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Objective: The flow downstream from aortic stenoses is characterised by the onset of shear-induced turbulence that leads to irreversible pressure losses. These extra losses represent an increased resistance that impacts cardiac efficiency. A novel approach is suggested in this study to accurately evaluate the pressure gradient profile along the aorta centreline using modelling of haemodynamic stress at scales that are smaller than the typical resolution achieved in experiments. Methods: We use benchmark data obtained from direct numerical simulation (DNS) along with results from in silico and in vitro three-dimensional particle tracking velocimetry (3D-PTV) at three voxel sizes, namely 750 $\mu$ m, 1 mm and 1.5 mm. A differential equation is derived for the pressure gradient, and the subvoxel-scale (SVS) stresses are closed using the Smagorinsky and a new refined model. Model constants are optimised using DNS and in silico PTV data and validated based on pulsatile in vitro 3D-PTV data and pressure catheter measurements. Results: The Smagorinsky-based model was found to be more accurate for SVS stress estimation but also more sensitive to errors especially at lower resolution, whereas the new model was found to more accurately estimate the projected pressure gradient even for larger voxel size of 1.5 mm albeit at the cost of increased sensitivity at this voxel size. A comparison with other methods in the literature shows that the new approach applied to in vitro PTV measurements estimates the irreversible pressure drop by decreasing the errors by at least 20%. Conclusion: Our novel approach based on the modelling of subvoxel stress offers a validated and more accurate way to estimate pressure gradient, irreversible pressure loss and SVS stress. Significance: We anticipate that the approach may potentially be applied to image-based in vivo , in vitro 4D flow data or in silico data with limited spatial resolution to assess pressure loss and SVS stresses in disturbed aortic blood flow.

We present a novel stochastic model for quantifying gross solids (GS) physical disintegration under varying turbulent flow conditions and used a unique experimental setup for model calibration and validation. The stochastic deterioration model predicts faeces size evolution over time. It conceptually entails the two main processes of solid fragmentation, namely breakage and erosion. Model parameters were calibrated on synthetic faeces and validated with real human ones. A cylindrical reactor was used, where turbulent flow was forced by an array of water jets and the physical disintegration of the faeces was monitored using a high speed camera. Image analysis of breakage experiments obtained under backlight illumination allowed determination of the evolution of the solids' size over time. The flow field in the reactor was characterised by particle image velocimetry (PIV) using tracer particles seeded into the water. We found different disintegration behaviours depending on turbulence intensity and water content of the solid. In conditions of low shear stress, dense solids hardly disintegrated. Generally, the model predictions mirrored the broad range in the solids disintegration rate imparted by the high variability in flow conditions and in solids characteristics. It is expected that, similar to our experiments, also in real sewer systems both flow conditions and solid characteristics are highly variable and the stochastic model can be tailored to capture this variability. We thus anticipate that the model can be integrated into existing sewer models predicting sewer flows and solids' movement. From these, shear stress, flow velocities and transport of individual solids can be inferred. The integration of the present solids disintegration model may provide better predictions of hot-spots for solids accumulation and blockages in sewers.

Turbulent mixing layers in nature are often characterised by the presence of a mean shear and an unstable buoyancy gradient between two streams of different velocities. 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 mean shear, and a later regime dominated by buoyancy. The main theoretical result consists of the identification of a cross-over timescale that distinguishes between the shear- and the buoyancy-dominated turbulence. This cross-over time depends on three large-scale constants of the flow, namely, the buoyancy difference, the velocity difference between the two streams and the gravitational acceleration. We validate our theory against direct numerical simulations of a temporal turbulent mixing layer compounded with an unstable stratification. We observe that the cross-over time correctly predicts the transition from shear- to buoyancy-driven turbulence, in terms of turbulent kinetic energy production, energy spectra scaling and mixing layer thickness., Journal of Fluid Mechanics, 924, ISSN:0022-1120, ISSN:1469-7645

The surface area of turbulent/non-turbulent interfaces (TNTIs) is continuously produced and destroyed via stretching and curvature/propagation effects. Here, the mechanisms responsible for TNTI area growth and destruction are investigated in a turbulent flow with and without stable stratification through the time evolution equation of the TNTI area. We show that both terms have broad distributions and may locally contribute to either production or destruction. On average, however, the area growth is driven by stretching, which is approximately balanced by destruction by the curvature/propagation term. To investigate the contribution of different length scales to these processes, we apply spatial filtering to the data. In doing so, we find that the averages of the stretching and the curvature/propagation terms balance out across spatial scales of TNTI wrinkles and this scale-by-scale balance is consistent with an observed scale invariance of the nearby coherent vortices. Through a conditional analysis, we demonstrate that the TNTI area production (destruction) is localized at the front (lee) edge of the vortical structures in the interface proximity. Finally, we show that while basic mechanisms remain the same, increasing stratification reduces the rates at which TNTI surface area is produced as well as destroyed. We provide evidence that this reduction is largely connected to a change in the multiscale geometry of the interface, which tends to flatten in the wall-normal direction at all active length scales of the TNTI.

In this paper, we investigate the enstrophy dynamics in relation to objective Eulerian coherent structures (OECSs) and their impact on the enstrophy and scalar transport near the turbulent/non-turbulent interface (TNTI) in flows with and without stable stratification. We confirm that vortex-stretching produces enstrophy inside the boundaries of the OECSs, while viscous diffusion transfers the enstrophy across the boundaries of the structures. Although often overlooked in the literature, viscous dissipation of enstrophy within the boundaries of vortical structures is significant. Conversely, for the weakly stratified flows also investigated here, the effect of the baroclinic torque is negligible. We provide evidence that the OECSs advect the passive/active scalar and redistribute it via molecular diffusion. Finally, we use conditional analysis to show that the typical profiles of the enstrophy and scalar transport equation terms across the TNTI are compatible with the presence of OECSs positioned at the edge between the turbulent sublayer and the turbulent core region. We show that when these profiles are further conditioned to the presence of OECSs, their magnitude is considerably higher.

Flow fields in rotary blood pumps (RBPs) have a significant influence on hemocompatibility. Because flow characteristics vary with flow rate, different operating conditions play a role. Furthermore, turbulence is crucial in the evaluation of blood damage potential, but the level of turbulence in implantable RBPs is still unknown. In this study, we addressed both research aspects and for the first time measured turbulent flow fields in the HeartMate 3 (HM3) at different operating flows. The averaged, three-dimensional velocity field including fluctuating velocity components in a HM3 with a transparent lower housing was measured using three-dimensional particle tracking velocimetry (3D-PTV). In vitro results were compared with computational fluid dynamic (CFD) simulations for two flow cases, representing the lower and upper physiologic flow range (2.7 and 5.7 L/min), using two different turbulence models that account for fluctuating velocity fields: the k-ω shear stress transport and the Reynolds stress model (RSM). The measurements revealed higher mean and turbulent kinetic energies (TKEs) for the low-flow condition especially within the gap beneath the impeller. Computed mean fields agree well with 3D-PTV for both models, but the RSM predicts the TKE levels better than the k-ω model. Computational fluid dynamic results further show wall shear stresses higher than 150 Pa, a commonly used damage threshold, in the bottom gap for the lower flow condition. In conclusion, the low-flow condition was found to be more prone to blood damage. Furthermore, CFD predictions for turbulence must be carefully experimentally validated.

Climate model parametrization relies strongly on the prediction of snow precipitation, which in turn depends upon the snowflakes falling motion in air. The falling attitudes of such particles are elaborate because of the particles' irregular shapes, which produce meandering and turbulent wakes and give rise to convoluted trajectories. This also has an impact on the drag experienced by the particle. Especially for large snow particles falling close to the ground, Stokesian dynamics is not applicable, and the dependency of drag coefficient on Reynolds number becomes non-linear. This trend arises from the complex interaction between snowflakes and the surrounding air. We investigate the wake of complex-shaped snow particles using a validated delayed-detached eddy simulation model of airflow around a fixed snowflake, combined with experimental observations of free-falling, 3D-printed snowflake analogs. This novel approach allows us to analyze the wake topology and decompose its momentum flux to investigate the influence of shape and wake flow on the drag coefficient and its implications on falling attitudes by comparison with experiments. At low Re, the presence of separated vortex rings is connected to particle porosity and produces an increase in the drag coefficient. At moderate flow regimes, the particle flatness impacts the shear layer separation and the momentum loss in the wake, while at high Re the drag coefficient has almost the same value among the tested geometries although the contribution of different momentum flux terms differs. These results represent a further step toward a deeper understanding the drag of complex-shaped particles.

Significance Zooplankton possess narrow swimming capabilities, yet are capable of active locomotion amid turbulence. By decoupling the relative velocity of swimming zooplankton from that of the underlying flow, we provide evidence for an active adaptation that allows these small organisms to modulate their swimming effort in response to background flow. This behavioral response results in reduced diffusion at substantial turbulence intensity. Adjusting motility provides fitness advantage because it enables zooplankton to retain the benefits of self-locomotion despite the constraints enforced by turbulence transport. Vigorous swimming and reduced diffusion oppose turbulence advection, can directly affect the dispersal of zooplankton populations, and may help these organisms to actively control their distribution in dynamic environments., Calanoid copepods are among the most abundant metazoans in the ocean and constitute a vital trophic link within marine food webs. They possess relatively narrow swimming capabilities, yet are capable of significant self-locomotion under strong hydrodynamic conditions. Here we provide evidence for an active adaptation that allows these small organisms to adjust their motility in response to background flow. We track simultaneously and in three dimensions the motion of flow tracers and planktonic copepods swimming freely at several intensities of quasi-homogeneous, isotropic turbulence. We show that copepods synchronize the frequency of their relocation jumps with the frequency of small-scale turbulence by performing frequent relocation jumps of low amplitude that seem unrelated to localized hydrodynamic signals. We develop a model of plankton motion in turbulence that shows excellent quantitative agreement with our measurements when turbulence is significant. We find that, compared with passive tracers, active motion enhances the diffusion of organisms at low turbulence intensity whereas it dampens diffusion at higher turbulence levels. The existence of frequent jumps in a motion that is otherwise dominated by turbulent transport allows for the possibility of active locomotion and hence to transition from being passively advected to being capable of controlling diffusion. This behavioral response provides zooplankton with the capability to retain the benefits of self-locomotion despite turbulence advection and may help these organisms to actively control their distribution in dynamic environments. Our study reveals an active adaptation that carries strong fitness advantages and provides a realistic model of plankton motion in turbulence.

We investigate the effect of buoyancy on the small-scale aspects of turbulent entrainment by performing direct numerical simulation of a gravity current and a wall jet. In both flows, we detect the turbulent/nonturbulent interface separating turbulent from irrotational ambient flow regions using a range of enstrophy iso-levels spanning many orders of magnitude. Conform to expectation, the relative enstrophy isosurface velocity vn in the viscous superlayer scales with the Kolmogorov velocity for both flow cases. We connect the integral entrainment coefficient E to the small-scale entrainment and observe excellent agreement between the two estimates throughout the viscous superlayer. The contribution of baroclinic torque to vn is negligible, and we show that the primary reason for reduced entrainment in the gravity current as compared to the wall-jet are 1) the reduction of vn relative to the integral velocity scale uT; and 2) the reduction in the surface area of the isosurfaces., Environmental Fluid Mechanics, 18 (1), ISSN:1567-7419, ISSN:1573-1510

Zooplankton live in dynamic environments where turbulence may challenge their limited swimming abilities. How this interferes with fundamental behavioral processes remains elusive. We reconstruct simultaneously the trajectories of flow tracers and calanoid copepods and we quantify their ability to find mates when ambient flow imposes physical constrains on their motion and impairs their olfactory orientation. We show that copepods achieve high encounter rates in turbulence due to the contribution of advection and vigorous swimming. Males further convert encounters within the perception radius to contacts and then to mating via directed motion toward nearby organisms within the short time frame of the encounter. Inertial effects do not result in preferential concentration, reducing the geometric collision kernel to the clearance rate, which we model accurately by superposing turbulent velocity and organism motion. This behavioral and physical coupling mechanism may account for the ability of copepods to reproduce in turbulent environments., eLife, 9, ISSN:2050-084X

In this paper, we employ the theory of Lagrangian coherent structures for 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 Lagrangian coherent structures (VLCSs), a fully automated three-dimensional 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 analysed 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, consequently affecting 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 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 $\mathit{Ri}_{f}$, gradient Richardson number $\mathit{Ri}_{g}$ and turbulent flux coefficient $\unicode[STIX]{x1D6E4}$ are constant across a large portion of the depth. Changing the slope angle $\unicode[STIX]{x1D6FC}$ modifies these mixing parameters, and the flow approaches a maximum Richardson number $\mathit{Ri}_{max}\approx 0.15$ as $\unicode[STIX]{x1D6FC}\rightarrow 0$ at which the entrainment coefficient $E\rightarrow 0$. The turbulent Prandtl number remains $O(1)$ for all slope angles, demonstrating that $E\rightarrow 0$ is not caused by a switch-off of the turbulent buoyancy flux as conjectured by Ellison (J. Fluid Mech., vol. 2, 1957, pp. 456–466). Instead, $E\rightarrow 0$ occurs as the result of the turbulence intensity going to zero as $\unicode[STIX]{x1D6FC}\rightarrow 0$, due to the flow requiring larger and larger shear to maintain the same level of turbulence. We develop an approximate model valid for small $\unicode[STIX]{x1D6FC}$ which is able to predict accurately $\mathit{Ri}_{f}$, $\mathit{Ri}_{g}$ and $\unicode[STIX]{x1D6E4}$ as a function of $\unicode[STIX]{x1D6FC}$ and their maximum attainable values. The model predicts an entrainment law of the form $E=0.31(\mathit{Ri}_{max}-\mathit{Ri})$, which is in good agreement with the simulation data. The simulations and model presented here contribute to a growing body of evidence that an approach to a marginally or critically stable, relatively weakly stratified equilibrium for stratified shear flows may well be a generic property of turbulent stratified flows.

This study considers complex ice particles falling in the atmosphere: predicting the drag of such particles is important for developing of climate models parameterizations. A Delayed-Detached Eddy Simulation model is developed to predict the drag coefficient of snowflakes falling at Reynolds number between 50 and 2200. We first consider the case where the orientation of the particle is known a posteriori, and evaluate our results against laboratory experiments using 3D-printed particles of the same shape, falling at the same Reynolds number. Close agreement is found in cases where the particles fall stably, while a more complex behavior is observed in cases where the flow is unsteady. The second objective of this study is to evaluate methods for estimating the drag coefficient when the orientation of the particles is not known a posteriori. We find that a suitable average of two orientations corresponding to the minimum and maximum eigenvalues of the inertia tensor provides a good estimate of the particle drag coefficient. Meanwhile, existing correlations for the drag on non-spherical particles produce large errors ( ≈ 50%). A new formula to estimate snow particles settling velocity is also proposed. Our approach provides a framework to investigate the aerodynamics of complex snowflakes and is relevant to other problems that involve the sedimentation of irregular particles in viscous fluids.

We study the growth of concentration fluctuations of weakly inertial particles in the turbulent channel flow starting with a smooth initial distribution. The steady-state concentration is singular and multifractal so the growth describes the increasingly rugged structure of the distribution. We demonstrate that inhomogeneity influences the growth of concentration fluctuations profoundly. For homogeneous turbulence the growth is exponential and is fully determined by Kolmogorov scale eddies.We derive lognormality of the statistics in this case. The growth exponents of the moments are proportional to the sum of Lyapunov exponents, which is quadratic in the small inertia of the particles. In contrast, for inhomogeneous turbulence the growth is linear in inertia. It involves correlations of inertial range and viscous scale eddies that turn the growth into a stretched exponential law with exponent three halves. We demonstrate using direct numerical simulations that the resulting growth rate can differ by orders of magnitude over channel height. This strong variation might have relevance in the planetary boundary layer.

Biofilms are ubiquitous bacterial communities that grow in various porous media including soils, trickling, and sand filters. In these environments, they play a central role in services ranging from degradation of pollutants to water purification. Biofilms dynamically change the pore structure of the medium through selective clogging of pores, a process known as bioclogging. This affects how solutes are transported and spread through the porous matrix, but the temporal changes to transport behavior during bioclogging are not well understood. To address this uncertainty, we experimentally study the hydrodynamic changes of a transparent 3‐D porous medium as it experiences progressive bioclogging. Statistical analyses of the system's hydrodynamics at four time points of bioclogging (0, 24, 36, and 48 h in the exponential growth phase) reveal exponential increases in both average and variance of the flow velocity, as well as its correlation length. Measurements for spreading, as mean‐squared displacements, are found to be non‐Fickian and more intensely superdiffusive with progressive bioclogging, indicating the formation of preferential flow pathways and stagnation zones. A gamma distribution describes well the Lagrangian velocity distributions and provides parameters that quantify changes to the flow, which evolves from a parallel pore arrangement under unclogged conditions, toward a more serial arrangement with increasing clogging. Exponentially evolving hydrodynamic metrics agree with an exponential bacterial growth phase and are used to parameterize a correlated continuous time random walk model with a stochastic velocity relaxation. The model accurately reproduces transport observations and can be used to resolve transport behavior at intermediate time points within the exponential growth phase considered., Key Points Experimental three‐dimensional particle tracking of flow tracers provides pore‐scale hydrodynamics in a progressively bioclogged porous mediumBiofilm growth induces formation of preferential flow paths and stagnation zones, leading to an increase of anomalous transportA continuous time random walk model based on a gamma distribution of the pore‐scale velocities captures transport dynamics

Aggregates grown in mild shear flow are released, one at a time, into homogeneous isotropic turbulence where their breakup is recorded by three-dimensional particle tracking velocimetry (3D-PTV). T ...

Aggregates grown in mild shear flow are released, one at a time, into homogeneous isotropic turbulence, where their motion and intermittent breakup is recorded by three-dimensional particle tracking velocimetry (3D-PTV). The aggregates have an open structure with a fractal dimension of ∼2.2, and their size is 1.4 ± 0.4 mm, which is large, compared to the Kolmogorov length scale (• = 0.15 mm). 3D-PTV of flow tracers allows for the simultaneous measurement of aggregate trajectories and the full velocity gradient tensor along their pathlines, which enables us to access the Lagrangian stress history of individual breakup events. From this data, we found no consistent pattern that relates breakup to the local flow properties at the point of breakup. Also, the correlation between the aggregate size and both shear stress and normal stress at the location of breakage is found to be weaker, when compared with the correlation between size and drag stress. The analysis suggests that the aggregates are mostly broken due to the accumulation of the drag stress over a time lag on the order of the Kolmogorov time scale. This finding is explained by the fact that the aggregates are large, which gives their motion inertia and increases the time for stress propagation inside the aggregate. Furthermore, it is found that the scaling of the largest fragment and the accumulated stress at breakup follows an earlier established power law, i.e., dfrag ∼ ∼-0.6 obtained from laminar nozzle experiments. This indicates that, despite the large size and the different type of hydrodynamic stress, the microscopic mechanism causing breakup is consistent over a wide range of aggregate size and stress magnitude.

Purpose To investigate the limits of phase contrast MRI (PC-MRI)–based measurements of viscous losses and turbulent kinetic energy (TKE) pertaining to spatial resolution, signal-to-noise ratio (SNR), and non-Gaussian intravoxel velocity distributions. Theory and Methods High-resolution particle tracking velocimetry data obtained in a realistic aortic phantom with stenotic flow were used to simulate PC-MRI measurements at different resolutions and noise levels. Laminar viscous losses were computed using the spatial gradients of the mean velocity vector field, and TKE levels were derived based on the intravoxel phase dispersion of flow-sensitized PC-MRI measurements. Results Increasing the voxel size from 0.625 to 2.5 mm resulted in an underestimation of viscous losses of up to 83%, whereas total TKE values showed errors of

We consider Lagrangian velocity differences of zooplankters swimming in still water and in turbulence. Using cumulants, we quantify the intermittency properties of their motion recorded using three-dimensional particle tracking velocimetry. Copepods swimming in still water display an intermittent behaviour characterized by a high probability of small velocity increments, and by stretched exponential tails. Low values arise from their steady cruising behaviour while heavy tails result from frequent relocation jumps. In turbulence, we show that at short time scales, the intermittency signature of active copepods clearly differs from that of the underlying flow, and reflects the frequent relocation jumps displayed by these small animals. Despite these differences, we show that copepods swimming in still and turbulent flow belong to the same intermittency class that can be modelled by a log-stable model with non-analytical cumulant generating function. Intermittency in swimming behaviour and relocation jumps may enable copepods to display oriented, collective motion under strong hydrodynamic conditions and thus, may contribute to the formation of zooplankton patches in energetic environments., The European Physical Journal E, 38 (10), ISSN:1292-8941, ISSN:1292-895X

Journal of Fluid Mechanics, 738, ISSN:0022-1120, ISSN:1469-7645

Journal of Fluid Mechanics, 765, ISSN:0022-1120, ISSN:1469-7645

We report on effects of mean shear on the turbulent entrainment process, focusing in particular on their relation to small-scale processes in the proximity of the turbulent/non-turbulent interface (TNTI). Three-dimensional particle tracking velocimetry (3D-PTV) measurements of an axisymmetric jet are compared to data from a direct numerical simulation (DNS) of a zero-mean-shear (ZMS) flow. First, conditional statistics relative to the interface position are investigated in a pseudo-Eulerian view (i.e. in a fixed frame relative to the interface position) and in a Lagrangian view. We find that in a pseudo-Eulerian frame of reference, both vorticity fluctuations and mean shear contribute to the vorticity jump at the boundary between irrotational and turbulent regions. In contrast, the Lagrangian evolution of enstrophy along trajectories crossing the entrainment interface is almost exclusively dominated by vorticity fluctuations, at least during the first Kolmogorov time scales after passing the interface. A mapping between distance to the instantaneous interface versus conditional time along the trajectory shows that entraining particles remain initially close to the TNTI and therefore attain lower average enstrophy values. The ratio between the rate of change of enstrophy in the two frames of references defines the local entrainment velocity νn = -(Dω2/ ∂xn), where ω2 is enstrophy and xn is the coordinate normal to the TNTI. The quantity νn is decomposed into mean and fluctuating components and it is found that mean shear enhances the local entrainment velocity via inviscid and viscous effects. Further, the analysis substantiates that for all investigated flow configurations the local entrainment velocity depends considerably on the geometrical shape of the interface. Depending on the surface shape, different small-scale mechanisms are dominant for the local entrainment process, i.e. viscous effects for convex shapes and vortex stretching for concave shapes, looking from the turbulent region towards the convoluted boundary. Moreover, turbulent fluctuations display a stronger dependence on the shape of the interface than mean shear effects. © 2013 Cambridge University Press., Journal of Fluid Mechanics, 731, ISSN:0022-1120, ISSN:1469-7645

Journal of Fluid Mechanics, 739, ISSN:0022-1120, ISSN:1469-7645

It was previously observed by Krug et al. (J. Fluid Mech., vol. 765, 2015, pp. 303–324) that the surface area $A_{\unicode[STIX]{x1D702}}$ of the turbulent/non-turbulent interface (TNTI) in gravity currents decreases with increasing stratification, significantly reducing the entrainment rate. Here, we consider the multiscale properties of this effect using direct numerical simulations of temporal gravity currents with different gradient Richardson numbers $Ri_{g}$. Our results indicate that the reduction of $A_{\unicode[STIX]{x1D702}}$ is caused by a decrease of the fractal scaling exponent $\unicode[STIX]{x1D6FD}$, while the scaling range remains largely unaffected. We further find that convolutions of the TNTI are characterized by different length scales in the streamwise and wall-normal directions, namely the integral scale $h$ and the shear scale $l_{Sk}=k^{1/2}/S$ (formed using the mean shear $S$ and the turbulent kinetic energy $k$) respectively. By recognizing that the anisotropy implied by the different scaling relations increases with increasing $Ri_{g}$, we are able to model the $Ri_{g}$ dependence of $\unicode[STIX]{x1D6FD}$ in good agreement with the data.

Cardiovascular diseases can lead to abnormal blood flows, some of which are linked to hemolysis and thrombus formation. Abnormal turbulent flows of blood in the vessels with stenosis create strong shear stresses on blood elements and may cause blood cell destruction or platelet activation. We implemented a Lagrangian (following the fluid elements) measurement technique of three dimensional particle tracking velocimetry that provides insight on the evolution of viscous and turbulent stresses along blood element trajectories. We apply this method to study a pulsatile flow in a compliant phantom of an aorta and compare the results in three cases: the reference case (called "healthy" case), and two cases of abnormal flows due to mild and severe stenosis, respectively. The chosen conditions can mimic a clinical application of an abnormal flow due to a calcific valve. We estimate the effect of aortic stenosis on the kinetic energy of the mean flow and the turbulent kinetic energy, which increases about two orders of magnitude as compared with the healthy flow case. Measuring the total flow stress acting on a moving fluid element that incorporates viscous stresses and the apparent turbulent-induced stresses (the so-called Reynolds stresses) we find out similar increase of the stresses with the increased severity of the stenosis. Furthermore, these unique Lagrangian measurements provide full acceleration and, consequently, the forces acting on the blood elements that are estimated to reach the level that can considerably deform red blood cells. These forces are strong and abrupt due to the contribution of the turbulent fluctuations which is much stronger than the typically measured phase-averaged values.

Parallel to the massive use of image-based computational hemodynamics to study the complex flow establishing in the human aorta, the need for suitable experimental techniques and ad hoc cases for the validation and benchmarking of numerical codes has grown more and more. Here we present a study where the 3D pulsatile flow in an anatomically realistic phantom of human ascending aorta is investigated both experimentally and computationally. The experimental study uses 3D particle tracking velocimetry (PTV) to characterize the flow field in vitro, while finite volume method is applied to numerically solve the governing equations of motion in the same domain, under the same conditions. Our findings show that there is an excellent agreement between computational and measured flow fields during the forward flow phase, while the agreement is poorer during the reverse flow phase. In conclusion, here we demonstrate that 3D PTV is very suitable for a detailed study of complex unsteady flows as in aorta and for validating computational models of aortic hemodynamics. In a future step, it will be possible to take advantage from the ability of 3D PTV to evaluate velocity fluctuations and, for this reason, to gain further knowledge on the process of transition to turbulence occurring in the thoracic aorta.

Aggregates prepared under fully destabilized conditions by the action of Brownian motion were exposed to an extensional flow generated at the entrance of a sudden contraction. Two noninvasive techniques were used to monitor their breakup process [i.e. light scattering and three-dimensional (3D) particle tracking velocimetry (3D-PTV)]. While the first one can be used to measure the size and the morphology of formed fragments after the breakage event, the latter is capable of resolving trajectories of individual aggregates up to the breakage point as well as the trajectories of formed fragments. Furthermore, measured velocity gradients were used to determine the local hydrodynamic conditions at the breakage point. All this information was combined to experimentally determine for the first time the breakage rate of individual aggregates, given in the form of a size reduction rate K(R), as a function of the applied strain rate, as well as the properties of the formed fragments (i.e., the number of formed fragments and the size ratio between the largest fragment and the original aggregate). It was found that K(R) scales with the applied strain rate according to a power law with the slope being dependent on the initial fractal dimension only, while the obtained data indicates a linear dependency of K(R) with the initial aggregate size. Furthermore, the probability distribution function (PDF) of the number of formed fragments and the PDF of the size ratio between the largest fragment and the original aggregate indicate that breakage will result with high probability (75%) in the formation of two to three fragments with a rather asymmetric ratio of sizes of about 0.8. The obtained results are well in agreement with the results from the numerical simulations published in the literature.

Turbulence is ubiquitous in nature yet even for the case of ordinary Newtonian fluids like water our understanding of this phenomenon is limited. Many liquids of practical importance however are more complicated (e.g. blood, polymer melts or paints), they exhibit elastic as well as viscous characteristics and the relation between stress and strain is nonlinear. We here demonstrate for a model system of such complex fluids that at high shear rates turbulence is not simply modified as previously believed but it is suppressed and replaced by a new type of disordered motion, elasto-inertial turbulence (EIT). EIT is found to occur at much lower Reynolds numbers than Newtonian turbulence and the dynamical properties differ significantly. In particular the drag is strongly reduced and the observed friction scaling resolves a longstanding puzzle in non-Newtonian fluid mechanics regarding the nature of the so-called maximum drag reduction asymptote. Theoretical considerations imply that EIT will arise in complex fluids if the extensional viscosity is sufficiently large.

Transition in shear flows is characterized by localized turbulent regions embedded in the surrounding laminar flow. These so-called turbulent spots or puffs are observed in a variety of shear flows and in certain Reynolds-number regimes, and they are advected by the flow while keeping their characteristic length. We show here for the case of pipe flow that this seemingly passive advection of turbulent puffs involves continuous entrainment and relaminarization of laminar and turbulent fluid across strongly convoluted interfaces. Surprisingly, interface areas are almost two orders of magnitude larger than the pipe cross-section, while local entrainment velocities are much smaller than the mean speed. Even though these velocities were shown to be small and proportional to the Kolmogorov velocity scale (in agreement with a prediction by Corrsin) in a flow without mean shear before, we find that, in pipe flow, local entrainment velocities are about an order of magnitude smaller than this scale. The Lagrangian method used to study the dynamics of the laminar–turbulent interfaces allows accurate determination of the leading and trailing edge speeds. However, to resolve the highly complex interface dynamics requires much higher numerical resolutions than for ordinary turbulent flows. This method also reveals that the volume flux across the leading edge has the same radial dependence but the opposite sign as that across the trailing edge, and it is this symmetry that is responsible for the puff shape remaining constant.

The effect of buoyancy on the turbulent/nonturbulent interface (TNTI) and viscous superlayer are studied by performing direct numerical simulation of penetrative convection. In this flow, rising turbulent thermals alternate with unmixed fluid entrained from above, forming a TNTI between the turbulent and irrotational flow regions. We detect the TNTI using a broad range of enstrophy iso-levels, from the very low levels of the outer fringes of the turbulent flow region to high levels located in the turbulent flow region. We study the local entrainment velocity vn by which the TNTI propagates outwards relative to the fluid flow while entraining unmixed fluid into the turbulent region. The relative entrainment velocity is decomposed into a viscous, an inertial and a baroclinic torque term, respectively. For low enstrophy levels we find a viscous superlayer (VSL) where viscous diffusion dominates, while inertial and baroclinic torque terms are small. It is only for higher iso-levels in the buffer region of the TNTI, which extends from the edge of the VSL to the threshold for which vn = 0, that the inertial enstrophy production term plays a significant role. Penetrative convection does not feature a turbulent core where vn > 0 (i.e. inward moving enstrophy isosurfaces) that has been previously identified in other entraining flows such as jets or gravity currents. Surprisingly, the baroclinic torque remains inactive throughout the whole range of enstrophy iso-levels. The smallness of the baroclinic torque against viscous effects in the TNTI is supported by a dimensional argument which predicts that at high Reynolds number the baroclinic torque term will be negligible.

Today, the functional and risk assessment of stenosed arteries is mostly based on ultrasound Doppler blood flow velocity measurements or catheter pressure measurements, which rely on several assumptions. Alternatively, blood velocity including turbulent kinetic energy (TKE) may be measured using MRI. The aim of the present study is to validate a TKE-based approach that relies on the fact that turbulence production is dominated by the flow's shear to determine the total irreversible energy loss from MRI scans. Three-dimensional particle tracking velocimetry (3D-PTV) and phase-contrast magnetic resonance imaging (PC-MRI) simulations were performed in an anatomically accurate, compliant, silicon aortic phantom. We found that measuring only the laminar viscous losses does not reflect the true losses of stenotic flows since the contribution of the turbulent losses to the total loss become more dominant for more severe stenosis types (for example, the laminar loss is 0.0094±0.0015W and the turbulent loss is 0.0361±0.0015W for the Remax=13,800 case, where Remax is the Reynolds number based on the velocity in the vena-contracta). We show that the commonly used simplified and modified Bernoulli's approaches overestimate the total loss, while the new TKE-based method proposed here, referred to as "shear scaling" approach, results in a good agreement between 3D-PTV and simulated PC-MRI (mean error is around 10%). In addition, we validated the shear scaling approach on a geometry with post-stenotic dilatation using numerical data by Casas et al. (2016). The shear scaling-based method may hence be an interesting alternative for irreversible energy loss estimation to replace traditional approaches for clinical use. We expect that our results will evoke further research, in particular patient studies for clinical implementation of the new method.

We present a technique capable of measuring in a Lagrangian manner the three components of the flow velocity simultaneously at two different spatial resolutions. We use two synchronized 3D Particle Tracking Velocimetry (3D-PTV) systems equipped with filters to separate the two types of seeding particles and measure in volumes of 55 × 55 × 50 mm3 and 15 × 15 × 15 mm3, respectively. In this way, we obtain (a) the velocity field in a large observation volume with focus on the large-scale flow features and (b) velocity derivatives in a small observation volume providing small-scale quantities associated with vorticity and strain. The small observation volume is located in the center of the large one, which allows the small-scale quantities to be related to the large-scale flow patterns. To illustrate the capability of the simultaneous two-scale 3D Particle Tracking Velocimetry (STS 3D-PTV) method, the behavior of vorticity and strain is analyzed in shear-free turbulence under the influence of system rotation. We find that in the quasi-2D region, vortex stretching is strongly suppressed only inside columnar vortex tubes.

From Lie-group (symmetry) analysis of the multi-point correlation equation Oberlack and Gunther (Fluid Dyn Res 33:453-476, 2003) found three different solutions for the behavior of shear-free turbulence: (i) a diffusion like solution, in which turbulence diffuses freely into the adjacent calm fluid, (ii) a deceleration wave like solution when there is an upper bound for the integral length scale and (iii) a finite domain solution for the case when rotation is applied to the system. This paper deals with the experimental validation of the theory. We use an oscillating grid to generate turbulence in a water tank and Particle Image Velocimetry (PIV) to determine the two-dimensional velocity and out-of-plane vorticity components. The whole setup is placed on a rotating table. After the forcing is initiated, a turbulent layer develops which is separated from the initially irrotational fluid by a sharp interface, the so-called turbulent/non-turbulent interface (TNTI). The turbulent region grows in time through entrainment of surrounding fluid. We measure the propagation of the TNTI and find quantitative agreement with the predicted spreading laws for case one and two. For case three (system rotation), we observe that there is a sharp transition between a 3D turbulent flow close to the source of energy and a more 2D-like wavy flow further away. We measure that the separation depth becomes constant and in this sense, we confirm the theoretical finite domain solution.

Intermittency of Lagrangian velocity and acceleration is a key to understanding transport in complex systems ranging from fluid turbulence to flow in porous media. High-resolution optical particle tracking in a three-dimensional (3D) porous medium provides detailed 3D information on Lagrangian velocities and accelerations. We find sharp transitions close to pore throats, and low flow variability in the pore bodies, which gives rise to stretched exponential Lagrangian velocity and acceleration distributions characterized by a sharp peak at low velocity, superlinear evolution of particle dispersion, and double-peak behavior in the propagators. The velocity distribution is quantified in terms of pore geometry and flow connectivity, which forms the basis for a continuous-time random-walk model that sheds light on the observed Lagrangian flow and transport behaviors. ©2015 American Physical Society., We acknowledge the contributions of R. Gallus and D. S¨agesser in the frame of a laboratory project, U. G¨ulan for help with data processing and W. Kinzelbach, T. LeBorgne, P. De Anna and P.K. Kang for stimulating discussions. Financial support is acknowledged from the Swiss National Science Foundation (SNF grant number 144645) for M.H., Marie Curie International Incoming Fellowships (FP7- PEOPLE-2012-SoilArchnAg) for V.L.M, and the European Research Council (ERC project MHetScale number 617511) for M.D.

A three-dimensional pulsatile aortic flow in a human ascending aorta is investigated in-vitro in this paper. A non-intrusive measurement technique, 3D Particle Tracking Velocimetry (3D-PTV), has been applied to the anatomically accurate silicon replicas. A compliant and a stiff aortic model were analyzed to better understand the influence of the arterial stiffness. The realistic models are transparent which allows optical access to the investigation domain. Our results showed that increasing the arterial stiffness considerably increases the systolic velocity and hencemean kinetic energy. Quite strikingly, the turbulent kinetic energy is about one order of magnitude higher in the stiffer model during the deceleration phase which manifests that a blood element is exposed to higher shear stresses in the stiffer model. Moreover, we found that the compliant model introduces pressure oscillations during the diastolic phase which are associated with the Windkessel effect.

The complex hemodynamics observed in the human aorta make this district a site of election for an in depth investigation of the relationship between fluid structures, transport and pathophysiology. In recent years, the coupling of imaging techniques and computational fluid dynamics (CFD) has been applied to study aortic hemodynamics, because of the possibility to obtain highly resolved blood flow patterns in more and more realistic and fully personalized flow simulations [1]. However, the combination of imaging techniques and computational methods requires some assumptions that might influence the predicted hemodynamic scenario. Thus, computational modeling requires experimental cross-validation. Recently, 4D phase contrast MRI (PCMRI) has been applied in vivo and in vitro to access the velocity field in aorta [2] and to validate numerical results [3]. However, PCMRI usually requires long acquisition times and suffers from low spatial and temporal resolution and a low signal-to-noise ratio. Anemometric techniques have been also applied for in vitro characterization of the fluid dynamics in aortic phantoms. Among them, 3D Particle Tracking Velocimetry (PTV), an optical technique based on imaging of flow tracers successfully used to obtain Lagrangian velocity fields in a wide range of complex and turbulent flows [4], has been very recently applied to characterize fluid structures in the ascending aorta [5].Copyright © 2013 by ASME

The special case of entrainment in a stratified flow, relevant to many geophysical flows such as oceanic overflows, so far has not been studied experimentally in terms of small-scale aspects around the turbulent/non- turbulent interface. In view of the fact that existing engineering concepts perform unsatisfactorily in practice, a new gravity current facility was designed with the goal to gain understanding of how stratification affects interfacial physics. Here, we present the design of the new setup and give details on the turbulence enhancement in the inflow and the refractive index matching technique used. Validation measurements ensure that there is negligible backflow and an essentially irrotational flow outside the current. Measurements via particle image velocimetry of a flow with inflow Reynolds and Richardson numbers of Re0 ≈ 4,000 and Ri 0 = 0.22 are reported. An analysis in a laboratory frame agrees well with flow features reported in the literature, i.e., a streamwise invariant top-hat velocity scale and a Reynolds stress distribution are matched closely by a mixing length model. In a second step, the instantaneous interface position is determined based on a threshold on the normal enstrophy component. An investigation in a frame of reference conditioned on the interface position reveals a strong interfacial shear layer that is much more pronounced than the one observed in jet flows. Its thickness is about two times the Taylor microscale. The data moreover suggest the existence of a fairly strong interfacial density jump across the shear layer. The entrainment parameter is estimated at E ≈ 0.04 congruently from the evaluations in laboratory and conditioned frame, respectively. © 2013 Springer-Verlag Berlin Heidelberg., Experiments in Fluids, 54 (5), ISSN:0723-4864, ISSN:1432-1114

Experiments in Fluids, 53 (5), ISSN:0723-4864, ISSN:1432-1114

In this Letter we present results from particle tracking velocimetry and direct numerical simulation that are congruent with the existence of a laminar superlayer, as proposed in the pioneering work of Corrsin and Kistler (NACA, Technical Report No. 1244, 1955). We find that the local superlayer velocity is dominated by a viscous component and its magnitude is comparable to the characteristic velocity of the smallest scales of motion. This slow viscous process involves a large surface area so that the global rate of turbulence spreading is set by the largest scales of motion. These findings are important for a better understanding of mixing of mass and momentum in a variety of flows where thin layers of shear exist. Examples are boundary layers, clouds, planetary atmospheres, and oceans.

Viscous depletion of vorticity is an essential and well known property of turbulent flows, balancing, in the mean, the net vorticity production associated with the vortex stretching mechanism. In this letter, we, however, demonstrate that viscous effects are not restricted to a mere destruction process, but play a more complex role in vorticity dynamics that is as important as vortex stretching. Based on the results from three dimensional particle tracking velocimetry experiments and direct numerical simulation of homogeneous and quasi-isotropic turbulence, we show that the viscous term in the vorticity equation can also locally induce production of vorticity and changes of the orientation of the vorticity vector (viscous tilting).

We present a comparative experimental study of a turbulent flow developing in clear water and dilute polymer solutions (25 and 50 wppm polyethylene oxide). The flow is forced by a planar grid that oscillates vertically with stroke S and frequency f in a square container of initially still fluid. Two-component velocity fields are measured in a vertical plane passing through the center of the tank by using time resolved particle image velocimetry. After the forcing is initiated, a turbulent layer develops that is separated from the initially irrotational fluid by a sharp interface, the so-called turbulent/nonturbulent interface (TNTI). The turbulent region grows in time through entrainment of surrounding fluid until the fluid in the whole container is in turbulent motion. From the comparison of the experiments in clear water and polymer solutions we conclude: (i) Polymer additives modify the large scale shape of the TNTI. (ii) Both, in water and in the polymer solution the mean depth of the turbulent layer, H(t), follows the theoretical prediction for Newtonian fluids H(t)∞√Kt, where K∞S^2f is the “grid action.” (iii) We find a larger grid action for dilute polymer solutions than for water. As a consequence, the turbulent kinetic energy of the flow increases and the rate of energy input becomes higher. (iv) The entrainment rate β=v_e/v_(rms) (where v_e=dH/dt is the interface propagation velocity and v_(rms) is the root mean square of the vertical velocity) is lower for polymers (β_p≈0.7) than for water (β_w≈0.8). The measured values for β are in good agreement with similarity arguments, from which we estimate that in our experiment about 28% of the input energy is dissipated by polymers.

In preparation of simultaneous large-scale / small-scale 3D Particle Tracking Velocimetry (3D-PTV) experiments in a developing turbulent flow we performed two types of measurements separately: (i) the velocity and coarse-grained velocity derivatives were measured in a large observation volume with focus on the large-scale flow features and (ii) spatially resolved velocity derivatives were measured in a small observation volume with the goal to obtain small-scale quantities associated with vorticity and strain. In this contribution we demonstrate that the characteristic flow structures were captured and velocity derivatives were accessed with sufficient accuracy. The problem of measuring velocity derivatives both in the Lagrangian and Eulerian frame of reference is also addressed. Although comparable accuracies in both settings could be achieved with our method, only statistics obtained from the spatially resolved measurement were found to be practically the same in both settings.

In this contribution we analyze properties of the turbulent/nonturbulent interface (TNTI) in a flow without mean shear. The approach is numerical and based on a Direct Numerical Simulation (DNS). For the final paper the results will be complemented with Particle Tracking Velocimetry measurements. The focus is on the ‘local’ entrainment velocity, vn, defined as the velocity of the TNTI relative to the fluid and directed towards the irrotational ambient. We provide an expression for vn that consists of two parts: a viscous and an inviscid one. The results show that the viscous contribution is stronger than the inviscid part and governs the local entrainment velocity towards the ambient. We also propose a measure to characterize the characteristic length scale or ‘thickness’ of the TNTI.

We present a comparative experimental study of a turbulent flow developing in clear water and dilute polymer solutions (25 and 50 wppm polyethylene oxide). The flow is forced by a planar grid that oscillates vertically in a square container of initially still fluid. The two-component velocity fields are measured in a vertical plane passing through the center of the tank by using time resolved Particle Image Velocimetry (PIV).We obtain a lower entrainment rate for polymer solutions as compared to clear water. Extending arguments based on similarity and fractal theory to the case of dilute polymer solutions, we derive a relation between the entrainment rate and the fraction of input energy dissipated by the polymers.

Journal of Fluid Mechanics, 639, ISSN:0022-1120, ISSN:1469-7645

Journal of Fluid Mechanics, 598, ISSN:0022-1120, ISSN:1469-7645