Multi-particle and tetrad statistics in numerical simulations of turbulent relative dispersion

et al. 2012

Physics of Fluids

The length distribution of streamline segments in homogeneous isotropic decaying turbulence Phys. Fluids 24, 045104 (2012) Conditional vorticity budget of coherent and incoherent flow contributions in fully developed homogeneous isotropic turbulence Phys. Fluids 24, 035108 (2012) Near-field investigation of turbulence produced by multi-scale grids Phys. Fluids 24, 035103 (2012) Reynolds number effect on the velocity increment skewness in isotropic turbulence Phys. Fluids 24, 015108 (2012) Spectral approach to finite Reynolds number effects on Kolmogorov's 4/5 law in isotropic turbulence Phys. Fluids 24, 015107 (2012) In turbulence, ideas of energy cascade and energy flux, substantiated by the exact Kolmogorov relation, lead to the determination of scaling laws for the velocity spatial correlation function. Here we ask whether similar ideas can be applied to temporal correlations. We critically review the relevant theoretical and experimental results concerning the velocity statistics of a single fluid particle in the inertial range of statistically homogeneous, stationary and isotropic turbulence. We stress that the widely used relations for the second structure function, D 2 (t) ≡ [v(t) − v(0)] 2 ∝ εt, relies on dimensional arguments only: no relation of D 2 (t) to the energy cascade is known, neither in two-nor in three-dimensional turbulence. State of the art experimental and numerical results demonstrate that at high Reynolds numbers, the derivative d D 2 (t) dt has a finite non-zero slope starting from t ≈ 2τ η . The analysis of the acceleration spectrum A (ω) indicates a possible small correction with respect to the dimensional expectation A (ω) ∼ ω 0 but present data are unable to discriminate between anomalous scaling and finite Reynolds effects in the second order moment of velocity Lagrangian statistics. C 2012 American Institute of Physics.

Section: B Acceleration Spectramentioning

confidence: 99%

On Lagrangian single-particle statistics

Falkovich

et al. 2012

Physics of Fluids

“…The difficulty in obtaining experimental results on collisions in turbulence makes numerical investigations an essential tool. The investigation of fundamental issues in turbulence rests on direct integration of the Navier-Stokes equation, (14) and (15), in a triply periodic domain (effectively a torus) [41,42,43]. In such a configuration, the Navier-Stokes can be efficiently integrated using pseudo-spectral methods, based on a (truncated) Fourier series decompositions of the velocity field u.…”

Section: Numerical Investigationsmentioning

confidence: 99%

Collisional Aggregation Due to Turbulence

Annu. Rev. Condens. Matter Phys.

Wilkinson

2016

105

103

Collisions between particles suspended in a fluid play an important role in many physical processes. As an example, collisions of microscopic water droplets in clouds are a necessary step in the production of macroscopic raindrops. Collisions of dust grains are also conjectured to be important for planet formation in the gas surrounding young stars, and also to play a role in the dynamics of sand storms. In these processes, collisions are favoured by fast turbulent motions. Here we review recent advances in the understanding of collisional aggregation due to turbulence. We discuss the role of fractal clustering of particles, and caustic singularities of their velocities. We also discuss limitations of the Smoluchowski equation for modelling these processes. These advances lead to a semi-quantitative understanding on the influence of turbulence on collision rates, and point to deficiencies in the current understanding of rainfall and planet formation.

“…In this work, we followed tetrahedra that are initially regular (close to regular in experiments), so as to identify flow properties at a single scale. The alignment dynamics studied here occurs before the tetrahedra become strongly deformed 21,22 or we did not use the highly deformed tetrahedra in the analysis. As shown in Section IV the fraction of highly-flattened tetrahedra is negligible up to t 0 /4 and only approximately 10% are highly-deformed at t 0 /2.…”

Section: Definition Of the Perceived Velocity Gradient Tensor Mmentioning

confidence: 99%

Tetrahedron deformation and alignment of perceived vorticity and strain in a turbulent flow

Bodenschatz

2013

Physics of Fluids

We describe the structure and dynamics of turbulence by the scale-dependent perceived velocity gradient tensor as supported by following four tracers, i.e., fluid particles, that initially form a regular tetrahedron. We report results from experiments in a von Kármán swirling water flow and from numerical simulations of the incompressible Navier-Stokes equation. We analyze the statistics and the dynamics of the perceived rate of strain tensor and vorticity for initially regular tetrahedron of size r 0 from the dissipative to the integral scale. Just as for the true velocity gradient, at any instant, the perceived vorticity is also preferentially aligned with the intermediate eigenvector of the perceived rate of strain. However, in the perceived rate of strain eigenframe fixed at a given time t = 0, the perceived vorticity evolves in time such as to align with the strongest eigendirection at t = 0. This also applies to the true velocity gradient. The experimental data at the higher Reynolds number suggests the existence of a self-similar regime in the inertial range. In particular, the dynamics of alignment of the perceived vorticity and strain can be rescaled by t 0, the turbulence time scale of the flow when the scale r 0 is in the inertial range. For smaller Reynolds numbers we found the dynamics to be scale dependent