bluuebunny/crossref_metadata_2025_split huggingface dataset:
High-intensity light propagation and induced natural laminar flow
Authors: Lehnigk Siegfried H. , Steverding Bernard 
Published: March 2006

The objective of this paper is to describe approximately the coupled steady-state processes of light propagation and induced laminar incompressible fluid flow in the case of natural convection.For the case of a homogeneous fluid and under the assumptions that light energy is instantaneously transformed into heat and that the induced velocities are not too large, it is reasonable to use the boundary-layer equations to describe the induced natural flow. These equations are augmented by the conservation of energy equation. The velocity, temperature and intensity functions are expected to exhibit similarity properties.A high-intensity light beam with a given rotationally symmetric Gaussian initial intensity distribution is propagating vertically upwards into a fluid initially at rest. The fluid characteristics are assumed to be constant. A stream function is introduced to satisfy the conservation of mass equation. The conservation of momentum equation leads to conditions on the unknown functions involved in the stream function. Additional conditions follow from the conservation of energy equation, which involves the local light intensity as a driving term.Under the assumptions made, self-defocusing (thermal blooming) will occur. The main results are an exponential increase of the boundary-layer thickness and an exponential decrease of temperature and of light intensity due to the blooming effect in addition to the exponential decrease due to absorption.
Measurements of the nearly isotropic turbulence behind a uniform jet grid
Authors: Gad-El-Hak Mohamed , Corrsin Stanley 
Published: March 2006

Wind-tunnel turbulence behind a parallel-rod grid with jets evenly distributed along each rod is nearly isotropic. Homogeneity improvement over prior related experiments was attained by the use of controllable nozzles. Compared with the ‘passive’ case, the downwind-jet ‘active’ grid has a smaller static pressure drop across it and gives a smaller turbulence level at a prescribed distance from it, while the upwind-jet grid gives a larger static pressure drop and larger turbulence level. ‘Counterflow injection’ generates larger turbulence energy and larger scales, both events being evidently associated with instability of the jet system. This behaviour is much like that commonly observed behind passive grids of higher solidities.If the turbulent kinetic energy is approximated as an inverse power law in distance, the (positive) exponent decreases with increasing (downwind or upwind) jet strength, corresponding to slower absolute decay rates. No peculiar decay behaviour occurs when the jet grid is ‘self-propelled’ (zero net average force), or when the static pressure drop across it is zero.The injection does not change the general behaviour of the energy spectra, although the absolute spectra change inasmuch as the turbulence kinetic energy changes.
Distorted gas bubbles at large Reynolds number
Authors: Sawi M. El 
Published: March 2006

The distortion of a gas bubble rising steadily in an inviscid incompressible liquid of infinite extent under the action of surface tension forces is investigated theoretically using an appropriate extension of the tensor virial theorem. A convenient parameter for distinguishing the bubble shape is the Weber numberW. The virial method leads to an expression relatingWand the axis ratio χ, of the transverse and longitudinal axes of the bubble. To first order inW, this relation agrees with the linear theory established by Moore (1959). Also, comparison of the results with his (1965) approximate theory reveals similar features and excellent agreement up to χ = 2. In particular, it confirms his prediction of the existence of a maximum Weber number. Although the present work does not consider the stability of these bubbles, it is interesting to note that the maximum value of 3.271 attained byWdiffers only by about 2.8% from the critical Weber number obtained by Hartunian & Sears (1957) for the onset of instability.An approximate method for the study of slightly distorted spheroidal gas bubbles is also formulated and the resulting boundary-value problem solved numerically. The theory is then extended to include gravity. The joint effect of surface tension as well as gravitational forces has not been included in earlier theories. The shapes of the bubbles are traced and compared with the unperturbed spheroids. Comparisons for the velocity of bubble rise are made between the present predictions and some experimental results. In particular the results are compared with recent experimental data for the motion of gas bubbles in liquid metals.
Vortex shedding from spheres
Authors: Achenbach Elmar 
Published: March 2006

Vortex shedding from spheres has been studied in the Reynolds number range 400 < Re < 5 × 106. At low Reynolds numbers, i.e. up to Re = 3 × 103, the values of the Strouhal number as a function of Reynolds number measured by Möller (1938) have been confirmed using water flow. The lower critical Reynolds number, first reported by Cometta (1957), was found to be Re = 6 × 103. Here a discontinuity in the relationship between the Strouhal and Reynolds numbers is obvious. From Re = 6 × 103 to Re = 3 × 105 strong periodic fluctuations in the wake flow were observed. Beyond the upper critical Reynolds number (Re = 3.7 × 105) periodic vortex shedding could not be detected by the present measurement techniques.The hot-wire measurements indicate that the signals recorded simultaneously at different positions on the 75° circle (normal to the flow) show a phase shift. Thus it appears that the vortex separation point rotates around the sphere. An attempt is made to interpret this experimental evidence.
A measurement of Lagrangian velocity autocorrelation in approximately isotropic turbulence
Authors: Shlien D. J. , Corrsin S. 
Published: March 2006

By measuring the heat dispersion behind a heated wire stretched across a wind tunnel (Taylor 1921, 1935), the Lagrangian velocity autocorrelation was determined in an approximately isotropic, grid-generated turbulent flow. The techniques were similar to previous ones, but the scatter is less. Assuming self-preservation of the Lagrangian velocity statistics in a form consistent with recent measurements of decay in this flow (Comte-Bellot & Corrsin 1966, 1971), a stationary and an approximately self-preserving form for the dispersion were derived and approximately verified over the range of the experiment.Possibly the most important aspect of this experiment is that data were available in the same flow on the simplest Eulerian velocity autocorrelation in time, the correlation at a fixed spatial point translating with the mean flow (Comte-Bellot & Corrsin 1971). Thus, the Lagrangian velocity autocorrelation coefficient function calculated from the dispersion data could be compared with this corresponding Eulerian function. It was found that the Lagrangian Taylor micro-scale is very much larger than the analogous Eulerian microscale (76 ms compared with 6.2ms), contrary to an estimate of Corrsin (1963). The Lagrangian integral time scale is roughly equal to the Eulerian one, being larger by about 25 %.
On Kolmogorov's inertial-range theories
Authors: Kraichnan Robert H. 
Published: March 2006

Consistency and uniqueness questions raised by both the 1941 and 1962 Kolmogorov inertial-range theories are examined. The 1941 theory, although unlikely from the viewpoint of vortex-stretching physics, is not ruled out just because the dissipation fluctuates; but self-consistency requires that dissipation fluctuations be confined to dissipation-range scales by a spacewise mixing mechanism. The basic idea of the 1962 theory is a self-similar cascade mechanism which produces systematically increasing intermittency with a decrease of scale size. This concept in itself requires neither the third Kolmogorov hypothesis (log-normality of locally averaged dissipation) nor the first hypothesis (universality of small-scale statistics as functions of scale-size ratios and locally averaged dissipation). It does not even imply that the inertial range exhibits power laws. A central role for dissipation seems arbitrary since conservation alone yields no simple relation between the local dissipation rate and the corresponding proper inertial-range quantity: the local rate of energy transfer. A model rate equation for the evolution of probability densities is used to illustrate that even scalar nonlinear cascade processes need not yield asymptotic log-normality. The approximate experimental support for Kolmogorov's hypothesis takes on added significance in view of the wide variety ofa prioriadmissible alternatives.If the Kolmogorov law$E(k) \propto k^{-\frac{5}{3}-\mu}$is asymptotically valid, it is argued that the value of μ depends on the details of the nonlinear interaction embodied in the Navier–Stokes equation and cannot be deduced from overall symmetries, invariances and dimensionality. A dynamical equation is exhibited which has the same essential invariances, symmetries, dimensionality and equilibrium statistical ensembles as the Navier–Stokes equation but which has radically different inertial-range behaviour.
Application of an inner expansion method to plane, inviscid, compressible flow stability studies
Authors: Beckemeyer Roy J. 
Published: March 2006

The inviscid compressible flow stability problem is mathematically similar to that of sound propagation in a sheared flow field. This similarity has been exploited by applying an inner expansion technique to study the effect of finite shear gradients on free parallel flow instabilities. This technique had previously been used to investigate the effect of thin boundary layers on sound propagation in ducts. The expansion, which is applicable to flow profiles involving thin, but finite, shear layers separating regions of uniform flow, offers a significant computational advantage over the numerical methods commonly employed to determine the stability of continuous mean flow profiles. Although equally applicable to three-dimensional and to spatially growing hydrodynamic instabilities, the procedure is demonstrated by application to the eigenvalue problem for temporal instabilities of shear layers and jets in plane inviscid compressible flow.For the case of vanishingly thin shear layers, the eigenvalue equations derived here reduce to those obtained by Miles (1958) for parallel flows bounded by vortex sheets. The series solution of Graham & Graham (1969), valid for linear shear-layer profiles of arbitrary thickness, provides a basis of comparison for the expansion-method results. Unstable-mode eigenvalues obtained using the two methods are found to be in good agreement for a significant range of values of the ratio of shear-layer thickness to axial wavelength.
Phase and amplitude discrepancies in the surface wave due to a wedge-ended hull form
Authors: Standing R. G. 
Published: March 2006

A deep surface-piercing wedge-ended hull model was towed through still water. Measurements of the surface wave pattern confirmed earlier findings for ship models, that the measured bow-wave cusp line often lies well forward of the position predicted by thin-ship theory, and that this shift increases with bow water-line angle and with decreasing model speed. Two possible explanations are considered here in terms of changes of wave phase speed with wave convection and steepness. Calculations based on a transformation method due to Guilloton predict more realistic wave profiles than linear theory, but account for less than half the observed shift. Some tentative conclusions are drawn.The singularity in the Green's function double integral is removed by an improved method, which simplifies the numerical integration. The new integrand decays within one oscillation.
Generalized Eady waves
Authors: Williams Gareth P. 
Published: March 2006

Solutions are obtained for the baroclinic instability problem for situations in which the static stability and mean shear vary geminately with height. The simple solution given by Eady is shown to be a special limiting case of a class of exact solutions for flows whose basic states have a vanishing interior potential vorticity gradient. The generalized solutions show that the temperature amplitude distribution is particularly sensitive to vertical variations in static stability but that phases and other amplitudes are only slightly influenced by such variations. When the static stability and shear increase (decrease) with height an enhanced temperature maximum occurs at the upper (lower) surface in comparison with the standard Eady solution.The generalized solutions also help to explain the character of annulus waves and predict a short-wave cut-off that is the same as that given by Eady's theory provided that it is based on the vertically averaged gravitational frequency.
Topological pumping of magnetic flux by three-dimensional convection
Authors: Drobyshevski E. M. , Yuferev V. S. 
Published: March 2006

Attention is drawn to a principal difference between the transfer of a horizontal magnetic field by turbulence and by three-dimensional cell convection.If the motion of the conducting medium in the cells is such that the heated material ascends at the centre while descending along the sides of the cells, then the magnetic tubes of force will be carried downwards by peripheral flows. Discrete ascending flows separated from one another by descending material carry only closed magnetic field loops. Such loops do not transfer net magnetic flux. As a result, the magnetic flux becomes blocked at the base of the convective layer.
The effects of surface roughness and tunnel blockage on the flow past spheres
Authors: Achenbach Elmar 
Published: March 2006

The effect of surface roughness on the flow past spheres has been investigated over the Reynolds number range 5 × 104 < Re < 6 × 106. The drag coefficient has been determined as a function of the Reynolds number for five surface roughnesses. With increasing roughness parameter the critical Reynolds number decreases. At the same time the transcritical drag coefficient rises, having a maximum value of 0·4.The vortex shedding frequency has been measured under subcritical flow conditions. It was found that the Strouhal number for each of the various roughness conditions was equal to its value for a smooth sphere. Beyond the critical Reynolds number no prevailing shedding frequency could be detected by the measurement techniques employed.The drag coefficient of a sphere under the blockage conditions 0·5 < ds/dt < 0·92 has been determined over the Reynolds number range 3 × 104 < Re < 2 × 106. Increasing blockage causes an increase in both the drag coefficient and the critical Reynolds number. The characteristic quantities were referred to the flow conditions in the smallest cross-section between sphere and tube. In addition the effect of the turbulence level on the flow past a sphere under various blockage conditions was studied.
Shock-wave structure and intermolecular collision laws
Authors: Yen Shee-Mang , Ng Winnie 
Published: March 2006

The nonlinear Boltzmann equation has been solved for shock waves in a Max-wellian gas for eight upstream Mach numbers M1 ranging from 1·1 to 10. The numerical solutions were obtained by using Nordsieck's method, which was revised for use with the differential cross-section corresponding to an intermolecular force potential following an inverse fifth-power law. The accuracy of the calculations of microscopic and macroscopic properties for this collision law is comparable with that for elastic spheres published earlier (Hicks, Yen & Reilly 1972).We have made comparisons of the detailed characteristics of the internal shock structure in a Maxwellian gas with those in a gas of elastic spheres. The purpose of this comparative study is to find the shock properties that are sensitive as well as those which are insensitive to the change in collision law and to find effective ways to study them.The variation of thermodynamic and transport properties of interest with respect to density and to each other was found to depend only weakly on the change in collision law. The principal effect on the macroscopic shock structure due to the change in intermolecular potential is in the spatial variation of the macroscopic properties. The spatial variation of macroscopic properties may be determined accurately from the corresponding moments of the collision integral, especially in the upstream and downstream wings of the shock wave. The results for the velocity distribution function exhibit the microscopic shock characteristics influenced by a difference in intermolecular collisions, in particular the departure from equilibrium in the upstream wing of the shock and the relaxation towards equilibrium in the downstream wing. The departure of several characteristics of weak shock waves from those of the Chapman-Enskog linearized theory and the Navier-Stokes shock is also insensitive to the change in collision law. The deviation of the half-width of the function ∫fdvyduz from the Chapman-Enskog first iterate at M1 = 1·59 is in agreement with an experiment (Muntz & Harnett 1969).
A Markovian random coupling model for turbulence
Authors: Frisch U. , Lesieur M. , Brissaud A. 
Published: March 2006

The Markovian random coupling (MRC) model is a modified form of the stochastic model of the Navier-Stokes equations introduced by Kraichnan (1958, 1961). Instead of constant random coupling coefficients, white-noise time dependence is assumed for the MRC model. Like the Kraichnan model, the MRC model preserves many structural properties of the original Navier-Stokes equations and should be useful for investigating qualitative features of turbulent flows, in particular in the limit of vanishing viscosity. The closure problem is solved exactly for the MRC model by a technique which, contrary to the original Kraichnan derivation, is not based on diagrammatic expansions. A closed equation is obtained for the functional probability distribution of the velocity field which is a special case of Edwards’ (1964) Fokker-Planck equation; this equation is an exact consequence of the stochastic model whereas Edwards’ equation constitutes only the first step in a formal expansion based directly on the Navier-Stokes equations. From the functional equation an exact master equation is derived for simultaneous second-order moments which happens to be essentially a Markovianized version of the single-time quasi-normal approximation characterized by a constant triad-interaction time.The explicit form of the MRC master equation is given for the Burgers equation and for two- and three-dimensional homogeneous isotropic turbulence.
Laser anemometer measurements of trailing vortices in water
Authors: Baker G. R. , Barker S. J. , Bofah K. K. , Saffman P. G. 
Published: March 2006

A series of measurements of trailing vortices behind lifting hydrofoils is described. These measurements were made in the Caltech Free-Surface Water Tunnel, using a laser-Doppler velocimeter to measure two components of velocity in the vortex wake. Two different model planforms were tested, and measurements were made at several free-stream velocities and angles of attack for each. Velocity profiles were measured at distances downstream of the model of from five to sixty chord lengths. These measurements are the first results of a continuing experimental programme.In § 3 of this paper, the theory of trailing vortices is discussed. The effects of ‘vortex wandering’ upon the measurements are computed, and the corrected results are seen to be in reasonable agreement with the theory.
The structure of the viscous sublayer and the adjacent wall region in a turbulent channel flow
Authors: Eckelmann Helmut 
Published: March 2006

Hot-film anemometer measurements have been carried out in a fully developed turbulent channel flow. An oil channel with a thick viscous sublayer was used, which permitted measurements very close to the wall. In the viscous sublayer betweeny+≃ 0·1 andy+= 5, the streamwise velocity fluctuations decreased at a higher rate than the mean velocity; in the regiony+[lsim ] 0·1, these fluctuations vanished at the same rate as the mean velocity.The streamwise velocity fluctuationsuobserved in the viscous sublayer and the fluctuations (∂u/∂y)0of the gradient at the wall were almost identical in form, but the fluctuations of the gradient at the wall were found to lag behind the velocity fluctuations with a lag time proportional to the distance from the wall. Probability density distributions of the streamwise velocity fluctuations were measured. Furthermore, measurements of the skewness and flatness factors made by Kreplin (1973) in the same flow channel are discussed. Measurements of the normal velocity fluctuationsvat the wall and of the instantaneous Reynolds stress −ρuvwere also made. Periods of quiescence in the − ρuvsignal were observed in the viscous sublayer as well as very active periods where ratios of peak to mean values as high as 30:1 occurred.
Symmetrical flow past a uniformly accelerated circular cylinder
Authors: Collins W. M. , Dennis S. C. R. 
Published: March 2006

The flow normal to an infinite circular cylinder which is uniformly accelerated from rest in a viscous fluid is considered. The flow is assumed to remain symmetrical about the direction of motion of the cylinder. Two types of solution are presented. In the first an expansion in powers of the time from the start of the motion is given which extends the results of boundary-layer theory by taking into account corrections for finite Reynolds numbers. Physical properties of the flow for small times and finite but large Reynolds numbers are calculated from this expansion. In the second method of solution the Navier-Stokes equations are integrated by an accurate procedure which is a logical extension of the solution in powers of the time. Results are obtained forR2= 97·5, 5850, 122 × 103and ∞, whereRis the Reynolds number. This is defined asR= 2a(ab)½/v, whereais the radius of the cylinder,bthe uniform acceleration andvthe kinematic viscosity of the fluid. The methods are in good agreement for small times.The numerical method of integration has been carried to moderate times and various flow properties have been calculated. The growth of the length of the separated wake behind the cylinder forR2= 97·5, 5850 and 122 × 103is compared with the results of recent experimental measurements. The agreement is only moderate forR2= 97·5 but it improves greatly asRincreases. The numerical integrations were continued in each case until the implicit method of integration failed to converge, which terminated the procedure. A secondary vortex appeared on the surface of the cylinder for the caseR2= 122 × 103.
Universal similarity at high grid Reynolds numbers
Authors: Schedvin J. , Stegen G. R. , Gibson C. H. 
Published: March 2006

Kolmogorov's second hypothesis has been examined for the case of turbulence generated behind a very large grid. The turbulent Reynolds number RΛ = 280 was sufficient to obtain a short inertial subrange. The one-dimensional subrange constant a1 = 0·48 ± 0·06 is in agreement with recent determinations made in geophysical flows. Isotropy was tested by comparing the transverse velocity spectrum with the transverse spectrum predicted from the longitudinal spectrum using the isotropic relations. The comparison showed the flow to be isotropic everywhere except at the largest scales.It was observed that at high wavenumbers the spectra were attenuated by effects of finite wire length. The wire-length corrections suggested by Wyngaard (1968) were found to be inadequate. New corrections based on experimentally determined universal spectra are proposed.