Holger Homann

Universal intermittent properties of particle trajectories in highly turbulent flows

We present a collection of eight data sets from state-of-the-art experiments and numerical simulations on turbulent velocity statistics along particle trajectories obtained in different flows with Reynolds numbers in the range R{lambda}in[120:740]. Lagrangian structure functions from all data sets are found to collapse onto each other on a wide range of time lags, pointing towards the existence of a universal behavior, within present statistical convergence, and calling for a unified theoretical description. Parisi-Frisch multifractal theory, suitably extended to the dissipative scales and to the Lagrangian domain, is found to capture the intermittency of velocity statistics over the whole three decades of temporal scales investigated here.

Finite-size effects in the dynamics of neutrally buoyant particles in turbulent flow

The dynamics of neutrally buoyant particles transported by a turbulent flow is investigated for spherical particles with radii of the order of the Kolmogorov dissipative scale or larger. The pseudo-penalization spectral method that has been proposed by Pasquetti et al . ( Appl. Numer. Math. , vol. 58, 2008, pp. 946–954) is adapted to integrate numerically the simultaneous dynamics of the particle and of the fluid. Such a method gives a unique handle on the limit of validity of point-particle approximations, which are generally used in applicative situations. Analytical predictions based on such models are compared to result of very well-resolved direct numerical simulations. Evidence is obtained that Faxen corrections reproduce dominant finite-size effects on velocity and acceleration fluctuations for particle diameters up to four times the Kolmogorov scale. The dynamics of particles with larger diameters is consistent with predictions obtained from dimensional analysis.

Numerical simulations of possible finite time singularities in the incompressible Euler equations : Comparison of numerical methods

Abstract The numerical simulation of the 3D incompressible Euler equations is analyzed with respect to different integration methods. The numerical schemes we considered include spectral methods with different strategies for dealiasing and two variants of finite difference methods. Based on this comparison, a Kida–Pelz-like initial condition is integrated using adaptive mesh refinement and estimates on the necessary numerical resolution are given. This estimate is based on analyzing the scaling behavior similar to the procedure in critical phenomena and present simulations are put into perspective.

Lagrangian Statistics of Navier-Stokes- and MHD-Turbulence

We report on a comparison of high-resolution numerical simulations of Lagrangian particles advected by incompressible turbulent hydro- and magneto- hydrodynamic (MHD) flows. Numerical simulations were performed with up to 1024 3 collocation points and 10 million particles in the Navier-Stokes case and 512 3 collocation points and 1 million particles in the MHD case. In the hydrodynamics case our findings compare with recent experiments from Mordant et al. (2004 New J. Phys. 6, 116) and Xu et al. (2006 Phys. Rev. Lett.96, 024503). They differ from the simulations of Biferale et al. (2004 Phys. Rev. Lett. 93, 064502) due to differences of the ranges chosen for evaluating the structure functions. In Navier- Stokes turbulence intermittency is stronger than predicted by the multifractal approach of Biferale et al. (2004 Phys. Rev. Lett. 93, 064502) whereas in MHD tur- bulence the predictions from the multifractal approach are more intermittent than observed in our simulations. In addition, our simulations reveal that Lagrangian Navier-Stokes turbulence is more intermittent than MHD turbulence, whereas the situation is reversed in the Eulerian case. Those findings can not consistently be described by the multifractal modeling. The crucial point is that the geometry of the dissipative structures have different implications for Lagrangian and Eulerian intermittency. Application of the multifractal approach for the modeling of the acceleration probability density functions works well for the Navier-Stokes case but in the MHD case just the tails are well described.

Slipping motion of large neutrally buoyant particles in turbulence

Direct numerical simulations are used to investigate the individual dynamics of large spherical particles suspended in a developed homogeneous turbulent flow. A definition of the direction of the particle motion relative to the surrounding flow is introduced and used to construct the mean fluid velocity profile around the particle. This leads to an estimate of the particle slipping velocity and its associated Reynolds number. The flow modifications due to the particle are then studied. The particle is responsible for a shadowing effect that occurs in the wake up to distances of the order of its diameter: the particle calms turbulent fluctuations and reduces the energy dissipation rate compared to its average value in the bulk. Dimensional arguments are presented to draw an analogy between particle effects on turbulence and wall flows. Evidence is obtained for the presence of a logarithmic sublayer at distances between the thickness of the viscous boundary layer and the particle diameter

Gravity-driven enhancement of heavy particle clustering in turbulent flow.

{D}_{p}

Bridging from Eulerian to Lagrangian statistics in 3D hydro- and magnetohydrodynamic turbulent flows

. Finally, asymptotic arguments are used to relate the viscous sublayer quantities to the particle size and the properties of the outer turbulence. It is shown in particular that the skin-friction Reynolds number behaves as

Impact of the floating-point precision and interpolation scheme on the results of DNS of turbulence by pseudo-spectral codes

R{e}_{\tau } \propto {({D}_{p} / \eta )}^{4/ 3}

Geometry and violent events in turbulent pair dispersion

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Longitudinal and transverse structure functions in high-Reynolds-number turbulence

Heavy particles suspended in a turbulent flow settle faster than in a still fluid. This effect stems from a preferential sampling of the regions where the fluid flows downward and is quantified here as a function of the level of turbulence, of particle inertia, and of the ratio between gravity and turbulent accelerations. By using analytical methods and detailed, state-of-the-art numerical simulations, settling is shown to induce an effective horizontal two-dimensional dynamics that increases clustering and reduce relative velocities between particles. These two competing effects can either increase or decrease the geometrical collision rates between same-size particles and are crucial for realistic modeling of coalescing particles.