Acceleration statistics of tracer particles in filtered turbulent fields

Lalescu, Cristian; Wilczek, Michael

doi:10.1017/jfm.2018.381

Cited by 11 publications

(12 citation statements)

References 45 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We note in passing that a fit over the entire range of α values can be achieved by an interpolation between an alge- Conditional statistics Next, we demonstrate that conditioning on α leads to approximately Gaussian statistics. As an extreme example, we choose the PDF of the strongly non-Gaussian Lagrangian acceleration, for which events up to several hundred standard deviations have been observed [3,18,40,41]. The heavy tails of this distribution are indicative of the frequent occurrence of extreme events, which play an important role, for example, in the context of cloud microphysics [42].…”

Section: Resultsmentioning

confidence: 99%

Persistent accelerations disentangle Lagrangian turbulence

2019

Self Cite

View full text Add to dashboard Cite

Particles in turbulence frequently encounter extreme accelerations between extended periods of quiescence. The occurrence of extreme events is closely related to the intermittent spatial distribution of intense flow structures such as vorticity filaments. This mixed history of flow conditions leads to very complex particle statistics with a pronounced scale dependence, which presents one of the major challenges on the way to a non-equilibrium statistical mechanics of turbulence. Here, we introduce the notion of persistent Lagrangian acceleration, quantified by the squared particle acceleration coarse-grained over a viscous time scale. Conditioning Lagrangian particle data from simulations on this coarse-grained acceleration, we find remarkably simple, close-to-Gaussian statistics for a range of Reynolds numbers. This opens the possibility to decompose the complex particle statistics into much simpler sub-ensembles. Based on this observation, we develop a comprehensive theoretical framework for Lagrangian single-particle statistics that captures the acceleration, velocity increments as well as single-particle dispersion.

show abstract

Section: Resultsmentioning

confidence: 99%

Persistent accelerations disentangle Lagrangian turbulence

2019

Self Cite

View full text Add to dashboard Cite

show abstract

“…The temporally and spatially filtered force is obtained from the resolved velocity field, u f , while the random force accounts for fluctuations at unresolved scales. The filtered contribution presents much less intense fluctuations than the total acceleration as can be verified in Lalescu & Wilczek (2018). In line with the Kolmogorov hypothesis, it is assumed that the main source of randomness in the acceleration is attributed to the fluctuation of the local energy transfer rate.…”

Section: Introductionmentioning

confidence: 63%

Model for the dynamics of micro-bubbles in high-Reynolds-number flows

2019

View full text Add to dashboard Cite

We propose a model for the acceleration of micro-bubbles (smaller than the dissipative scale of the flow) subjected to the drag and fluid inertia forces in a homogeneous and isotropic turbulent flow. This model, that depends on the Stokes number, Reynolds number and the density ratio, reproduces the evolution of the acceleration variance as well as the relative importance and alignment of the two forces as observed from direct numerical simulations (DNS). We also report that the bubble acceleration statistics conditioned on the local kinetic energy dissipation rate are invariant with the Stokes number and the dissipation rate. Based on this observation, we propose a stochastic model for the instantaneous bubble acceleration vector accounting for the small-scale intermittency of the turbulent flows. The norm of the bubble acceleration is obtained by modelling the dissipation rate along the bubble trajectory from a log-normal stochastic process, whereas its orientation is given by two coupled random walks on a unit sphere in order to model the evolution of the joint orientation of the drag and inertia forces acting on the bubble. Furthermore, the proposed stochastic model for the bubble acceleration is used in the context of large eddy simulations (LES) of turbulent flows laden with small bubbles. To account for the turbulent motion at scales smaller than the mesh resolution, we decompose the instantaneous bubble acceleration in its resolved and residual parts. The first part is given by the drag and fluid inertia forces computed from the resolved velocity field, and the second term refers to the random contribution of small unresolved turbulent scales and is estimated with the stochastic model proposed in the paper. Comparisons with DNS and standard LES, show that the proposed model improves significantly the statistics of the bubbly phase.

show abstract

“…Using the root-mean-squared velocity component u and the energy spectrum , the integral length is defined as and the large eddy turn-over time as . To generate filtered flow fields, the velocity field is filtered at length scale using a Gaussian filter as detailed in Lalescu & Wilczek (2018). Values for vary from zero (no filtering) to (the integral scale).…”

Section: Direct Numerical Simulationsmentioning

confidence: 99%

“…Values for vary from zero (no filtering) to (the integral scale). Preliminary datasets were generated using all three spherically symmetric filter types described in Lalescu & Wilczek (2018) (i.e. ball filter, Gaussian filter, sharp spectral filter), but the filter type resulted in only small changes in the results with the overall trend being insensitive to the precise filter type.…”

Section: Direct Numerical Simulationsmentioning

confidence: 99%