Two Particle

is a graduate student supported by internal institutional funds. He is relatively new in the project and has been mainly spending time learning to use the various software tools available. He is also working with researchers from France who would like to use our simulation data for purposes of wavelet analyses and Coherent Vortex Simulation.

Lagrangian data can provide relevant information on the advection and diffusion properties of geophysical flows at different scales of motion. In this study, the dispersion properties of an ensemble of trajectories transported by a surface ocean flow are analyzed. The data come from a set of Lagrangian drifters released in the South Brazilian Bight, during several oceanographic campaigns. Adopting a dynamical systems approach, the attention is primarily focused on scale-dependent indicators, like the finite-scale Lyapunov exponent. The relevance of mechanisms like two-dimensional turbulence for the dispersion process is addressed. Some deviations from the classical turbulent dispersion scenario in two-dimensions are found, likely to be ascribed to the nonstationary and nonhomogeneous characteristics of the flow. Relatively small-scale features (of order 1-10 km) are also considered to play a role in determining the properties of relative dispersion as well as the shape of the kineti...

In quantum scattering processes between two particles, aspects characterizing the strong and Coulomb forces can be observed in kinematic distributions of the particle pairs. The sensitivity to the interaction potential reaches a maximum at low relative momentum and vanishing distance between the two particles. Ultrarelativistic heavy-ion collisions at the LHC provide an abundant source of many hadron species and can be employed as a measurement method of scattering parameters that is complementary to scattering experiments. This study confirms that momentum correlations of particles produced in Pb-Pb collisions at the LHC provide an accurate measurement of kaon-proton scattering parameters at low relative momentum, allowing precise access to the K − p → K − p process. This work also validates the femtoscopic measurement in ultrarelativistic heavy-ion collisions as an alternative to scattering experiments and a complementary tool to the study of exotic atoms with comparable precision. In this work, the first femtoscopic measurement of momentum correlations of K − p (K + p) and K + p (K − p) pairs in Pb-Pb collisions at centre-of-mass energy per nucleon pair of √ s NN = 5.02 TeV registered by the ALICE experiment is reported. The components of the K − p complex scattering length are extracted and found to be f 0 = −0.91 ± 0.03(stat) +0.17 −0.03 (syst) and f 0 = 0.92 ± 0.05(stat) +0.12 −0.33 (syst). The results are compared with chiral effective field theory predictions as well as with existing data from dedicated scattering and exotic kaonic atom experiments.

In quantum scattering processes between two particles, aspects characterizing the strong and Coulomb forces can be observed in kinematic distributions of the particle pairs. The sensitivity to the interaction potential reaches a maximum at low relative momentum and vanishing distance between the two particles. Ultrarelativistic heavy-ion collisions at the LHC provide an abundant source of many hadron species and can be employed as a measurement method of scattering parameters that is complementary to scattering experiments. This study confirms that momentum correlations of particles produced in Pb-Pb collisions at the LHC provide an accurate measurement of kaon-proton scattering parameters at low relative momentum, allowing precise access to the K − p → K − p process. This work also validates the femtoscopic measurement in ultrarelativistic heavy-ion collisions as an alternative to scattering experiments and a complementary tool to the study of exotic atoms with comparable precision. In this work, the first femtoscopic measurement of momentum correlations of K − p (K + p) and K + p (K − p) pairs in Pb-Pb collisions at centre-of-mass energy per nucleon pair of √ s NN = 5.02 TeV registered by the ALICE experiment is reported. The components of the K − p complex scattering length are extracted and found to be f 0 = −0.91 ± 0.03(stat) +0.17 −0.03 (syst) and f 0 = 0.92 ± 0.05(stat) +0.12 −0.33 (syst). The results are compared with chiral effective field theory predictions as well as with existing data from dedicated scattering and exotic kaonic atom experiments.

In quantum scattering processes between two particles, aspects characterizing the strong and Coulomb forces can be observed in kinematic distributions of the particle pairs. The sensitivity to the interaction potential reaches a maximum at low relative momentum and vanishing distance between the two particles. Ultrarelativistic heavy-ion collisions at the LHC provide an abundant source of many hadron species and can be employed as a measurement method of scattering parameters that is complementary to scattering experiments. This study confirms that momentum correlations of particles produced in Pb-Pb collisions at the LHC provide an accurate measurement of kaon-proton scattering parameters at low relative momentum, allowing precise access to the K − p → K − p process. This work also validates the femtoscopic measurement in ultrarelativistic heavy-ion collisions as an alternative to scattering experiments and a complementary tool to the study of exotic atoms with comparable precision. In this work, the first femtoscopic measurement of momentum correlations of K − p (K + p) and K + p (K − p) pairs in Pb-Pb collisions at centre-of-mass energy per nucleon pair of √ s NN = 5.02 TeV registered by the ALICE experiment is reported. The components of the K − p complex scattering length are extracted and found to be f 0 = −0.91 ± 0.03(stat) +0.17 −0.03 (syst) and f 0 = 0.92 ± 0.05(stat) +0.12 −0.33 (syst). The results are compared with chiral effective field theory predictions as well as with existing data from dedicated scattering and exotic kaonic atom experiments.

Submitted for the DFD15 Meeting of The American Physical Society The Decay of Turbulence After it Stops Rotating. 1 J. BLAIR PEROT, CHRIS ZUSI, Univ of Mass-Amherst-It is well known that the value of the power-law decay rate is reduced when turbulence is rotated. Less well known is how rotating turbulence behaves when system rotation stops. 512 3 DNS simulations of properly initialized isotropic turbulence at a variety of Reynolds numbers and rotation rates are used to show that immediately after rotation stops decaying turbulence has an exponential and not a classical power-law decay. Exponential decay is equivalent to an infinite power-law decay exponent and is a result of a constant physical turbulent timescale. In contrast, classical power-law decaying turbulence has a turbulent timescale that is proportional to the time itself. The implications for the modeling of the dissipation rate, and the physics of the turbulent decay process, are discussed.

We perform direct numerical simulations to study the effects of the finite Reynolds number and domain size on the decay law of Saffman turbulence. We observe that the invariant for Saffman turbulence, u2ℓ3, and non-dimensional dissipation coefficient, Cϵ = ϵ/(u3/ℓ), are sensitive to finite domain size; here, u is the rms velocity, ℓ is the integral length scale, and ϵ is the energy dissipation rate. Consequently, the exponent n in the decay law u2 ∼ t−n for Saffman turbulence deviates from 6/5. Due to the finite Reynolds number and the domain size, Saffman turbulence decays at a faster rate (i.e., n > 6/5). However, the exponent n = 6/5 is more sensitive to the domain size than to the Reynolds number. From the simulations, we find that n remains close to 6/5 as long as Rλ ≳ 10 and ℓ ≲ 0.3Lbox; here, Rλ is the Reynolds number based on the Taylor microscale and Lbox is the domain size. We also notice that n becomes slightly lower than 6/5 for a part of the decay period. Interesting...

We study motion of small particles in turbulence when the particle relaxation time falls in the range of inertial time-scales of the flow. Due to inertia, particles drift relative to the fluid. We show that the drift velocity is close to the Lagrangian velocity increments of turbulence at the particle relaxation time. We demonstrate that the collective drift of two close particles makes them see local velocity increments fluctuate fast and we introduce the corresponding Langevin description for separation dynamics. This allows to describe the behavior of the Lyapunov exponent and give the analogue of Richardson's law for separation above viscous scale.

We perform direct numerical simulations to study the effects of the finite Reynolds number and domain size on the decay law of Saffman turbulence. We observe that the invariant for Saffman turbulence, u2ℓ3, and non-dimensional dissipation coefficient, Cϵ = ϵ/(u3/ℓ), are sensitive to finite domain size; here, u is the rms velocity, ℓ is the integral length scale, and ϵ is the energy dissipation rate. Consequently, the exponent n in the decay law u2 ∼ t−n for Saffman turbulence deviates from 6/5. Due to the finite Reynolds number and the domain size, Saffman turbulence decays at a faster rate (i.e., n > 6/5). However, the exponent n = 6/5 is more sensitive to the domain size than to the Reynolds number. From the simulations, we find that n remains close to 6/5 as long as Rλ ≳ 10 and ℓ ≲ 0.3Lbox; here, Rλ is the Reynolds number based on the Taylor microscale and Lbox is the domain size. We also notice that n becomes slightly lower than 6/5 for a part of the decay period. Interesting...

We perform direct numerical simulations to study the effects of the finite Reynolds number and domain size on the decay law of Saffman turbulence. We observe that the invariant for Saffman turbulence, u2ℓ3, and non-dimensional dissipation coefficient, Cϵ = ϵ/(u3/ℓ), are sensitive to finite domain size; here, u is the rms velocity, ℓ is the integral length scale, and ϵ is the energy dissipation rate. Consequently, the exponent n in the decay law u2 ∼ t−n for Saffman turbulence deviates from 6/5. Due to the finite Reynolds number and the domain size, Saffman turbulence decays at a faster rate (i.e., n > 6/5). However, the exponent n = 6/5 is more sensitive to the domain size than to the Reynolds number. From the simulations, we find that n remains close to 6/5 as long as Rλ ≳ 10 and ℓ ≲ 0.3Lbox; here, Rλ is the Reynolds number based on the Taylor microscale and Lbox is the domain size. We also notice that n becomes slightly lower than 6/5 for a part of the decay period. Interesting...

In quantum scattering processes between two particles, aspects characterizing the strong and Coulomb forces can be observed in kinematic distributions of the particle pairs. The sensitivity to the interaction potential reaches a maximum at low relative momentum and vanishing distance between the two particles. Ultrarelativistic heavy-ion collisions at the LHC provide an abundant source of many hadron species and can be employed as a measurement method of scattering parameters that is complementary to scattering experiments. This study confirms that momentum correlations of particles produced in Pb-Pb collisions at the LHC provide an accurate measurement of kaon-proton scattering parameters at low relative momentum, allowing precise access to the K − p → K − p process. This work also validates the femtoscopic measurement in ultrarelativistic heavy-ion collisions as an alternative to scattering experiments and a complementary tool to the study of exotic atoms with comparable precision. In this work, the first femtoscopic measurement of momentum correlations of K − p (K + p) and K + p (K − p) pairs in Pb-Pb collisions at centre-of-mass energy per nucleon pair of √ s NN = 5.02 TeV registered by the ALICE experiment is reported. The components of the K − p complex scattering length are extracted and found to be f 0 = −0.91 ± 0.03(stat) +0.17 −0.03 (syst) and f 0 = 0.92 ± 0.05(stat) +0.12 −0.33 (syst). The results are compared with chiral effective field theory predictions as well as with existing data from dedicated scattering and exotic kaonic atom experiments.

We study pair dispersion in a three-dimensional incompressible high Reynolds number turbulent flow generated by Fourier transforming the dynamics of the GOY shell model into real space. We show that GOY shell model can successfully reproduce both the Batchelor and the Richardson-Obukhov regimes of turbulent relative dispersion. We also study how the cross-over time scales with the initial separations of a particle pair and compare it to the prediction by Batchelor.

We perform direct numerical simulations to study the effects of the finite Reynolds number and domain size on the decay law of Saffman turbulence. We observe that the invariant for Saffman turbulence, u 2 ℓ 3 , and non-dimensional dissipation coefficient, Cϵ = ϵ/(u 3 /ℓ), are sensitive to finite domain size; here, u is the rms velocity, ℓ is the integral length scale, and ϵ is the energy dissipation rate. Consequently, the exponent n in the decay law u 2 ∼ t −n for Saffman turbulence deviates from 6/5. Due to the finite Reynolds number and the domain size, Saffman turbulence decays at a faster rate (i.e., n > 6/5). However, the exponent n = 6/5 is more sensitive to the domain size than to the Reynolds number. From the simulations, we find that n remains close to 6/5 as long as R λ ≳ 10 and ℓ ≲ 0.3L box ; here, R λ is the Reynolds number based on the Taylor microscale and L box is the domain size. We also notice that n becomes slightly lower than 6/5 for a part of the decay period. Interestingly, this trend n < 6/5 is also observed earlier in freely decaying grid-generated turbulence.

We perform direct numerical simulations to study the effects of the finite Reynolds number and domain size on the decay law of Saffman turbulence. We observe that the invariant for Saffman turbulence, u 2 ℓ 3 , and non-dimensional dissipation coefficient, Cϵ = ϵ/(u 3 /ℓ), are sensitive to finite domain size; here, u is the rms velocity, ℓ is the integral length scale, and ϵ is the energy dissipation rate. Consequently, the exponent n in the decay law u 2 ∼ t −n for Saffman turbulence deviates from 6/5. Due to the finite Reynolds number and the domain size, Saffman turbulence decays at a faster rate (i.e., n > 6/5). However, the exponent n = 6/5 is more sensitive to the domain size than to the Reynolds number. From the simulations, we find that n remains close to 6/5 as long as R λ ≳ 10 and ℓ ≲ 0.3L box ; here, R λ is the Reynolds number based on the Taylor microscale and L box is the domain size. We also notice that n becomes slightly lower than 6/5 for a part of the decay period. Interestingly, this trend n < 6/5 is also observed earlier in freely decaying grid-generated turbulence.

An experimental investigation of the fine-scale structure of turbulence was carried out. Five different shear flows were studied: three in a wind tunnel with an open working section and an elliptical nozzle and two in a wind tunnel of closed working section and square cross-section. The experiments tested two approaches to the theory of fine-scale turbulence structure : one based on the Navier-Stokes equations and the other on some similarity hypotheses. The variability of all fine-scale constants (including exponents in inertial-subrange power laws and the Kolmogorov constant) is revealed. A correlation between all fine-scale constants and the external intermittency coefficient is established.

Deformation and breakup of drops in an isotropic turbulent flow has been studied by numerical simulation. The numerical method involves a pseudospectral representation of the turbulent outer flow field coupled to three-dimensional boundary integral simulations of the local drop dynamics. A statistical analysis based on an ensemble of drop trajectories is presented; results include breakup rates, the distribution of primary daughter drops produced by breakup events, and stationary distributions for drop deformation and orientation. Depending on the local flow history, drops may break at modest length or become highly elongated and relax without breaking. Drop deformation is the dominant mechanism of drop reorientation. The volume of the primary daughter drops, produced by a given fluctuation in flow strength, scales with the volume of the corresponding critical drop size for the fluctuation. A simplified description for the evolution of the drop size distribution, based on this scaling, is presented.

Kinematic simulation (KS) is a means of generating a turbulent-like velocity field, in a manner that enforces a desired input Eulerian energy spectrum. Such models have also been applied in particle-laden flows, due to their ability to enforce spatial organization of the fluid velocity field when simulating the trajectories of individual Lagrangian particles. A critical evaluation of KS is presented; in particular, we examine its ability to reproduce single-particle Lagrangian statistics. Also the ability of KS to reproduce the preferential concentration of inertial particles is examined. Some computational results are presented, in which particles are transported alternatively by (1) turbulence generated by direct numerical simulation (DNS) of the incompressible Navier-Stokes equations, and (2) KS. The effect of unsteadiness formulation in particular is examined. We find that even steady KS qualitatively reproduces the continuity effect, clustering of inertial particles, the elevated dispersion of inertial particles over fluid particles, and the intermittency of Lagrangian velocity signals, but generally not to the same extent as is seen in the DNS.

DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal. If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the "Taverne" license above, please follow below link for the End User Agreement:

We study the direct enstrophy cascade in a two-dimensional flow generated in an electromagnetically driven thin layer of fluid. Due to the presence of bottom friction, the energy spectrum deviates from the classical Kraichnan prediction k −3. We find that the correction to the spectral slope depends on the thickness on the layer, in agreement with a theoretical prediction based on the analogy with passive scalar statistics.

We study the direct enstrophy cascade in a two-dimensional flow generated in an electromagnetically driven thin layer of fluid. Due to the presence of bottom friction, the energy spectrum deviates from the classical Kraichnan prediction k −3. We find that the correction to the spectral slope depends on the thickness on the layer, in agreement with a theoretical prediction based on the analogy with passive scalar statistics.

The extraordinary complexity of turbulence has motivated the study of some of its key features in flows with similar structure but simpler or even trivial dynamics. Recently, a novel class of such flows has been developed in the laboratory by applying multiscale electromagnetic forcing to a thin layer of conducting fluid. In spite of being stationary, planar, and laminar these flows have been shown to resemble turbulent ones in terms of energy spectra and particle dispersion. In this thesis, some extensions of these flows are investigated through simulations of a layer-averaged model carried out using a bespoke semi-Lagrangian spline code. The selected forcings generalise the experimental ones by allowing for various kinds of self-similarity and planetary motion of the multiple scales. The spatiotemporal structure of the forcings is largely reflected on the flows, since they mainly arise from a linear balance between forcing and bottom friction. The exponents of the approximate powe...

Three-dimensional particle tracking velocimetry (3D-PTV) was applied to measure acceleration and spatial velocity gradients in quasi-homogeneous and isotropic turbulent flow. Structural aspects such as: spatial distribution of extreme values of acceleration in respect to the fields of vorticity and/or rate-of-strain, decomposition of the total acceleration a = Du/Dt into convective, a c =

This paper presents an attempt to realize experimental isotropic turbulence at low Reynolds number. For this aim an experimental apparatus, a turbulence chamber "Box", was designed and built to generate a turbulent flow field in the center of the chamber. The turbulent airflow field was generated by eight electrical fans placed symmetrically at the eight internal corners of the externally cubic chamber. The turbulence intensity was controlled by the fans speed. Laser Doppler velocimeter (LDV) in single and two-point velocity measurements was used to fully characterize the turbulent field inside the chamber. The main results indicate that the turbulence is homogeneous and isotropic with a quasi-zero mean velocity within a spherical region of 20 mm radius from the center of the chamber. The measured turbulent integral length scale was found to be constant and independent of the turbulence intensity (or fans speed). Furthermore, a noticeable spectral inertial subrange as prescribed by the Kolmogorov theory has not been observed at the range of Reynolds number explored here, where Re λ < 100. But rather a scaling region characterized by an exponent that is lower than the Kolmogorov value, -5/3, has been identified. Moreover, the value of this exponent showed no defined trend, while the width of the inertial scaling region expands as the microscale Reynolds number increases.

Super-diffusive mixing in geophysics occurs in atmospheric turbulence, near surface currents in oceans, and macro-pore flow in the subsurface to name three of many areas. Models of super-diffusion have been around for almost a century, yet here we put forth a new perspective on the topic which clarifies and substantially expands on classical approaches. Eighty years after it was introduced, we trivially derive Richardson's scaling law for atmospheric super-diffusion, where the mean square separation of two tracer particles goes as t 3 , by assuming the Lagrangian velocity can be represented as a Brownian process. Next we generalize in the spirit of Mandelbrot's intermittency to other types of flows by employing Lagrangian velocities represented as a-stable Lévy processes. For a specific flow field, we show how to obtain the stability parameter, a, from tracer experiments and the finite-size Lyapunov exponent.

We review the modern view of fluid dynamics as an effective low-energy, long-wavelength theory of many-body systems at finite temperature. We introduce the concept of a nearly perfect fluid, defined by a ratio η/s of shear viscosity to entropy density of order /k B or less. Nearly perfect fluids exhibit hydrodynamic behavior at all distances down to the microscopic length scale of the fluid. We summarize arguments that suggest that there is fundamental limit to fluidity, and we review the current experimental situation of measurements of η/s in strongly coupled quantum fluids.

We review the modern view of fluid dynamics as an effective low-energy, long-wavelength theory of many-body systems at finite temperature. We introduce the concept of a nearly perfect fluid, defined by a ratio η/s of shear viscosity to entropy density of order /k B or less. Nearly perfect fluids exhibit hydrodynamic behavior at all distances down to the microscopic length scale of the fluid. We summarize arguments that suggest that there is fundamental limit to fluidity, and we review the current experimental situation of measurements of η/s in strongly coupled quantum fluids.

Richardson&#39;s theory of turbulent particle pair diffusion [Richardson, L. F. Proc. Roy. Soc. Lond. A 100, 709--737, 1926], based upon observational data, is equivalent to a locality hypothesis in which the turbulent pair diffusivity (K) scales with the pair separation (σ_l) with a 4/3-power law, K∼σ_l^4/3. Here, a reappraisal of the 1926 dataset reveals that one of the data-points is from a molecular diffusion context; the remaining data from geophysical turbulence display an unequivocal non-local scaling, K ∼σ_l^1.564. Consequently, the foundations of pair diffusion theory have been re-examined, leading to a new theory based upon the principle that both local and non-local diffusional processes govern pair diffusion in homogeneous turbulence. Through a novel mathematical approach the theory is developed in the context of generalised power law energy spectra, E(k)∼ k^-p for 1&lt;p&lt; 3, over extended inertial subranges. The theory predicts the scaling, K(p)∼σ_l^γ_p, with γ_p int...

We perform direct numerical simulations to study the effects of the finite Reynolds number and domain size on the decay law of Saffman turbulence. We observe that the invariant for Saffman turbulence, u 2 ℓ 3 , and non-dimensional dissipation coefficient, Cϵ = ϵ/(u 3 /ℓ), are sensitive to finite domain size; here, u is the rms velocity, ℓ is the integral length scale, and ϵ is the energy dissipation rate. Consequently, the exponent n in the decay law u 2 ∼ t −n for Saffman turbulence deviates from 6/5. Due to the finite Reynolds number and the domain size, Saffman turbulence decays at a faster rate (i.e., n > 6/5). However, the exponent n = 6/5 is more sensitive to the domain size than to the Reynolds number. From the simulations, we find that n remains close to 6/5 as long as R λ ≳ 10 and ℓ ≲ 0.3L box ; here, R λ is the Reynolds number based on the Taylor microscale and L box is the domain size. We also notice that n becomes slightly lower than 6/5 for a part of the decay period. Interestingly, this trend n < 6/5 is also observed earlier in freely decaying grid-generated turbulence.

We explore the concept of local and non-local diffusion processes [Malik N. A., PLoS ONE 12(12): e0189917 (2017)] in application to the diffusion of inertial particle pairs in the limit of Stoke's drag. Inertial particles are arguably more important than fluid particles because most real world applications are related to inertial particle motion, from hail and pollen to sandstorms. The inertial pair diffusion regimes depend upon the local Stokes' number St (l), where l is the pair separation distance. For St (l) 1, the inertia dominates and we observe ballistic motion for inertial pair separation. For St (l) 1, the turbulent energy dominates the diffusion process which asymptotes to the fluid non-local pair regime for very large inertial ranges. A numerical model, Kinematic Simulations, is used to generate inertia particle trajectories and we observe the predicted inertial pair diffusion regimes in the limit of large inertial subranges.

DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal. If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the "Taverne" license above, please follow below link for the End User Agreement:

We review the Parisi-Frisch [1] MultiFractal formalism for Navier-Stokes turbulence with particular emphasis on the issue of statistical fluctuations of the dissipative scale. We do it for both Eulerian and Lagrangian Turbulence. We also show new results concerning the application of the formalism to the case of Shell Models for turbulence. The latter case will allow us to discuss the issue of Reynolds number dependence and the role played by vorticity and vortex filaments in real turbulent flows.

We present a detailed review of some of the most recent developments on Eulerian and Lagrangian turbulence in homogeneous and isotropic statistics. In particular, we review phenomenological and numerical results concerning the issue of universality with respect to the large scale forcing and the viscous dissipative physics. We discuss the state-of-the-art of numerical versus experimental comparisons and we discuss the dicotomy between phenomenology based on coherent structures or on statistical approaches. A detailed discussion of finite Reynolds effects is also presented.

Alvaro Galan et al. we observe that mixing is increased in the area due to waves. Besides, the methodology presented here is tested by deploying a set of eight Lagrangian drifters at different locations. This dynamical approach is shown as a valuable tool to extract information about transport, mixing and residence embedded in the Eulerian time dependent velocity fields obtained from numerical models.

In three-dimensional turbulent flows, the flux of energy from large to small scales breaks time symmetry. We show here that this irreversibility can be quantified by following the relative motion of several Lagrangian tracers. We find by analytical calculation, numerical analysis and experimental observation that the existence of the energy flux implies that, at short times, two particles separate temporally slower forwards than backwards, and the difference between forward and backward dispersion grows as $t^3$. We also find the geometric deformation of material volumes, surrogated by four points spanning an initially regular tetrahedron, to show sensitivity to the time-reversal with an effect growing linearly in $t$. We associate this with the structure of the strain rate in the flow.

We present a detailed review of some of the most recent developments on Eulerian and Lagrangian turbulence in homogeneous and isotropic statistics. In particular, we review phenomenological and numerical results concerning the issue of universality with respect to the large scale forcing and the viscous dissipative physics. We discuss the state-of-the-art of numerical versus experimental comparisons and we discuss the dicotomy between phenomenology based on coherent structures or on statistical approaches. A detailed discussion of finite Reynolds effects is also presented.

A recent experiment indicates that clouds in the atmosphere have fractal surfaces which are characterized by a fractal dimension D -2.35. Here we present a theory of the fractal dimension of clouds. We show that the fractal dimension of clouds is calculable from the theory of relative tur- bulent diffusion. We claim that previous approaches to the theory of relative diffusion are in con- tradiction with this experiment and that a newly developed theory gives D -2.35 as a natural conse- quence. The new theory of relative diffusion is simultaneously in agreement with the intermittency-modified "3 (power) law" [i.e., the (4+2p)/3 (power) law, where p is the intermit- tency exponent].

Thomson, D. J. & Devenish, B. J. [J. Fluid Mech. 526, 277 (2005)] and others have suggested that sweeping effects make Lagrangian properties in Kinematic Simulations (KS), Fung et al [Fung J. C. H., Hunt J. C. R., Malik N. A. & Perkins R. J. J. Fluid Mech. 236, 281 (1992)], unreliable. However, such a conclusion can only be drawn under the assumption of locality. The major aim here is to quantify the sweeping errors in KS without assuming locality. Through a novel analysis based upon analysing pairs of particle trajectories in a frame of reference moving with the large energy containing scales of motion it is shown that the normalized integrated error e I K in the turbulent pair diffusivity (K) due to the sweeping effect decreases with increasing pair separation (σ l), such that e I K ! 0 as σ l /η ! 1; and e I K ! 1 as σ l /η ! 0. η is the Kolmogorov turbulence microscale. There is an intermediate range of separations 1 < σ l /η < 1 in which the error e I K remains negligible. Simulations using KS shows that in the swept frame of reference, this intermediate range is large covering almost the entire inertial subrange simulated, 1 < σ l /η < 10 5 , implying that the deviation from locality observed in KS cannot be atributed to sweeping errors. This is important for pair diffusion theory and modeling.

A new method is proposed to calculate two-particle statistics of turbulent di!usion in complex #ows. The method is a combination of a single-particle Lagrangian stochastic model and a two-particle model applicable to isotropic turbulence. An encouraging preliminary evaluation of the method is presented.

We have developed a new experimental technique to measure the Lagrangian velocity of tracer particles in a turbulent flow, based on ultrasonic Doppler tracking. This method yields a direct access to the velocity of a single particle at a turbulent Reynolds number R λ = 740. Its dynamics is analyzed with two decades of time resolution, below the Lagrangian correlation time. We observe that the Lagrangian velocity spectrum has a Lorentzian form E L (ω) = u 2 rms TL/(1 + (TLω) 2 ), in agreement with a Kolmogorov-like scaling in the inertial range. The probability density function (PDF) of the velocity time increments displays a change of shape from quasi-Gaussian a integral time scale to stretched exponential tails at the smallest time increments. This intermittency, when measured from relative scaling exponents of structure functions, is more pronounced than in the Eulerian framework.

Statistical properties of random distribution of strained vortices (Burgers' vortices) in turbulence are studied, and the scaling behavior of structure functions is investigated. It is found within the scale range of interest (corresponding to the inertial range) that the third-order structure function is negative and the scaling exponent is nearly unity in accordance with Kolmogorov's four-fifths law. The inertialrange scaling exponents are estimated up to the 25th order, which are in good agreement with those obtained from experiments and direct numerical simulations once the probability distribution of the vortex strength is taken into account. [S0031-9007(97)03840-4] PACS numbers: 47.27.Gs, 47.27.Jv, 47.32.Cc In recent computer simulations and experiments of homogeneous isotropic turbulence at high Reynolds numbers, a number of elongated intense vortex structures are observed to distribute randomly in space, which are often called worms . Each worm structure is found to be approximately a Burgers' vortex under local straining and is responsible for the signals usually referred to as the intermittency . Bearing this in mind, we investigate the statistical properties of a model field associated with the random distribution of Burgers' vortices.

We introduce a time-dependent Eulerian-Lagrangian length-scale and an inverse locality hypothesis which explain scalings of second order one-particle Lagrangian structure functions observed in kinematic simulations ͑KS͒ of homogeneous isotropic turbulence. Our KS results are consistent with the physical picture that particle trajectories are more/less autocorrelated if they are smoother/ rougher as a result of encountering less/more straining stagnation points, thus leading to enhanced/ reduced turbulent diffusion.

Using a multi-scaled, chaotic flow known as the KS model of turbulence , we investigate the dependence of Lyapunov exponents on various characteristics of the flow. We show that the KS model yields a power law relation between the Reynolds number and the maximum Lyapunov exponent, which is similar to that for a turbulent flow with the same energy spectrum. Our results show that the Lyapunov exponents are sensitive to the advection of small eddies by large eddies, which can be explained by considering the Lagrangian correlation time of the smallest scales. We also relate the number of stagnation points within a flow to the maximum Lyapunov exponent, and suggest a linear dependence between the two characteristics.

Two-particle dispersion is of central importance to a wide range of natural and industrial applications. It has been an active area of research since seminal paper. This review emphasizes recent results from experiments, high-end direct numerical simulations, and modern theoretical discussions. Our approach is complementary to , whose review focused primarily on stochastic models of pair dispersion. We begin by reviewing the theoretical foundations of relative dispersion, followed by experimental and numerical findings for the dissipation subrange and inertial subrange. We discuss the findings in the context of the relevant theory for each regime. We conclude by providing a critical analysis of our current understanding and by suggesting paths toward further progress that take full advantage of exciting developments in modern experimental methods and peta-scale supercomputing. 405 Annu. Rev. Fluid Mech. 2009.41:405-432. Downloaded from arjournals.annualreviews.org by University of California -San Diego on 04/09/09. For personal use only. Click here for quick links to Annual Reviews content online, including: • Other articles in this volume • Top cited articles • Top downloaded articles • Our comprehensive search Further ANNUAL REVIEWS

This book series is a collection of the main contributions from the first five workshops held by Ercoftac Special Interest Group on Synthetic Turbulence Models (SIG42), a summary of each workshop can be found in Ercoftac Bulletin.
It is intended as an illustration of the sig’s activities and of the latest developments in the field.
Synthetic turbulence can be traced back to the 80's, in which diffusion was simulated
on a one dimensional grid with a random velocity field. Kraichnan  continued with a random flow field in three dimensions, and constructed incompressible fields
as an isotropically random sum of unsteady Fourier waves with distributed frequencies.
Most of the applications really started with what was to be called Kinematic
Simulation (KS) . Kinematic simulation are perhaps the best known of the synthetic turbulence models. They are based on a simplified incompressible velocity field which kinematically simulates the Eulerian velocity field and is generated as a sum of random incompressible Fourier modes with a given wavenumber-energy spectrum.

We examine the applicability of the weak wave turbulence theory in explaining experimental scaling results obtained for the diffusion and relative diffusion of particles moving on turbulent surface waves. For capillary waves our theoretical results are shown to be in good agreement with experimental results, where a distinct crossover in diffusive behavior is observed at the driving frequency. For gravity waves our results are discussed in the light of ocean wave studies.