Timescales of Turbulent Relative Dispersion

Tracers in a turbulent flow separate according to the celebrated $t^{3/2}$ Richardson--Obukhov law, which is usually explained by a scale-dependent effective diffusivity. Here, supported by state-of-the-art numerics, we revisit this argument. The Lagrangian correlation time of velocity differences is found to increase too quickly for validating this approach, but acceleration differences decorrelate on dissipative timescales. This results in an asymptotic diffusion $\propto t^{1/2}$ of velocity differences, so that the long-time behavior of distances is that of the integral of Brownian motion. The time of convergence to this regime is shown to be that of deviations from Batchelor's initial ballistic regime, given by a scale-dependent energy dissipation time rather than the usual turnover time. It is finally argued that the fluid flow intermittency should not affect this long-time behavior of relativeComment: 4 pages, 3 figure

Geometry and violent events in turbulent pair dispersion

The statistics of Lagrangian pair dispersion in a homogeneous isotropic flow is investigated by means of direct numerical simulations. The focus is on deviations from Richardson eddy-diffusivity model and in particular on the strong fluctuations experienced by tracers. Evidence is obtained that the distribution of distances attains an almost self-similar regime characterized by a very weak intermittency. The timescale of convergence to this behavior is found to be given by the kinetic energy dissipation time measured at the scale of the initial separation. Conversely the velocity differences between tracers are displaying a strongly anomalous behavior whose scaling properties are very close to that of Lagrangian structure functions. These violent fluctuations are interpreted geometrically and are shown to be responsible for a long-term memory of the initial separation. Despite this strong intermittency, it is found that the mixed moment defined by the ratio between the cube of the longitudinal velocity difference and the distance attains a statistically stationary regime on very short timescales. These results are brought together to address the question of violent events in the distribution of distances. It is found that distances much larger than the average are reached by pairs that have always separated faster since the initial time. They contribute a stretched exponential behavior in the tail of the inter-tracer distance probability distribution. The tail approaches a pure exponential at large times, contradicting Richardson diffusive approach. At the same time, the distance distribution displays a time-dependent power-law behavior at very small values, which is interpreted in terms of fractal geometry. It is argued and demonstrated numerically that the exponent converges to one at large time, again in conflict with Richardson's distribution.Comment: 21 page

Lidar investigations of M-zone

The creation of pulse dye lasers tuned to resonant line of meteor produced admixtures of atmospheric constituents has made it possible to begin lidar investigations of the vertical distribution of mesospheric sodium concentration and its dynamics in the upper atmosphere. The observed morning increase of sodium concentration in the vertical column is probably caused by diurnal variations of sporadic meteors. The study of the dynamics of the sodium column concentration in the period of meteor streams activity confirms the suggestion of cosmic origin of these atoms. The short lived increase of sodium concentration brought about by a meteor stream, however, exceeds by one order the level of the sporadic background

Lagrangian statistics of particle pairs in homogeneous isotropic turbulence

We present a detailed investigation of the particle pair separation process in homogeneous isotropic turbulence. We use data from direct numerical simulations up to Taylor's Reynolds number 280 following the evolution of about two million passive tracers advected by the flow over a time span of about three decades. We present data for both the separation distance and the relative velocity statistics. Statistics are measured along the particle pair trajectories both as a function of time and as a function of their separation, i.e. at fixed scales. We compare and contrast both sets of statistics in order to gain an insight into the mechanisms governing the separation process. We find very high levels of intermittency in the early stages, that is, for travel times up to order ten Kolmogorov time scales. The fixed scale statistics allow us to quantify anomalous corrections to Richardson diffusion in the inertial range of scales for those pairs that separate rapidly. It also allows a quantitative analysis of intermittency corrections for the relative velocity statistics.Comment: 16 pages, 16 figure

Exponential bounds for the probability deviations of sums of random fields

Non-asymptotic exponential upper bounds for the deviation probability for a sum of independent random fields are obtained under Bernstein's condition and assumptions formulated in terms of Kolmogorov's metric entropy. These estimations are constructive in the sense that all the constants involved are given explicitly. In the case of moderately large deviations, the upper bounds have optimal log-asymptotices. The exponential estimations are extended to the local and global continuity modulus for sums of independent samples of a random field

Random field sampling for a simplified model of melt-blowing considering turbulent velocity fluctuations

In melt-blowing very thin liquid fiber jets are spun due to high-velocity air streams. In literature there is a clear, unsolved discrepancy between the measured and computed jet attenuation. In this paper we will verify numerically that the turbulent velocity fluctuations causing a random aerodynamic drag on the fiber jets -- that has been neglected so far -- are the crucial effect to close this gap. For this purpose, we model the velocity fluctuations as vector Gaussian random fields on top of a k-epsilon turbulence description and develop an efficient sampling procedure. Taking advantage of the special covariance structure the effort of the sampling is linear in the discretization and makes the realization possible

Coagulation of Aerosol Particles in Turbulent Flows

. -- Coagulation of particles in turbulent flows is studied. The size distribution of particles is governed by Smoluchowski equation with random collision coefficient. The random coagulation coefficient is derived by a generalization of the approach suggested by Saffman and Turner [12]. The coagulation process is analysed in three main cases: (1) T c , the characteristic coagulation time is much less than Tw , the characteristic Lagrangian time of the turbulent flow, (2) conversely, Tw !! T c , and (3), these times are of the same order: Tw ¸ T c . A special stochastic time is introduced which drastically simplifies the analysis of the influence of the intermittency. A detailed numerical study is given for two cases with known explicit solutions of Smoluchowski equation. The numerical analysis in the turbulent collision regime is based on the stochastic algorithm presented in the book [9] and developed in [11], [10], and [4]. 1 Introduction The coagulation processes of aerosol particl..

Lognormal random field approximations to LIBOR market models

We study several approximations for the LIBOR market models presented in [1, 2, 5]. Special attention is payed to log-normal approximations and their simulation by using direct simulation methods for log-normal random fields. In contrast to the conventional numerical solution of SDE's this approach simulates the solution directly at the desired point and is therefore much more efficient. We carry out a path-wise comparison of the approximations and give applications to the valuation of the swaption and the trigger swap. 1 Introduction By far the most important class of traded interest rate derivatives is constituted by derivatives which are specified in terms of LIBOR rates. The LIBOR 1 rate L is the annualized effective interest rate over a forward period [T 1 ; T 2 ] and can be expressed in terms of two zero-coupon bonds B 1 and B 2 with face value $1; maturing at T 1 and T 2 ; respectively, L(t; T 1 ; T 2 ) := B1 (t) B2 (t) \Gamma 1 T 2 \Gamma T 1 ; (1) where as usual T 2 is..

Efficient simulation of random fields for fiber-fluid interactions in isotropic turbulence

In some processes for spinning synthetic fibers the filaments are exposed to highly turbulent flows to achieve a high degree of stretching. The quality of the resulting fabric is thus determined essentially by the turbulent fiber-fluid interactions. Due to the required fine resolution, direct numerical simulations fail. Therefore we model the flow fluctuations as random field in R4 on top of a k-ε turbulence description and describe the interactions in the context of slender-body theory as one-way-coupling with a corresponding stochastic aerodynamic drag force on the fibers. Hereby we exploit the special covariance structure of the random field, namely isotropy, homogeneity and decoupling of space and time. In this work we will focus on the construction and efficient simulation of the turbulent fluctuations assuming constant flow parameters and give an outlook on applications