Lagrangian Turbulence Research Articles

Structure of Lagrangian turbulence

A structure function describing the geometrical properties of Lagrangian turbulence is proposed. This function yields the asymptotic mixing properties of inertial range turbulence. The form of the structure function is deduced from Richardson’s particle dispersion law. Scaling relationships for the mixing volume fraction, the surface area of boundaries between materials, and the chord lengths defined by the intersection points of a ray with material boundaries are obtained. Scaling laws are also deduced for the area fraction, perimeter length, and chord lengths in a two-dimensional section, and for the trajectory of a single particle. The predictions for the two-dimensional case have been verified in several examples of mixing, using data obtained from numerical integration of the Navier–Stokes equations.

Particle size effects on Lagrangian turbulence

Perturbation methods are used to show that the equations of motion for a small rigid sphere in a steady laminar flow take the form of a dynamical system in which phase volume is not conserved. In the absence of stagnation points, particle inertia and virtual mass effects destroy Lagrangian turbulence and the particles are captured by periodic or quasiperiodic orbits that are associated with the vortices of the flow. When gravitational effects are included, it is found that point particles can sediment chaotically, but that particle inertia and virtual mass effects tend to eliminate the chaotic behavior. An interesting consequence of the latter phenomenon is that finite particles which are denser than the fluid can be permanently suspended in three-dimensional cellular flows. Numerical results are presented for the Arnold–Beltrami–Childress [C. R. Acad. Sci. Paris 261, 17 (1965)] flows.

Lagrangian turbulence and spatial complexity in a Stokes flow

A simple Stokes flow problem, corresponding to an incompressible flow between two eccentric cylinders rotating alternately, is investigated numerically. It is demonstrated that for a wide range of system parameters the fluid particles can evolve along highly chaotic orbits, thereby providing an example of so called ‘‘Lagrangian turbulence.’’ Passive scalar distributions can rapidly evolve into structures of remarkable spatial complexity that can be characterized in terms of the underlying phase space dynamics. An investigation is made of the ability of simple area preserving mappings, deduced from the physical problem, to reproduce the dynamics obtained from the exact solution.

Experimental study of Lagrangian turbulence in a Stokes flow

Experimental studies are made of chaotic particle motion in a simple Stokes flow system. Surfaces-of-section that exhibit a generic mixture of regular and chaotic particle motions in good agreement with computer simulations are constructed experimentally. Deformations of line ele­ments exhibit ‘ whorl ’ and ‘ tendril ’ structures of great complexity that can be correlated directly with the underlying particle dynamics and that agree well with numerical computations. In some cases, the laboratory studies are able to resolve dynamical features more accurately than the computer studies. Experiments demonstrating that the flows exhibit poor time reversal in régimes of chaotic particle motion are also performed.

On the lagrangian turbulence in continua

Lagrangian turbulence in continua is introduced as a failure of euclidian metric of a material (frozen) system of coordinates. Criteria of such a turbulence for fluids and solids are derived.

A laser method to determine turbulent intensity using probability after-effects

A novel way to use particle arrival statistics in two-spot laser anemometry of turbulent flow is developed. For two cylindrical scattering volumes spaced a fixed distance apart in the flow direction, a relationship between the classical 'probability after-effects function' and the mean square displacement of a fluid particle in a turbulent flow can be established. Determination of this displacement as a function of the separation of the probe centers gives a measure of the turbulent Lagrangian correlation function. Experimental measurements are given for short separation distances for turbulent flow in a submerged water jet. The turbulence intensity obtained directly from the 'probability after-effects function' agrees favorably with other laser velocity measurements. The experimental technique can be combined with a laser Doppler velocimeter to measure Lagrangian and Eulerian turbulence quantities simultaneously at a point in the flow.

Lagrangian and Eulerian Time-Scale Relations in the Daytime Boundary Layer

Abstract Lagrangian (neutral balloon) and Eulerian (tower and aircraft) turbulence observations were made in the daytime mixed layer near Boulder, Colorado. Average sampling time was ∼25 min. Average Lagrangian time scale is ∼70 s and average ratio of Lagrangian to Eulerian time scales (β = TL/TE) is about 1.7. The ratio β is inversely proportional to turbulence intensity i. These data support the formula β = 0.7/i. Lagrangian time scale for the vertical component of turbulence at heights above ∼100 m is given by the formula TL = 0.17zi/σμ where zi is mixing depth. This formula is valid for the horizontal components of turbulence at all heights in the mixed layer. Lagrangian spectra in the inertial subrange are best represented by the formula Fr(n) = 0.2ϵn−2.

A scheme for simulating particle pair motions in turbulent fluid

A technique is developed for simulating the random motion of particles in turbulent fluid. The technique is applicable to single particles or to pairs of particles whose motions are correlated. The method is intended for use in determining one or two-particle Lagrangian turbulence statistics either from instantaneous velocity fields generated by turbulence simulation models or from Eulerian statistics of the turbulence acquired either from observations, from theory, or from a turbulence closure model. In the latter capacity the scheme provides a basis for Monte Carlo type models of turbulent diffusion. The scheme requires as inputs the probability density of the Eulerian velocity, or at least its mean and variance; the autocorrelation of the Eulerian velocity, or at least its integral time scale; and the energy dissipation rate of the turbulence.

Atmospheric turbulence and diffusion estimates derived from observations of a smoke plume

Plan view and elevation photographs of a smoke plume are used to estimate horizontal and vertical dispersion rates. Dispersion rates measured from individual photographs agree with Batchelor's theoretical analysis of relative diffusion. Dispersion rates measured from a composite of plume photographs agree with Taylor's theoretical analysis of single-particle diffusion. These dispersion rates are then used to calculate Eulerian turbulence parameters which are compared with observations made on a 60 m tower near the smoke-plume source. In addition, the Lagrangian turbulence time scale and the horizontal eddy diffusivity are estimated. The comparisons of estimated with observed parameters are good, suggesting that the smoke-plume technique for estimating atmospheric dispersion is realistic.

Determination of Lagrangian Deformations from Analysis of Current Followers

Abstract Methods are presented to determine Lagrangian deformations and turbulence statistics from current followers (drogues, neutrally buoyant floats, etc.). Such determinations allow general advection-diffusion equations such as in Okubo (1966) to be directly evaluated. Methods are also presented to transform these deformations into oceanic velocity gradients.

Use of statistical wind characteristics for theoretical and experimental estimation of passive particle diffusion

Research on smoke plumes and small particles has shown the possibility of using the Lagrangian model of diffusion and that, for practical purposes, a connection between Lagrangian and Eulerian turbulence enables us to compute small-scale dispersion in the atmosphere. Comparison of turbulence characteristics (turbulent energy dissipation, Lagrangian time scale) obtained from Lagrangian and Eulerian measurements showed good correlation.

Lagrangian Statistics from Numerically Integrated Turbulent Shear Flow

Lagrangian turbulence statistics were obtained from a three-dimensional numerical model of plane Poiseuille flow at large Reynolds number. Single-particle Lagrangian correlations were computed and compared with Eulerian space correlations. Although the curves were not self-similar, a dimensionless scale ratio defined at the e-folding time was comparable to Eulerian-Lagrangian scale ratios found in the literature. The numerically obtained mean-square particle displacements exhibited correct short- and long-time behavior. Mean-square particle separations were analyzed, and two-particle Lagrangian velocity correlations taken at the same time were more persistent than Lagrangian autocorrelations. A semiempirical functional form was constructed for the two-particle velocity correlations which yielded two-particle distance correlations in good agreement with those of the numerical model. The effect of mean shear on downstream separation was examined. Results indicate a t3 or steeper dependence for downstream mean-square separation 〈(xa − xb)2〉, with strong shear and Reynolds stress. Batchelor's similarity law, namely, that 〈(xaj − xbj)2〉 ∝ εt3 in directions not controlled by shear, is postulated for the direction of shear when shear generates ε. This postulate was tested numerically and found to be consistent.

The Imperial Intellect: A Study of Cardinal Newman's Educational Ideal. A. Dwight Culler

Previous articleNext article No AccessCritical ReviewsThe Imperial Intellect: A Study of Cardinal Newman's Educational Ideal. A. Dwight Culler Harvey ArnoldHarvey Arnold Search for more articles by this author PDFPDF PLUS Add to favoritesDownload CitationTrack CitationsPermissionsReprints Share onFacebookTwitterLinkedInRedditEmail SectionsMoreDetailsFiguresReferencesCited by The Journal of Religion Volume 45, Number 3Jul., 1965 Article DOIhttps://doi.org/10.1086/485804 Views: 1Total views on this site Citations: 1Citations are reported from Crossref Copyright 1965 The University of ChicagoPDF download Crossref reports the following articles citing this article:John B. McLaughlin Particle size effects on Lagrangian turbulence, Physics of Fluids 31, no.99 (Sep 1988): 2544–2553.https://doi.org/10.1063/1.866607

Eddy Diffusion in Homogeneous Turbulence

Taylor's theory of diffusion by continuous movements and Einstein's equation of diffusion were applied to eddy diffusion of particles in two dimensional field of homogeneous turbulence in broad shallow channel with extreme bottom roughness; method of determining Lagrangian eddy size, eddy diffusivity, turbulence intensity, and mixing length; experimental verification of Kilmogoroff similarity principle.

Eddy Diffusion in Homogeneous Turbulence

Taylor's theory of diffusion by continuous movements and Einstein's equation of diffusion were applied to eddy diffusion of particles in two dimensional field of homogeneous turbulence in broad shallow channel with extreme bottom roughness; method of determining Lagrangian eddy size, eddy diffusivity, turbulence intensity, and mixing length; experimental verification of Kilmogoroff similarity principle.