Direct assessment of vorticity alignment with local and nonlocal strain rates in turbulent flows

Hamlington, Peter E.; Schumacher, Jörg; Dahm, Werner J. A.

doi:10.1063/1.3021055

Cited by 72 publications

(81 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The picture of the cascade of TKE described by Leung et al [30] is based upon the vorticity stretching term being largely fed by the alignment of the small-scale (local) vorticity vector with the extensive strain rate of the large-scale (or background in the terminology of Hamlington et al [26]) strain field. Regions for which this alignment is |e 1 ·ω| 0.8 provide the majority of the overall positive contribution to ω i s ij ω j and are thus responsible for the transfer of turbulent kinetic energy from large scales to smaller ones [30].…”

Section: Resultsmentioning

confidence: 99%

“…However, Buxton and Ganapathisubramani [24] observed that the alignment preference between ω and e 1 determines the sign of ω i s ij ω j , with parallel alignment favored for concurrent ω i s ij ω j > 0 and perpendicular alignment favored for ω i s ij ω j < 0. Subsequently, the commonly reported tendency for |e 2 ·ω| ≈ 1 has been explained by the preferential alignment between the vorticity vector and the local intermediate strain-rate eigenvector, particularly in regions of high enstrophy [25], while ω preferentially aligns with the extensive eigenvector of the background strain field [26]. The preferential alignment of the vorticity vector, filtered at a length scale of the characteristic diameter of the high-enstrophy worms [27][28][29], with the large-scale extensive strain-rate eigenvector has been confirmed by Leung et al [30].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Scale dependence of the alignment between strain rate and rotation in turbulent shear flow

et al. 2016

View full text Add to dashboard Cite

The scale dependence of the statistical alignment tendencies of the eigenvectors of the strain-rate tensor e i , with the vorticity vector ω, is examined in the self-preserving region of a planar turbulent mixing layer. Data from a direct numerical simulation are filtered at various length scales and the probability density functions of the magnitude of the alignment cosines between the two unit vectors |e i ·ω| are examined. It is observed that the alignment tendencies are insensitive to the concurrent large-scale velocity fluctuations, but are quantitatively affected by the nature of the concurrent large-scale velocity-gradient fluctuations. It is confirmed that the small-scale (local) vorticity vector is preferentially aligned in parallel with the large-scale (background) extensive strain-rate eigenvector e 1 , in contrast to the global tendency for ω to be aligned in parallel with the intermediate strain-rate eigenvector [Hamlington et al., Phys. Fluids 20, 111703 (2008)]. When only data from regions of the flow that exhibit strong swirling are included, the so-called high-enstrophy worms, the alignment tendencies are exaggerated with respect to the global picture. These findings support the notion that the production of enstrophy, responsible for a net cascade of turbulent kinetic energy from large scales to small scales, is driven by vorticity stretching due to the preferential parallel alignment between ω and nonlocal e 1 and that the strongly swirling worms are kinematically significant to this process.

show abstract

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Scale dependence of the alignment between strain rate and rotation in turbulent shear flow

et al. 2016

View full text Add to dashboard Cite

show abstract

“…Jiménez 6 offered another explanation for the alignment using a kinematic model and attributed it to purely kinematic effects. There have been many more studies about the vorticity alignment, [7][8][9][10][11][12][13] considering various flows like isotropic turbulence, turbulent channel flow (TCF), turbulent boundary layer (TBL), atmospheric turbulence, and magnetohydrodynamic turbulence.…”

Section: Introductionmentioning

confidence: 99%

Universality and scaling phenomenology of small-scale turbulence in wall-bounded flows

et al. 2014

View full text Add to dashboard Cite

The Reynolds number scaling of flow topology in the eigenframe of the strain-rate tensor is investigated for wall-bounded flows, which is motivated by earlier works showing that such topologies appear to be qualitatively universal across turbulent flows. The databases used in the current study are from direct numerical simulations (DNS) of fully developed turbulent channel flow (TCF) up to friction Reynolds number Re τ ≈ 1500, and a spatially developing, zero-pressure-gradient turbulent boundary layer (TBL) up to Re θ ≈ 4300 (Re τ ≈ 1400). It is found that for TCF and TBL at different Reynolds numbers, the averaged flow patterns in the local strain-rate eigenframe appear the same consisting of a pair of co-rotating vortices embedded in a finite-size shear layer. It is found that the core of the shear layer associated with the intense vorticity region scales on the Kolmogorov length scale, while the overall height of the shear layer and the distance between the vortices scale well with the Taylor micro scale. Moreover, the Taylor micro scale collapses the height of the shear layer in the direction of the vorticity stretching. The outer region of the averaged flow patterns approximately scales with the macro scale, which indicates that the flow patterns outside of the shear layer mainly are determined by large scales. The strength of the shear layer in terms of the peak tangential velocity appears to scale with a mixture of the Kolmogorov velocity and root-mean-square of the streamwise velocity scaling. A quantitative universality in the reported shear layers is observed across both wall-bounded flows for locations above the buffer region. C 2014 AIP Publishing LLC. [http://dx

show abstract

“…The alignment properties between the rotation directionê ω and the stretching directionê i at the same time have been investigated for the true velocity gradient tensor [22][23][24][25][26][27][28][29] . On the basis of the intuitive notion that stretching is strongest in the directionê 1 , it was expected that there would be a strong alignment ofê ω witĥ e 1 .…”

mentioning

confidence: 99%

“…Thus, the alignment with the initially strongest stretching direction is a dynamical process: not surprisingly, the alignment betweenê ω (t ) andê 1 (0) builds up over time. Understanding the alignment properties betweenê ω and the eigenvectors of the strainê 1 at equal time (Eulerian point of view) requires a proper description of the rotation of the eigenvectors (ê 1 (t ),ê 2 (t ),ê 3 (t )), which is affected by nonlocal (pressure) effects 28 . The time of decorrelation between the direction ofê 1 (t ) andê 1 (0) is found to be on the order of 0.2t 0 , comparable to the time of alignment ofê ω (t ) andê 1 (0), thus explaining the lack of observed alignment between e ω (t ) andê 1 (t ).…”

mentioning

confidence: 99%

The pirouette effect in turbulent flows

2011

View full text Add to dashboard Cite

The disorganized fluctuations of turbulence are crucial in the transport of particles or chemicals 1,2 and could play a decisive role in the formation of rain in clouds 3 , the accretion process in protoplanetary disks 4 , and how animals find their mates or prey 5,6 . These and other examples 7 suggest a yet-to-bedetermined unifying structure of turbulent flows 8,9 . Here, we unveil an important ingredient of turbulence by taking the perspective of an observer who perceives its world with respect to three distant neighbours all swept by the flow. The time evolution of the observer's world can be decomposed into rotation and stretching. We show that, in this Lagrangian frame, the axis of rotation aligns with the initially strongest stretching direction, and that the dynamics can be understood by the conservation of angular momentum. This 'pirouette effect' thus appears as an important structural component of turbulence, and elucidates the mechanism for small-scale generation in turbulence.To an observer who perceives its world with respect to three distant fluid tracers, all carried by the flow, the seemingly random turbulent motion modifies the distances to and between them. Turbulent motion, on average, separates two tracers [10][11][12] . However, as shown in Fig. 1, given a set of four tracers initially located on a regular tetrahedron, that is, with all pairs equally separated by a distance R 0 , the growth of the distance between pairs is very uneven, resulting in strong shape deformation [13][14][15][16] . As first observed in ref. 17, the resulting 'minimal' four-point description provides important insights into the dynamics of turbulence.Remarkably, our study of the relative motion between these neighbouring particles, as shown in Fig. 1, reveals the alignment of the rotation towards the direction of the initially strongest stretching, while the angular momentum remains constant (statistically, see Supplementary Information). This is a manifestation of the 'pirouette effect', well known from classical ballet or ice-skating.We used a particle tracking technique to follow several hundreds of nearly neutrally buoyant, 30 µm size polystyrene particles as tracers in a turbulent water flow 11,18,19 with high turbulence intensities as defined by the Taylor microscale Reynolds number 10,20 350 ≤ R λ ≤ 815. We recorded tracer motion in volumes as large as (5 cm) 3 with a spatial resolution of approximately 20 µm and a time resolution of 0.04 ms by stereoscopic observation using three high-speed cameras. We accurately determined the trajectories and velocities of millions of tracers in three dimensions, from which we extracted the dynamics of initially regular tetrahedra by conditioning statistics on four tracers with nearly equal mutual distances (as in ref. 15 and Supplementary Information). We complemented the experiments by direct numerical simulations (DNS) of the Navier-Stokes equations for 100 ≤ R λ ≤ 170 (ref. 14).The time evolution of the observer's world can be decomposed into rotation and stretching, ...

show abstract

Direct assessment of vorticity alignment with local and nonlocal strain rates in turbulent flows

Cited by 72 publications

References 14 publications

Scale dependence of the alignment between strain rate and rotation in turbulent shear flow

Scale dependence of the alignment between strain rate and rotation in turbulent shear flow

Universality and scaling phenomenology of small-scale turbulence in wall-bounded flows

The pirouette effect in turbulent flows

Contact Info

Product

Resources

About