Linear Velocity Field Research Articles

Tracing large-scale fluctuations back in time

view Abstract Citations (101) References (14) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Tracing Large-Scale Fluctuations Back in Time Nusser, Adi ; Dekel, Avishai Abstract A quasi-linear method for recovering the growing mode of the initial fluctuations of a cosmological gravitating system from the present large-scale peculiar velocity of density field is presented and tested. A velocity-potential field is extracted from the observed velocities as in the POTENT procedure, or from the density as in the analysis of IRAS redshift surveys, assuming that the velocity field, smoothed on a scale of a few megaparsecs, is irrotational. Assuming the Zel'dovich approximation with no orbit crossing, the potential is traced back in time by integrating a simple differential equation in Eulerian space - the Zel'dovich-Bernoulli equation. The linear velocity and density fields are computed from the linear potential by differentiation. The method is demonstrated to reconstruct the initial conditions of an N-body simulation, recovering in particular the initial Gaussian distribution of densities; the initial hills are lower and the valleys are deeper than predicted by linear theory. Maps of the initial density field in the local cosmological neighborhood based on the POTENT and IRAS analysis are presented as an illustration of a possible application. Publication: The Astrophysical Journal Pub Date: June 1992 DOI: 10.1086/171360 Bibcode: 1992ApJ...391..443N Keywords: Cosmology; Dark Matter; Galactic Clusters; Gravitation; Distribution Functions; Potential Flow; Power Spectra; Spatial Distribution; Velocity Distribution; Astrophysics; COSMOLOGY: DARK MATTER; COSMOLOGY: LARGE-SCALE STRUCTURE OF UNIVERSE; COSMOLOGY: THEORY; GALAXIES: CLUSTERING; GRAVITATION; METHODS: NUMERICAL full text sources ADS |

Linear velocity fields in non-Gaussian models for large-scale structure

Linear velocity fields in two types of physically motivated non-Gaussian models are examined for large-scale structure: seed models, in which the density field is a convolution of a density profile with a distribution of points, and local non-Gaussian fields, derived from a local nonlinear transformation on a Gaussian field. The distribution of a single component of the velocity is derived for seed models with randomly distributed seeds, and these results are applied to the seeded hot dark matter model and the global texture model with cold dark matter. An expression for the distribution of a single component of the velocity in arbitrary local non-Gaussian models is given, and these results are applied to such fields with chi-squared and lognormal distributions. It is shown that all seed models with randomly distributed seeds and all local non-Guassian models have single-component velocity distributions with positive kurtosis.

Analytic synthetic seismograms for depth migration testing

By using the fact that raypaths in a linear acoustic velocity field are circular arcs, we analytically generate a number of distinct nontrivial synthetic seismograms. The seismograms yield accurate traveltimes from reflection events, but they do not give reflection amplitudes. The seismograms are useful for testing seismic migration programs for both speed and accuracy, in settings where lateral velocity variations can be arbitrarily high and dipping reflectors arbitrarily steep. Two specific examples are presented as illustrations.

Role of basset force on particle deposition in stagnation flow

Deposition of nondiffusive aerosols in stagnation point flow was examined. The complete equations of particle motion, including the Basset and virtual mass effects for a particle in a linear velocity field with a constant body force acting on it, were solved, and a general solution was obtained from which particle trajectories and velocities may be predicted. It was found that Basset force generally tends to hinder deposition by keeping particles in flight for longer times than in their absence. However, when particle Stokes numbers are sub-critical Basset force can actually enhance particle fluxes. As a consequence, inertial enrichment of particle concentrations at the deposition plane was increased. An analytical solution for a particle coming to rest in a quiescent fluid was obtained and compared to numerical results of Pearcey and Hill [Pearcey, T. and Hill, G. W. (1956) Aust. J. Phys. 9, 19–30].

Dirichlet problem in stellar dynamics. I. General case of the motion of a collisionless homogeneous gravitating ellipsoid

The problem of the most general motion of ellipsoidal systems with quadratic potential (ellipsoids, elliptic cylinders, and flat disks) in posed from the stellar-dynamic point of view. It is established that in the general case an ellipsoid (the cylinder and disk are limiting configurations) admits the following dynamical descriptions: a) a gravitating homogeneous cluster of particles rotates with angular velocity about the center of inertia; (b) in the intrinsic frame of reference there is motion of the centroids with a linear velocity field. As a consequence, the vorticity of this velocity field does not depend on the coordinates; (c) the principal semiaxes and the volume of the ellipsoid depend on the time, and the configuration pulsates with a finite amplitude; (d) the internal stresses in the collisionless ellipsoid depend on its dynamical state. The velocity dispersion tensor has six independent components, including skew stresses. On the surface there are no stresses; (e) the motion of the ellipsoid is described by a closed system of 15 differential equations. The system of these equations is obtained on the basis of the Boltzmann equation, for which its moments of first, second, and third order are needed. Special cases of oscillations of an ellipsoid,more » cylinder, and disk are considered.« less

The Upper Bound Approach to Plane Strain Problems Using Linear and Rotational Velocity Fields—Part I: Basic Concepts

This paper investigates an upper bound approach to plane strain deformation of a rigid, perfectly plastic material. In this approach the deformation region is divided into a finite number of rigid triangular bodies that slide with respect to one another. Neighboring rigid body zones are analyzed in specific cases where the zones are (1) both in rotational motion, (2) one in linear, the other in rotational motion and (3) both in linear motion. Specific equations are presented that describe surfaces of velocity discontinuity (shear boundaries) between the moving bodies, and the velocity discontinuities and shear power losses for each of the three cases. The shape of the surface of velocity discontinuity is uniquely determined by the velocity ratios of neighboring bodies, their relative directions of motion and, where applicable, the positions of their centers of rotation. Where one or both neighboring bodies exhibit rotational motion, the surface of velocity discontinuity is found to be a cylindrical surface. In the case of two neighboring bodies, each with linear motion, the surface of velocity discontinuity is found to be planar. The velocity discontinuity is found to be constant along the entire surface of velocity discontinuity. The characteristics of the surfaces of velocity discontinuity in plane strain deformation are investigated. The upper-bound approach to plane strain problems can be successfully adapted to real metal forming processes, including sheet and strip drawing, extrusion, forging, rolling, leveling, ironing, and machining.

The Upper Bound Approach to Plane Strain Problems Using Linear and Rotational Velocity Fields—Part II: Applications

Following Part I which investigated an upper bound approach to plane strain deformation of a rigid, perfectly plastic material, this Part II considers the same approach as applied to actual forming operations. The processes of drawing and extrusion, of metal cutting and of rolling are analyzed, and explicit equations are developed to calculate the surfaces of velocity discontinuity (shear boundaries), velocity discontinuities, and the upper bound on power for these processes. Both the simple, unielement velocity fields as well as the more complex multielement fields are explored. The upper bound solution is shown to be a function of the independent (input) and pseudoindependent (assumed) process parameters as minimized by an optimization procedure. Rules concerning the assumption of pseudoindependent parameters are presented and the optimization procedure is discussed. Final conclusions lead the way for the application of upper bound analyses to such industrial processes as sheet and strip drawing, extrusion, forging, rolling, leveling, ironing and machining, and to the investigation of such flow failure modes as central bursting, piping and end splitting (alligatoring).

Irrotational and zero angular momentum ellipsoids in the Dirichlet problem

Two classes of new exact solutions are found in the Dirichlet problem of the oscillations of a self-gravitating fluid ellipsoidal mass with linear velocity field. These solutions describe irrotational ellipsoids and ellipsoids with zero angular momemtum. For ellipsoids with stationary boundary surface it is established that irrotational and zero angular momentum figures exist not only when the ellipsoids rotate around the central symetry axis, but also for an inclined position of the rotation axis.

Instability of steady flows with constant vorticity in vessels of elliptic cross-section

The problem of the stability of steady flows of a perfect incompressible fluid in vessels of elliptic cross-section is studied. The flow velocity field of the main stream is a linear function of the coordinates and the vorticity is constant. The spectral problem for the linear perturbations is solved using the mehtod of consecutive approximations. The instability of the flows to a first approximation is demonstrated. A special case of the flow in a triaxial ellipsoid is analysed in detail. Theoretical predictions agree well with the experimental results /1/. The present paper, unlike the analysis carried out in /1/, deals with an appreciably wider class of perturbations and the Galerkin method of rough a priori approximation is not used. The problem of stability of flows of this type is of interest when describing the properties of a liquid-filled gyroscope /2–4/ and the behaviour of the star and planetary cores /5/. At the same time, a flow with a linear velocity field represents the simplest example of the realization of the new mechanism of instability of rotational flows connected with disturbance of the rotational symmetry /6–9/.

Kinematic dynamo problem in a linear velocity field

A magnetic field is shown to be asymptotically (t → ∞) decaying in a flow of finite conductivity with v = Cr, where C = Cζ(t) is a random matrix. The decay is exponential, and its rate does not depend on the conductivity. However, the magnetic energy increases exponentially owing to growth of the domain occupied by the field. The spatial distribution of the magnetic field is a set of thin ropes and (or) layers.

Effect of hydrodynamic interactions between the particles on the rheological properties of dilute emulsions

The form of mean stress tensor in monodisperse emulsions is studied in the second-order approximation with respect to the volume density of the particles, for a number of flows which are of rheological interest. It is shown how the particular features of the two-particle interaction between liquid spheres, especially the non-zero differences between the normal stresses in shear flows, give rise to non-Newtonian properties of the emulsion. We know /1, 2/ that in the case of the second-order approximation with respect to the volume concentration of the suspended disperse pháse the mean stress tensor is expressed in terms of two-particle interactions in a linear velocity field, and of the binary correlation function. The binary function is formed under the action of the macroscopic flow. Specific results, however, were obtained only for suspensions and rigid spheres /1, 2/. The present paper deals with the structural model of fluid spheres of equal radius, with hydrodynamic and “contact” interactions. A number of fundamental deviations from /1/ exist in the case of rheologically strong flows, since drop flocculation-deflocculation processes must be considered (i.e. the formation and disruption of aggregates). A strict analysis is given within the framework of the model, of the effect of these processes on the binary correlation function. A connection between the model of “contact” interaction and the result of the D.L.V.O. theory /3–5/ is considered. Numerical values are obtained for the Trouton viscosity in strong rheologically axisymmetric expanding flows. The differences in normal stresses in a strong shear flow are obtained and an approximate estimate is given for the shear viscosity and compared with experimental data /6/. A method given in /2/ is used to compute the effective viscosity of the emulsion in arbitrary, rheologically weak flows in which Brownian motion predomaintes. Considerable use is made of the exact computational methods and asymptotic representations of hydrodynamic functions determining the pairwise interaction of fluid spheres /7–9/.

Diffusion and mixing of passive impurities in a linear velocity field

It is shown that the mixing process is described by a Lagrangian Green's function. The latter is obtained at both the dynamical and the statistical levels, which permits application of the results to turbulent media.

Rotational correlations in rough sphere fluids

The coupling of the angular velocity of a test rough sphere to the collective modes of the surrounding bath of rough spheres is studied as a function of the mass and diameter of the test sphere using renormalized kinetic theory. As the diameter of the tagged particle increases, the collective contribution to the relaxation changes from a situation where coupling to the fluid transverse angular velocity field dominates to one in which coupling to the transverse linear velocity field dominates. As the mass of the test particle increases, the collective contribution becomes increasingly sensitive to the nonhydrodynamic states which appear in the kinetic theory. The long time behavior of the angular velocity correlation function and the associated memory kernels are found to have interesting dependence on the test sphere diameter. The results are used to elucidate some features of the hydrodynamic character of microscopic relaxation processes.

Determination of the Shear Rates of Non-Newtonian Fluids from Rotational Viscometric Data. II. Cone-and-Plate Viscometer

A method for determination of the shear rate in a cone-and-plate viscometer is developed. The method to obtain the shear rate is shown to overcome the limitation of the existing method which requires a small angle between the cone and the plate as well as a linear velocity field with respect to the angle. Examples for non-Newtonian fluids with and without prior knowledge of the rheological equation of state are presented to demonstrate the proposed method.

Horizontal dispersion of floatable particles in the vicinity of velocity singularities such as convergences

A singular point in a two-dimensional velocity field is a stationary point of flow. The simplest and most important singularities in oceanography are points of convergence (or divergence), neutral points, and lines of convergence (or divergence). In the neighbourhood of the singularity, the velocity field is approximated linearly in terms of coordinates whose origin is taken at the singularity. The linear velocity field thus considered consists of the rates of stretching deformation and shearing deformation, vorticity, and divergence (or negative convergence). A group of foreign particles initially arranged in a circle surrounding a singularity will be deformed into an ellipse the area of which increases or decreases with time depending on the sign of the divergence. When a random motion is superposed upon the velocity field, a group of particles will be subject to advection-diffusion. As a result of the combined action of the rates of stretching and shearing, vorticity, and random motion, the group size tends to grow against a collecting power of convergence toward the singularity. Asymptotically a stationary situation may be established in which a group of particles attains a certain limiting size. Only the theoretical aspect is considered.

Problem of boundary layers in the exchange diffusion of water across bimolecular lipid membranes

The correct value of the permeability of artificial lipid bilayers to water, as given by the diffusion of tritiated water, is in general difficult to obtain owing to the presence of relatively thick boundary layers. It is shown that forced convection usually ruptures the membrane before the boundary layers become insignificant. Three other approaches to the problem are described: the thickness of the equivalent stagnant layers has been estimated explicitly by the use of glass and cellophane membranes of known permeability, and the resulting data have been used to correct the apparent permeability of the lipid membrane, the possibility of determining the true permeability from the measurement of the apparent permeability and the time lag of the transient state has been examined and shown to be impracticable in the present systems, and the true lipid membrane permeability has been calculated from the diffusion of tritiated water in known linear velocity fields in the aqueous phases. The first and third methods give permeability coefficients in agreement with each other which are, within experimental error, equal to the osmotic permeability coefficient.

Determination of Macroscopic Velocities from Line Profile Asymmetries.

view Abstract Citations References Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Determination of Macroscopic Velocities from Line Profile Asymmetries. Kulander, John L. ; Jeffries, John T. Abstract Synthetic line profiles are generated for model atmospheres containing linear and quadratic velocity fields and various temperature distributions. LTE and non-LTE source functions and both weak and strong lines are considered. Comparison of the assumed velocity structures with those inferred from the bisector shifts of the asymmetrical profiles show qualitative correlation only in the line cores and in general only for velocities small compared with the thermal velocity. A constant asymptotic velocity is inferred in the semi-infinite atmospheres below certain limiting depths for both strong and weak lines. Approximate expressions relating observed profile parameters to atmospheric velocity parameters for small linear velocities are obtained and tested for the constant temperature case. The observed rms displacements in the solar Ha line are used to infer the amplitude of the oscillatory velocity field in that region of the solar chromosphere where the core is formed. Publication: The Astronomical Journal Pub Date: 1965 DOI: 10.1086/109641 Bibcode: 1965AJ.....70S.142K full text sources ADS |

ON THE SOLUTIONS OF THE EQUATIONS OF MOTION FOR LINIEAR FIELDS

Under the assumption that the geostrophic wind possesses a stream function which is quadratic in x, y, and t, the equations of horizontal motion are solved, neglecting variations of the Coriolis parameter. It is shown that the general solution may be split into two components, called the central and eccentric components. Each of these components satisfies the equations of a linear velocity field. The central field is proposed as a practical approximation to the real wind, to be regarded as a refinement of the geostrophic wind field taking into account the effects of contour curvature, contour convergence, geostrophic shear, and temporal changes of the gradient. The central field is found to be, in a certain sense, a stable approximation. This stability is achieved, however, only by defining the central field by two totally different expressions, these expressions being valid in two mutually exclusive domains of possible quadratic stream functions. The form of the eccentric component of the general solution suggests that horizontal oscillations of the wind may be observable, and the form and period of these oscillations are given.