10:30
Lagrangian aspects of turbulence 1
Chair: Gregory Falkovich
10:30
15 mins
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Settling of particles in homogeneous shear turbulence
Michel van Hinsberg, Herman Clercx, Federico Toschi
Abstract: The settling of (inertial) particles is studied in homogeneous shear turbulence. A drift velocity perpendicular to gravity is measured due to the interplay between the homogeneous shear turbulence and gravity acting on the particles. We introduce a model to predict and understand this phenomenon.
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10:45
15 mins
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Velocity-Gradient Probability Distribution Functions in a Lagrangian Model of Turbulence
Luca Moriconi, Rodrigo M. Pereira, Leonardo S. Grigorio
Abstract: The Recent Fluid Deformation Closure (RFDC) model of lagrangian turbulence is recast in path-integral language within the framework of the Martin-Siggia-Rose functional formalism. In order to derive analytical expressions for the velocity-gradient probability distribution functions (vgPDFs), we carry out noise renormalization in the low-frequency regime and find approximate extrema for the Martin-Siggia-Rose effective action. We verify, with the help of Monte Carlo simulations, that the vgPDFs so obtained yield a close description of the single-point statistical features implied by the original RFDC stochastic differential equations.
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11:00
15 mins
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Non-Gaussianity in turbulent pair dispersion
Benjamin Devenish, David Thomson
Abstract: We consider an extension of Thomson's (JFM, 1990) two-particle
Lagrangian stochastic model that is constructed to be consistent
with the 4/5 law of turbulence. It is shown that one effect of
non-zero skewness in the longitudinal relative velocity is to reduce
the value of Richardson's constant by approximately a factor
of two relative to the model with zero skewness and that this
value is close to recent measurements from direct numerical simulation
of homogeneous isotropic turbulence.
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11:15
15 mins
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DYNAMICS OF FINITE-SIZED LIGHT SPHERES IN TURBULENCE
Varghese Mathai, Vivek Prakash, Jon Brons, Chao Sun, Detlef Lohse
Abstract: We report experimental results on the Lagrangian dynamics of finite-size light particles in turbulence. Using an orthogonal camera setup and 3D particle tracking, we study the velocity and acceleration statistics of rigid light spheres in a water tunnel with nearly homogeneous and isotropic turbulence. The Reynolds number (Re) is varied from 180 to 300, and the study covers a range of size ratios (4 < D/η < 16) for marginally light spheres. We find that the normalised acceleration PDF decreases in intermittency with increasing size ratio - in qualitative agreement with the predictions of the Faxén corrected model. We also present preliminary results on the rotational dynamics of large light spheres in turbulence.
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11:30
15 mins
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Pair dispersion statistics and coherent structures
Manu Goudar, Gerrit Elsinga
Abstract: Pair dispersion is studied to model scalar transport in many natural and industrial applications. The link between the particle pair dispersion and coherent flow structures is explored in this work. This was done by kinematically simulating tracer particles in an ideal flow structure [Elsinga and Marusic (2010)] extracted from an isotropic turbulent flow. It was found that the variation of the mean and the mean square separation lengths with time were qualitative similar to the results in actual turbulent flows. It was also observed that the quantitative results matched till 4-5 Kolmogrov time units. Ideal structure with two vortices and a shear layer was able to emulate the qualitative results. Is the combination of shear layer and one/two vortices is sufficient or necessary to emulate pair dispersion statistics needs to be studied in the future.
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11:45
15 mins
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Universal Statistical Properties of Inertial-particle Trajectories in Three-dimensional, Homogeneous, Isotropic, Fluid Turbulence
Akshay Bhatnagar, Anupam Gupta, Dhrubaditya Mitra, Prasad Perlekar, Rahul Pandit
Abstract: We obtain new universal statistical properties
of heavy-particle trajectories in three-dimensional, statistically steady,
homogeneous, and isotropic turbulent flows by direct numerical
simulations. We show that the probability distribution functions (PDFs)
$P(\phi)$, of the angle $\phi$ between the Eulerian velocity
${\bf u}$ and the particle velocity ${\bf v}$, at a point and time,
scales as $P(\phi) \sim \phi^{-\gamma}$, with a new
universal exponent $\gamma \simeq 4$. The PDFs of the trajectory curvature $\kappa$
and modulus $\theta$
of the torsion $\vartheta$ scale, respectively, as
$P(\kappa) \sim \kappa^{-h_\kappa}$, as $\kappa \to \infty$, and $P(\theta)
\sim \theta^{-h_\theta}$, as $\theta \to \infty$, with exponents $h_\kappa
\simeq 2.5$ and $h_\theta \simeq 3$ that
do not depend on the Stokes number $St$.
We also show that $\gamma$, $h_\kappa$ and $h_\theta$ can be obtained by
using simple stochastic models.
We show that the number
$N_I(t,St)$ of points (up until time $t$), at which $\vartheta$ changes sign,
is such that $n_I(St) \equiv \lim_{t\to\infty} \frac{N_I(t,St)}{t} \sim St^{-\Delta}$,
with $\Delta \simeq 0.4$ a universal exponent.
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