The pirouette effect in turbulent flows

Abstract

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, ...

Flight–crash events in turbulence

“…The phenomenon discussed here is illustrated in Fig. 1 A and B, which show the evolution of EðtÞ along the trajectory of a fluid particle in a 3D laboratory water flow (17,18). It illustrates that to build up large kinetic energy requires a longer time than to dissipate the same amount.…”

“…The 3D experiments were performed in a so-called von Kármán mixer, which generates high-Reynolds-number turbulent water flow between two counterrotating disks (15,17). We measured 3D trajectories of tracer particles seeded in the flow using optical Lagrangian particle tracking (17,18). The Reynolds number of the turbulence was in the 350 ≤ R λ ≤ 690 range.…”

“…The recent advances in our ability to reliably measure the trajectories of small tracer particles in well-controlled laboratory flows (15)(16)(17)(18), as well as to simulate accurately the motion of particle tracers using the Navier-Stokes equation (16) allow us to investigate these fundamental issues. In this work, we restrict ourselves to statistically stationary and homogeneous flows.…”

Effects of Lewis number on vorticity and enstrophy transport in turbulent premixed flames

“…In particular, Chakraborty 18 showed that the statistical behaviour of vorticity alignment with local principal strain rates can be significantly different for the corrugated flamelets regime of combustion with Le = 1.0, and for the thin reaction zones regime of combustion with non-unity Lewis number, in comparison to earlier studies. [8][9][10][11][19][20][21][22][23][24][25][26][27][28] For example, in the corrugated flamelets regime, and for the cases with high Karlovitz number and low Le, where the most extensive principal strain rate is controlled by the local dilatation rate, 18 the vorticity vector ⃗ ω predominantly aligns with the intermediate and the most compressive principal strain rates. Such an alignment of the vorticity vector differs from the alignment observed earlier in premixed 11 and non-premixed [8][9][10] flames with unity Lewis number, or in non-reacting flows.…”

“…Such an alignment of the vorticity vector differs from the alignment observed earlier in premixed 11 and non-premixed [8][9][10] flames with unity Lewis number, or in non-reacting flows. [19][20][21][22][23][24][25][26][27][28] While each individual species j has its own Lewis number Le j , in simplified models of molecular transport, the Lewis number of the deficient reactant (fuel or oxidant) is often taken to be the characteristic global Lewis number Le 29 as was done in the aforementioned analysis by Chakraborty. 18 It is worth noting here that alternative methods of assigning a characteristic Lewis number have been proposed based on heat release measurements 30,31 and mole fractions of the mixture constituents.…”