Expanding the Q-R space to three dimensions

The two-dimensional space spanned by the velocity gradient invariants Q and R is expanded to three dimensions by the decomposition of R into its strain production −1/3sijsjkski and enstrophy production 1/4ωiωjsij terms. The {Q; R} space is a planar projection of the new three-dimensional representation. In the {Q; −sss; ωωs} space the Lagrangian evolution of the velocity gradient tensor Aij is studied via conditional mean trajectories (CMTs) as introduced by Martín et al. (Phys. Fluids, vol. 10, 1998, p. 2012). From an analysis of a numerical data set for isotropic turbulence of Reλ ~ 434, taken from the Johns Hopkins University (JHU) turbulence database, we observe a pronounced cyclic evolution that is almost perpendicular to the Q-R plane. The relatively weak cyclic evolution in the Q-R space is thus only a projection of a much stronger cycle in the {Q; −sss; ωωs} space. Further, we find that the restricted Euler (RE) dynamics are primarily counteracted by the deviatoric non-local part of the pressure Hessian and not by the viscous term. The contribution of the Laplacian of Aij, on the other hand, seems the main responsible for intermittently alternating between low and high intensity Aij state

Acceleration, pressure and related quantities in the proximity of the turbulent/non-turbulent interface

This paper presents an analysis of flow properties in the proximity of the turbulent/non-turbulent interface (TNTI), with particular focus on the acceleration of fluid particles, pressure and related small scale quantities such as enstrophy, ω2 = ωiωi, and strain, s2 = sijsij. The emphasis is on the qualitative differences between turbulent, intermediate and non-turbulent flow regions, emanating from the solenoidal nature of the turbulent region, the irrotational character of the non-turbulent region and the mixed nature of the intermediate region in between. The results are obtained from a particle tracking experiment and direct numerical simulations (DNS) of a temporally developing flow without mean shear. The analysis reveals that turbulence influences its neighbouring ambient flow in three different ways depending on the distance to the TNTI: (i) pressure has the longest range of influence into the ambient region and in the far region non-local effects dominate. This is felt on the level of velocity as irrotational fluctuations, on the level of acceleration as local change of velocity due to pressure gradients, Du/Dt ∂u/∂t − p/ρ, and, finally, on the level of strain due to pressure-Hessian/strain interaction, (D/Dt)(s2/2) (∂/∂t)(s2/2) −sijp,ij > 0; (ii) at intermediate distances convective terms (both for acceleration and strain) as well as strain production −sijsjkski > 0 start to set in. Comparison of the results at Taylor-based Reynolds numbers Reλ = 50 and Reλ = 110 suggests that the distances to the far or intermediate regions scale with the Taylor microscale λ or the Kolmogorov length scale η of the flow, rather than with an integral length scale; (iii) in the close proximity of the TNTI the velocity field loses its purely irrotational character as viscous effects lead to a sharp increase of enstrophy and enstrophy-related terms. Convective terms show a positive peak reflecting previous findings that in the laboratory frame of reference the interface moves locally with a velocity comparable to the fluid velocity fluctuation

3D-PTV measurements in a plane Couette flow

Genuine plane Couette flow is hard to realize experimentally, and no applications of modern spatially resolving measurement techniques have been reported for this flow so far. In order to resolve this shortcoming, we designed and built a new experimental facility and present our first results here. Our setup enables us to access the flow via 3D particle tracking velocimetry and therefore to obtain truly three-dimensional flow fields for the first time experimentally in plane Couette flow. Results are analyzed in terms of basic flow properties, and a clear distinction of flow regimes (laminar for Re 400) could be made. Comparison with DNS data shows good agreement in the turbulent regime and builds trust in our data. Furthermore, vortical coherent structures are studied in detail with the additional help of kalliroscope imaging, and the typical vortex spacing is determined to be roughly one gap width. As a noteworthy result, we find that the onset of the turbulent regime coincides with the range of Reynolds numbers at which a distance of 100 wall units is comparable to the gap width.Swiss National Science Foundation (Grant 2-77898-10

3D-PTV measurements in a plane Couette flow

Genuine plane Couette flow is hard to realize experimentally, and no applications of modern spatially resolving measurement techniques have been reported for this flow so far. In order to resolve this shortcoming, we designed and built a new experimental facility and present our first results here. Our setup enables us to access the flow via 3D particle tracking velocimetry and therefore to obtain truly three-dimensional flow fields for the first time experimentally in plane Couette flow. Results are analyzed in terms of basic flow properties, and a clear distinction of flow regimes (laminar for Re400) could be made. Comparison with DNS data shows good agreement in the turbulent regime and builds trust in our data. Furthermore, vortical coherent structures are studied in detail with the additional help of kalliroscope imaging, and the typical vortex spacing is determined to be roughly one gap width. As a noteworthy result, we find that the onset of the turbulent regime coincides with the range of Reynolds numbers at which a distance of 100 wall units is comparable to the gap widt

A Lagrangian investigation of the small-scale features of turbulent entrainment through particle tracking and direct numerical simulation

We report an analysis of small-scale enstrophy ω2 and rate of strain s2 dynamics in the proximity of the turbulent/non-turbulent interface in a flow without strong mean shear. The techniques used are three-dimensional particle tracking (3D-PTV), allowing the field of velocity derivatives to be measured and followed in a Lagrangian manner, and direct numerical simulations (DNS). In both experiment and simulation the Taylor-microscale Reynolds number is Reλ = 50. The results are based on the Lagrangian viewpoint with the main focus on flow particle tracers crossing the turbulent/non-turbulent interface. This approach allowed a direct investigation of the key physical processes underlying the entrainment phenomenon and revealed the role of small-scale non-local, inviscid and viscous processes. We found that the entrainment mechanism is initiated by self-amplification of s2 through the combined effect of strain production and pressure--strain interaction. This process is followed by a sharp change of ω2 induced mostly by production due to viscous effects. The influence of inviscid production is initially small but gradually increasing, whereas viscous production changes abruptly towards the destruction of ω2. Finally, shortly after the crossing of the turbulent/non-turbulent interface, production and dissipation of both enstrophy and strain reach a balance. The characteristic time scale of the described processes is the Kolmogorov time scale, τη. Locally, the characteristic velocity of the fluid relative to the turbulent/non-turbulent interface is the Kolmogorov velocity, u

Experimental study of entrainment and interface dynamics in a gravity current

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 $$Re_0\approx \hbox{4,000}$$ 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 $$E \approx 0.04$$ congruently from the evaluations in laboratory and conditioned frame, respectivel

Experimental study of aortic flow in the ascending aorta via Particle Tracking Velocimetry

A three-dimensional, pulsatile flow in a realistic phantom of a human ascending aorta with compliant walls is investigated in vitro. Three-Dimensional Particle Tracking Velocimetry (3D-PTV), an image-based, non-intrusive measuring method is used to analyze the aortic flow. The flow velocities and the turbulent fluctuations are determined. The velocity profile at the inlet of the ascending aorta is relatively flat with a skewed profile toward the inner aortic wall in the early systole. In the diastolic phase, a bidirectional flow is observed with a pronounced retrograde flow developing along the inner aortic wall, whereas the antegrade flow migrates toward the outer wall of the aorta. The spatial and temporal evolution of the vorticity field shows that the vortices begin developing along the inner wall during the deceleration phase and attenuate in the diastolic phase. The change in the cross-sectional area is more distinct distal to the inlet cross section. The mean kinetic energy is maximal in the peak systole, whereas the turbulent kinetic energy increases in the deceleration phase and reaches a maximum in the beginning of the diastolic phase. Finally, in a Lagrangian analysis, the temporal evolution of particle dispersion was studied. It shows that the dispersion is higher in the deceleration phase and in the beginning of the diastole, whereas in systole, it is smaller but non-negligibl

3D scanning particle tracking velocimetry

In this article, we present an experimental setup and data processing schemes for 3D scanning particle tracking velocimetry (SPTV), which expands on the classical 3D particle tracking velocimetry (PTV) through changes in the illumination, image acquisition and analysis. 3D PTV is a flexible flow measurement technique based on the processing of stereoscopic images of flow tracer particles. The technique allows obtaining Lagrangian flow information directly from measured 3D trajectories of individual particles. While for a classical PTV the entire region of interest is simultaneously illuminated and recorded, in SPTV the flow field is recorded by sequential tomographic high-speed imaging of the region of interest. The advantage of the presented method is a considerable increase in maximum feasible seeding density. Results are shown for an experiment in homogenous turbulence and compared with PTV. SPTV yielded an average 3,500 tracked particles per time step, which implies a significant enhancement of the spatial resolution for Lagrangian flow measurement

Long-term changes in bone metabolism, bone mineral density, quantitative ultrasound parameters, and fracture incidence after spinal cord injury: a cross-sectional observational study in 100 paraplegic men

To study the time course of demineralization and fracture incidence after spinal cord injury (SCI), 100 paraplegic men with complete motor loss were investigated in a cross-sectional study 3months to 30years after their traumatic SCI. Fracture history was assessed and verified using patients' files and X-rays. BMD of the lumbar spine (LS), femoral neck (FN), distal forearm (ultradistal part=UDR, 1/3 distal part=1/3R), distal tibial diaphysis (TDIA), and distal tibial epiphysis (TEPI) was measured using DXA. Stiffness of the calcaneus (QUI.CALC), speed of sound of the tibia (SOS.TIB), and amplitude-dependent SOS across the proximal phalanges (adSOS.PHAL) were measured using QUS. Z-Scores of BMD and quantitative ultrasound (QUS) were plotted against time-since-injury and compared among four groups of paraplegics stratified according to time-since-injury (20years (p10years. In paraplegic men early (trabecular) and persistent (cortical) bone loss occurs at the lower limbs and leads to an increasing fracture incidence with time-after-SC