances from the TNTI x_{2} much bigger than the integral scale L in the nearby turbulent region (x_{2}≫L), the variance of the velocity fluctuations 〈u_{i}^{2}〉 (i=1,2,3) depends on the shape of the kinetic energy spectrum in the infrared region E(k)∼k^{n} [O. M. Phillips, Proc. Camb. Phil. Soc. 51, 220 (1955)10.1017/S0305004100030073; Xavier etal., J. Fluid Mech. 918, A3 (2021)10.1017/jfm.2021.296]. Using rapid distortion theory, we derive the generalized scaling laws for the potential velocity fluctuations, at distances sufficiently far from the TNTI layer, for any value of n. While the cases n=4 (Batchelor turbulence) and n=2 (Saffman turbulence) have been previously derived, with 〈u_{i}^{2}〉∼x_{2}^{-4} and 〈u_{i}^{2}〉∼x_{2}^{-3}, for n=4 and n=2, respectively [O. M. Phillips, Proc. Camb. Phil. Soc. 51, 220 (1955)10.1017/S0305004100030073; Xavier etal., J. Fluid Mech. 918, A3 (2021)10.1017/jfm.2021.296.], we extend these results by including any other value of n. In particular, we obtain 〈u_{i}^{2}〉∼x_{2}^{-2} and 〈u_{i}^{2}〉∼x_{2}^{-4}, for n=1 and n≥5, respectively, while n=3 yields 〈u_{i}^{2}〉∼x_{2}^{-4}ln(x_{2}). These theoretical results are confirmed by direct numerical simulations of turbulent fronts evolving into an irrotational flow region in the absence of mean shear.

The fractal turbulent–non-turbulent interface in the atmosphere

Abstract. With their constant increase in size, wind turbines are reaching unprecedented heights. Therefore, at these heights, they are influenced by wind conditions that have not yet been studied in detail. With increasing height, a transition to laminar conditions becomes more and more likely. In this paper, the presence of the turbulent–non-turbulent interface (TNTI) in the atmosphere is investigated. Three different on- and offshore locations are investigated. Our fractal scaling analysis leads to typical values known from ideal laboratory and numerical studies. The height distribution of the probability of the TNTI is determined and shows a frequent occurrence at the height of the rotor of future multi-megawatt turbines. The indicated universality of the fractality of the TNTI allows the use of simplified models in laboratory and numerical investigations.

Local entrainment across a TNTI and a TTI in a turbulent forced fountain

Local instantaneous exchanges of volume, momentum and buoyancy across turbulent/non-turbulent interfaces (TNTIs) and turbulent/turbulent interfaces (TTIs) are studied using data from direct numerical simulations of a turbulent forced fountain. We apply a novel algorithm that enables independent calculation of the instantaneous local entrainment and detrainment fluxes, and therefore, for the first time, the entrainment and detrainment coefficients according to the fountain model (Bloomfield & Kerr, J. Fluid Mech., vol. 424, 2000, pp. 197–216) are determined explicitly. Across the interface between the fountain and the ambient fluid, which is a TNTI, only volume entrainment occurs, and it is well predicted by the fountain model. Across the interface between the rising upflow and falling downflow within the fountain, which is a TTI, both entrainment and detrainment of volume, momentum and buoyancy occur – with the magnitude of both entrainment and detrainment typically being large compared with the net for all exchanges. However, the model seems to be unable to capture the momentum exchanges due to its ignorance of the pressure. We find that each conditional entrainment and detrainment rate, of volume, momentum and buoyancy, can be described accurately by Gaussian profiles, while the net exchange that is the superposition of the entrainment and detrainment cannot. Moreover, the entrainment exchange rate has its maximum closer to the fountain centreline than that of detrainment, explaining the tendency for net entrainment closer to the fountain centreline and net detrainment further away.

Entrainment, detrainment and enstrophy transport by small-scale vortex structures

The interaction of small-scale vortical structures with the surrounding fluid are studied using a fully resolved three-dimensional experimental data set of homogeneous turbulence measured at the centre of a von Kármán mixing flow facility and a direct numerical simulation (DNS) data set of forced isotropic turbulence. To identify the small-scale vortices and their boundaries, an objective observer-independent definition was implemented to avoid arbitrariness and is the first implementation applied to experimental measurements of small-scale turbulence. Volume-averaged and conditional statistics are presented to demonstrate consistency between the experimental and DNS data sets. To examine the interaction of the structures with the surrounding flow field, we examine the flow across the boundary of vortex structures by adopting a similar methodological approach to that used to investigate the local entrainment and detrainment across the turbulent–non-turbulent interface. The probability density function (p.d.f.) of entrainment velocity conditioned on the vortex boundary exhibited a non-Gaussian distribution that skewed slightly in favour of entrainment and is remarkably similar to the p.d.f.s of entrainment velocity observed in boundary layers and jets. We analyse the enstrophy transport equation conditioned on radial and axial coordinates of the vortices to quantify the inviscid and viscous components of the entrainment/detrainment process. A comparison with Burgers vortices is made and it is found that the Burgers vortex model captures the vortex structure average size and the mechanisms of enstrophy transport in the radial direction, but is unable to capture local statistics and describe the governing physics along the axes of the vortices.

Length scales and the turbulent/non-turbulent interface of a temporally developing turbulent jet

The temporally developing self-similar turbulent jet is fundamentally different from its spatially developing namesake because the former conserves volume flux and has zero cross-stream mean flow velocity whereas the latter conserves momentum flux and does not have zero cross-stream mean flow velocity. It follows that, irrespective of the turbulent dissipation's power-law scalings, the time-local Reynolds number remains constant, and the jet half-width $\delta$ , the Kolmogorov length $\eta$ and the Taylor length $\lambda$ grow identically as the square root of time during the temporally developing self-similar planar jet's evolution. We predict theoretically and confirm numerically by direct numerical simulations that the mean centreline velocity, the Kolmogorov velocity and the mean propagation speed of the turbulent/non-turbulent interface (TNTI) of this planar jet decay identically as the inverse square root of time. The TNTI has an inner structure over a wide range of closely spatially packed iso-enstrophy surfaces with fractal dimensions that are well defined over a range of scales between $\lambda$ and $\delta$ , and that decrease with decreasing iso-enstrophy towards values close to $2$ at the viscous superlayer. The smallest scale on these isosurfaces is approximately $\eta$ , and the length scales between $\eta$ and $\lambda$ contribute significantly to the surface area of the iso-enstrophy surfaces without being characterised by a well-defined fractal dimension. A simple model is sketched for the mean propagation speeds of the iso-enstrophy surfaces within the TNTI of temporally developing self-similar turbulent planar jets. This model is based on a generalised Corrsin length, on the multiscale geometrical properties of the TNTI, and on a proportionality between the turbulent jet volume's growth rate and the growth rate of $\delta$ . A prediction of this model is that the mean propagation speed at the outer edge of the viscous superlayer is proportional to the Kolmogorov velocity multiplied by the $1/4$ th power of the global Reynolds number.

Spatial evolution of the turbulent/turbulent interface geometry in a cylinder wake

This study aims to examine the spatial evolution of the geometrical features of the turbulent/turbulent interface (TTI) in a cylinder wake. The wake is exposed to various turbulent backgrounds in which the turbulence intensity and the integral length scale are varied independently, and comparisons to a turbulent/non-turbulent interface (TNTI) are drawn. The turbulent wake was marked with a high Schmidt number ( $Sc$ ) scalar, and a planar laser induced fluorescence experiment was carried out to capture the interface between the wake and the ambient flow from $x/d = 5$ to 40, where $x$ is the streamwise coordinate from the centre of the cylinder, and $d$ is the cylinder's diameter. It is found that the TTI generally spreads faster towards the ambient flow than the TNTI. A transition region of the interfaces’ spreading is found at $x/d \approx 15$ , after which the interfaces propagate at a slower rate than previously (upstream), and the mean interface positions of both the TNTI and TTI scale with the local wake half-width. The locations of both the TNTI and TTI have non-Gaussian probability density functions (PDFs) in the near wake because of the influence of the large-scale coherent motions present within the flow. Further downstream, after the large-scale coherent motions have dissipated, the TNTI position PDF does become Gaussian. For the first time, we explore the spatial variation of the ‘roughness’ of the TTI, quantified via the fractal dimension, from near field to far field. The length scale in the background flow has a profound effect on the TTI fractal dimension in the near wake, whilst the turbulence intensity becomes important only for the fractal dimension farther downstream.

Turbulent/non-turbulent interfaces in equilibrium and non-equilibrium regions in the absence of mean shear

Direct numerical simulations (DNS) of turbulent fronts evolving into a non-turbulent flow region in the absence of mean shear are generated for both classical (equilibrium) and non-equilibrium turbulence in order to study the characteristics of the turbulent/non-turbulent interface (TNTI) that separates regions of turbulent from non-turbulent (or irrotational) flow. The effects of the non-equilibrium can be observed in a number of statistics computed in the turbulent core region of the turbulent evolving fronts, such as the Reynolds dependance of the normalised dissipation Cɛ, which exhibits a power law (for non-equilibrium turbulence) close to Cɛ∼Reλ−n, where Reλ is the Taylor based Reynolds number and n≈1 is a constant. However the non-equilibrium condition of the turbulent core region does not affect the main characteristics of the TNTI layer bounding this region, which is similar in equilibrium and non-equilibrium turbulence. In particular, the thickness of the TNTI layer is similar in both equilibrium and non-equilibrium turbulence.

Reynolds number dependence of the turbulent/non-turbulent interface in temporally developing turbulent boundary layers

Direct numerical simulations (DNS) of temporally developing turbulent boundary layers are performed with a wide range of Reynolds numbers based on the momentum thickness $Re_{\theta } = 2000$ – $13\,000$ for investigating the Reynolds number dependence of the turbulent/non-turbulent interface (TNTI) layer. The grid spacing in the DNS is determined carefully such that small-scale turbulent motions near the TNTI are well resolved. The outer edge of the TNTI layer, called the irrotational boundary, is detected with vorticity magnitude. The mean thicknesses of the TNTI layer, $\delta _{TNTI}$ , turbulent sublayer, $\delta _{TSL}$ , and viscous superlayer, $\delta _{VSL}$ , are found to be approximately $15\eta _{TI}$ , $10\eta _{TI}$ and $5\eta _{TI}$ , respectively, where $\eta _{TI}$ is the Kolmogorov scale taken in the turbulent region near the TNTI layer. The mean curvature of the irrotational boundary is also characterized by $\eta _{TI}$ . The shear parameter and the shear-to-vorticity ratio show that the mean shear effects near the TNTI layer are not significant for both large and small scales. The anisotropy tensors of Reynolds stress and vorticity suggest that the turbulence under the TNTI layer tends to be isotropic at high $Re_{\theta }$ , for which $\eta _{TI}/\delta \sim Re_{\theta }^{-3/4}$ is valid with the boundary layer thickness $\delta$ . The surface area of the irrotational boundary is consistent with the fractal analysis of the interface, where the fractal dimension $D_f$ is found to be $2.14$ – $2.20$ . The present results suggest that the mean entrainment rate per unit horizontal area normalized by the friction velocity varies slowly as $Re_{\theta }^{(3/4)(D_f-2)}$ for $Re_{\theta } \geq 4000$ .

Entrainment mechanism of turbulent synthetic jet flow

Synthetic jets have received extensive attention due to their superior mixing property. However, its mechanisms have not been investigated from the perspective of the turbulent/non-turbulent interface (TNTI). To shed new light on this issue, the entrainment and TNTI properties of a synthetic jet are experimentally investigated and compared with a continuous jet at $Re_j = 3150$ . The fuzzy clustering method is applied to select an appropriate vorticity threshold to detect the TNTI. Statistically, it is revealed that the entrainment coefficients of the two jets significantly differ in the near field, while they become almost identical in the far field. Instead of the vortex ring, the ‘breakdown of the vortex ring’ enhances the entrainment in the present synthetic jet. Instantaneously, the TNTI more violently fluctuates in the near field of the synthetic jet, which leads to a larger fluctuation in the TNTI radial position, a higher fractal dimension and enhanced local entrainment. Moreover, the transition of the probability density function of the TNTI orientation from the unimodal distribution in the near field to the bimodal distribution in the far field is found in both jets. The multi-scale analysis reveals a new mechanism for the bimodal distribution caused by the TNTI-thickness-scale structures.

On the definition, evolution, and properties of the outer edge of gravity currents: A direct-numerical and large-eddy simulation study

Gravity currents are flows driven by the action of gravity over fluids with different densities. Here, we focus on gravity currents where heavier fluid travels along the bottom of a sloping bed, underneath a large body of stagnant lighter ambient fluid. The thickness of the current increases due to entrainment of ambient fluid into the current. Direct numerical and large eddy simulations of gravity currents and a wall-jet transporting a passive scalar field are performed. We focus on the rate of penetration of mean momentum and mean concentration of the agent responsible for the density difference (temperature, salinity, or sediment volume fraction) into the ambient fluid. The rates of penetration of turbulence-related quantities (i.e., turbulent kinetic energy, Reynolds flux, and stress) into the ambient are analyzed. A robust methodology for defining the upper edge of these quantities and thereby defining the current thickness using these different mean and turbulent quantities is presented. A comparison between downstream evolution of the gravity current with the corresponding behaviors of canonical wall-bounded turbulent flows is presented. The present understanding of turbulent/non-turbulent interface (TNTI) is extended to include subcritical flows where, due to the strong effect of stratification, the TNTI is buried well within the upper edge of the current and confined right above the inner near-bed layer. The present work sheds light on the striking difference between the different definitions of thickness (momentum, concentration, turbulence, etc.) in subcritical gravity currents, where stratification suppresses turbulence in the upper region of the current.

Universal modulations of large-scale motions on entrainment of turbulent boundary layers

The modulations of high/low-speed large-scale motions (H/L-SMs) on the turbulent/non-turbulent interface (TNTI) and turbulent entrainment are investigated in turbulent boundary layers via both experimental and numerical studies. The spanwise locations of large-scale motions can be locked by the spanwise heterogeneity, so the boundary layers over such a configuration are investigated first as an instructive case. In the engulfment process, it is found that irrotational ‘bubbles’ near the TNTI are more likely to originate from engulfment, while bubbles far from the TNTI could be produced by the local turbulence itself. Additionally, H-SMs are found to enhance the engulfment by the sweep flow. In the nibbling process, a competition relationship is observed: L-SMs induce stronger instantaneous ‘nibbling’ events by transporting more fluids towards the TNTI, while the H-SMs induced a more distorted TNTI. Consequently, the integral nibbling flux is greater above H-SMs. Furthermore, the explored mechanisms are verified to be insensitive to the wall shapes such as smooth and homogeneous roughness walls, which demonstrates that these modulations are universal for turbulent boundary layers. Finally, a conceptual modulation model is proposed to illustrate the entrainment process above the large-scale motions.

Large eddy simulations of single and multiple turbulent round jets

We present results from three large eddy simulations (LES). The first two were those of a single jet at a Reynolds number of 11000 with different cell density distributions. The simulation results are validated with earlier experimental and computational studies at the same Reynolds number and almost the same boundary conditions. We establish the repeatability and reproducibility of the characterisation of a single axisymmetric jet. Additionally, we performed an LES of five round jets using the same discretisation schemes and boundary conditions. The five jets were placed in a cross or plus configuration, with a central jet surrounded by four outer jets. The mass flux, momentum flux and the Reynolds number of the five jet configuration were set to be equal to those of the single jet. Further, we analyse the near-field development of the multiple jets, along with entrainment and symmetry characteristics as the jet evolves. LES's ability to provide information about large-scale motions was used to compute conditional statistics. We, then, present details of an initial attempt to characterise the turbulent non-turbulent interface boundary and the coherent structures in the core of the jet in a unified manner using helicity density as the detector variable.

Turbulent entrainment in viscoelastic fluids

Direct numerical simulations (DNS) of turbulent fronts spreading into an irrotational flow region are used to analyse the turbulent entrainment mechanism for viscoelastic fluids. The simulations use the FENE-P fluid model and are initiated from DNS of isotropic turbulence with Weissenberg and turbulence Reynolds numbers varying in the ranges $1.30 \le Wi \le 3.46$ and $206 \le Re_{\lambda }^{0} \le 404$, respectively. The enstrophy dynamics near the turbulent/non-turbulent interface (TNTI) layer, that separates regions of turbulent and irrotational flow, includes a new mechanism – the viscoelastic production – caused by the interaction between the vorticity field and the polymer stresses. This term can be a sink or a source of enstrophy in the turbulent core region of the flow, depending on the Weissenberg number, and contributes to the initial growth of the enstrophy in the viscous superlayer, together with the viscous diffusion, which is the only mechanism present for Newtonian fluids. For low and moderate Weissenberg numbers the scaling of the TNTI layer is similar to the scaling of TNTI layers for Newtonian fluids, but this is no longer the case at high Weissenberg numbers where the enstrophy tends to be concentrated into thin vortex sheets instead of vortex tubes. Finally, it is shown that the substantial decrease of the entrainment rates observed in turbulent flows of viscoelastic fluids, compared with Newtonian fluids, is caused by a reduction of the surface area and fractal dimension of the irrotational boundary, originated by the depletion of ‘active’ scales of motion in the fluid solvent caused by the viscoelasticity.

Evolution of turbulent boundary layer over a three-dimensional bump

A bump is typically used in the inlet system of an aircraft engine to compress the incoming airflow and to reduce boundary layer thickness developed over fuselage. In this work, the turbulent flow over a three-dimensional bump is experimentally studied. The bump model is mounted in a closed return wind tunnel operated at the nominal velocity 10 m/s, corresponding to a friction Reynolds number of 2300. The flow field upstream the bump, along the bump centerline and at two different spanwise planes is measured with Particle Image Velocimetry (PIV). It is observed that a favorable pressure gradient develops until the suction peak of the bump, and that the average turbulence intensity within boundary layer is attenuated due to this favorable pressure gradient. The boundary layer thickness identified by examining profiles of streamwise velocity decreases significantly along the bump. The wall-normal position of the Turbulent/Non-Turbulent Interface (TNTI) identified with the vorticity criterion is also observed to decrease along the bump. When studying the behavior of the boundary layer thickness at different spanwise positions, we found that it tends to be larger in planes away from the centreline, which suggests that the bump diverts the flow.

Experimental investigations of the turbulent/non-turbulent interface over surface with spanwise heterogeneity

The sharp but irregular interface that separates the instantaneous turbulent and irrotational flows is termed as the turbulent/non-turbulent interface (TNTI). TNTI can be widely observed in various types of flow, such as turbulent boundary layers, jets and combustion flame fronts. Due to its importance on the intermittency and entrainment process, TNTI has been widely explored in its geometry and dynamic properties (da Silva et al., 2014). Most of the studies focus on the TNTIs in smooth plane boundary layer, while few investigate the effects of wall shapes. However, the wall conditions in many engineering applications are complex and heterogeneous, which will induce large-scale heterogeneity (Barros and Christensen, 2014) and require further investigations. To shed new light on the intermittency and entrainment above complex surfaces, the TNTI over spanwise heterogeneity are investigated here with time-resolved stereoscopic PIV (TR-SPIV). The model and TR-SPIV experimental set-up are shown in Fig. 1. The experiments are conducted in the low-speed water channel at Beijing University of Aeronautics and Astronautics. The spanwise distance S between two adjacent ridges is S/(δ) = 1.35, where (δ) is the spanwise-averaged boundary layer thickness. This spanwise distance is selected to induced strong secondary vortices (Vanderwel and Ganapathisubramani, 2015; Wangsawijaya et al., 2020). The Reynolds number based on the streamwise location x is Rex = 7.2×105. The field of view is around 2S×1.8S, and is captured by two CMOS cameras (2048×2048 pixel) with sampling rate as 500Hz. The averaged resolution is about 8 pixels per Kolmogorov scale (calculated at y/(δ) = 0.6), which is high enough for TNTI-related research (Borrell and Jimenez, 2016). The ´TNTI is detected by the magnitude of local enstrophy ω2/2, and the threshold is selected to be the value where changing the threshold has the smallest influence on the TNTI-mean-height (Watanabe et al., 2018). The time-mean velocity and TNTI location are present in Fig.2(a). A pair of counter-rotating largescale secondary vortices (SVs) are induced over the ridge-type roughness. At the position where SVs induce upwash flow, a low-momentum pathway (LMP) can be observed, while the time-mean height of TNTI (yI) is brought higher. As a contrast, where downwash flow induces high-momentum pathway (HMP), (yI) is lower. TNTI properties are further discussed from two aspect. The geometry properties are firstly investigated. The fractal dimension of the TNTI keeps as 2.3 along the spanwise direction. This value is consistent with the result over smooth plate (Borrell and Jimenez, 2016; Wu et al., 2020) and riblets plates(Cui et al., 2019),´ which indicates that the wall shapes do not influence the multiscale properties of the TNTI. The streamwise wavelength of the TNTI (λI) is further obtained by calculating the streamwise pre-multiplied spectrum of the TNTI. It is found that at each spanwise location, λI is identical to the wavelength of streamwise velocity fluctuation at the TNTI mean height. This shows that the large-scale fluctuation of TNTI is controlled by the large-scale streamwise velocity fluctuation structures. Secondly, the p.d.f. of TNTI instantaneous height is investigated, as shown in Fig. 2(b). It can be observed that the p.d.f. of TNTI height above LMP shows a negative skewness, while the p.d.f. above HMP skews positively. A closer look at instantaneous structures shows that the skewness is attributed to the different probability of Q2/Q4 events in LMP and HMP.

A Lagrangian Study of Interfaces at the Edges of Cumulus Clouds

AbstractInterfaces at the edge of an idealized, nonprecipitating, warm cloud are studied using direct numerical simulation (DNS) complemented with a Lagrangian particle tracking routine. Once a shell has formed, four zones can be distinguished: the cloud core, visible shell, invisible shell, and the environment. The union of the visible and invisible regions is the shell commonly referred to in literature. The boundary between the invisible shell and the environment is the turbulent–nonturbulent interface (TNTI), which is typically not considered in cloud studies. Three million particles were seeded homogeneously across the domain and properties were recorded along individual trajectories. The results demonstrate that the traditional cloud boundary (separating cloudy and noncloudy regions using thresholds applied on liquid condensate or updraft velocity) are some distance away from the TNTI. Furthermore, there is no dynamic difference between the traditional liquid-condensate boundary and the region extending to the TNTI. However, particles crossing the TNTI exhibit a sharp jump in enstrophy and a smooth increase in buoyancy. The traditional cloud boundary coincides with the location of minimum buoyancy in the shell. The shell premixes the entraining and detraining air and analysis reveals a highly skewed picture of entrainment and detrainment at the traditional cloud boundary. A preferential entrainment of particles with velocity and specific humidity higher than the mean values in the shell is observed. Large-eddy simulation of a more realistic setup detects an interface with similar properties using the same thresholds as in the DNS, indicating that the DNS results extrapolate beyond their idealized conditions.

Universality of small-scale motions within the turbulent/non-turbulent interface layer

Abstract

Mechanisms of entrainment in a turbulent boundary layer

Data from direct numerical simulation of a zero-pressure-gradient incompressible turbulent boundary layer (TBL) [You and Zaki, “Conditional statistics and flow structures in turbulent boundary layers buffeted by free-stream disturbances,” J. Fluid Mech. 866, 526 (2019)] are analyzed to examine the entrainment process. The two mechanisms by which the outer irrotational flow can be entrained into the turbulent region and their relative contribution to the growth of the spatially developing boundary layer are evaluated: (i) nibbling is the enstrophy transport across the turbulent/non-turbulent interface (TNTI), and (ii) engulfment is the entrapment of pockets of irrotational flow inside the TBL prior to finally breaking apart. The relative importance of the two mechanisms depends on the normalized vorticity threshold adopted to identify the TNTI. Our choice of this threshold highlights the structure of the TNTI and entrainment within this layer by engulfment of irrotational pockets. The sizes of the engulfed pockets are of the same order as the heads of the hairpin vortices underneath the TNTI. The vortices straddle larger streaky structures of internal layers and cause handle shaped deformations on the TNTI, which leads to engulfment as they fold onto themselves and entrap the external potential flow. Three dynamical regions are distinguished: a TNTI region (interface layer), an adjustment region, and the turbulent core. The first of these is further sub-divided into a viscous superlayer and a turbulent sublayer. It is shown as the irrotational fluid elements cross the interface layer toward the turbulent core, a smooth transition from the non-focal topology to the well-known primarily focal topology of fully developed turbulence occur. The viscous superlayer is similar to previously studied flow configurations, such as jets and mixing layers. In contrast, vorticity stretching in the turbulent sublayer is significantly weaker in the boundary layer relative to free-shear flows, which results in a smaller rate of entrainment by nibbling.