Taylor's Hypothesis Research Articles

画像解析による軸対称噴流の混合・拡散評価

Mixing and diffusion characteristics of an axisymmetric water jet were investigated by a flow visualization technique. A laser florescent dye and a laser light sheet were used to visualize the water jet. The three-dimensional views of vortical structures were constructed by applying the Taylor hypothesis to the jet cross-sectional images. From the images, the boundary surface area, the unmixed area, the complexity and the fractal dimension were calculated to discuss mixing and diffusion. The result suggests that the simultaneous enhancement of axisymmetric and streamwise vortices is very effective to increase mixing.

The effect of cross-flow velocity on mean-square derivatives measured using hot wires

It is well known that significant errors occur in the velocity derivative moments measured in turbulent flows when the measuring transducer is too large or Taylor's hypothesis is used in high-turbulence-intensity flows. An additional error occurs when velocity derivative moments are measured with hot wires in high-turbulence-intensity flows, because the wires cannot resolve the individual velocity components in these flows. Estimates of the error this causes in the derivative moments measured with single-, cross-, and parallel-wire probes are developed herein. The errors are significant in the derivative moments measured with cross-wire probes, but are smaller in derivative moments measured with single- and parallel-wire probes. For example, the relative errors in \(\) measured in the far field of the round jet are 30–50% smaller than predicted in previous analyses.

Observation of Mesoscale Fluxes During a Cold Front Process Passing Beijing

The mesoscale process is separated from a cold front passage by the spectral analysis of the turbulent data obtained from a tower in Beijing. Then the mesoscale fluxes are estimated according to the Taylor hypothesis. The results show that the turbulent momentum flux is much higher than the mesoscale momentum flux when the background wind is high, while the mesoscale flux can not be ignored when the background wind is low. The mesoscale sensible heat flux is influenced by many factors. Generally, the mesoscale sensible heat flux is higher than the turbulent sensible heat flux after the cold front. The analysis of the turbulent flux parameterization shows that it is necessary to include the modification of the mesoscale disturbance when parameterization method is applied on a long time scale. A reasonable parameterization method for flux calculations should include the turbulent flux, the mesoscale flux and the mesoscale modification on the turbulent flux.

Turbulent length‐scales in the marine atmospheric mixed layer

AbstractThe spectra of turbulence signals can be characterized by several independent scales. To provide a parametrization of these spectra requires knowledge of the relationships between these scales. This paper focuses on three independent scales: the integral scale (which is influenced by the low‐frequency behaviour of the spectra); the wavelength of the spectrum peak (which characterizes the energy‐containing domain); and the dissipation scale (which is relevant for the inertial subrange). First, we present definitions of these various scales, and the possible relationships between them. The profiles of the scales were computed from airborne measurements made in the atmospheric mixed layer over the open ocean, in a region where horizontal homogeneity can be assumed, at least for several tens of km. Furthermore, the diurnal cycle being very weak in this oceanic area, and aircraft moving at high speed through the air mass, stationarity is well verified on the runs, and Taylor's hypothesis may be used. The meteorological conditions correspond to a slightly unstable mixed layer, with weak to moderate winds. In a first part, we analyse the integral scales of various parameters on a 180‐km run and demonstrate that these parameters cannot be computed with any soundness from horizontal‐wind, temperature and moisture signals, because of the continuous increase in the spectral energy when moving towards lower frequencies. For the same reasons, the spectrum peak and the corresponding wavelength cannot be determined for these parameters. The computation of the integral and energy‐containing scale is therefore restricted to the vertical velocity, and to the various covariances. The turbulence field is characterized by a stretching of the eddies along the mean wind direction which results in greater integral and energy‐containing scales (but not in greater dissipation scales) when computed for along‐wind runs than for the cross‐wind runs. The profiles of the various scales increase with altitude and are well defined in the lower half of the mixed layer, but are much more scattered in the upper half. This behaviour is related to the source of turbulence, which lies in the surface buoyancy flux in the lower half of the mixed layer, and comes from higher altitude sources in the upper half. The integral scales have values comparable with those found in previous work, except for parameters related to temperature fluctuations, which have lower values. The ratio of the energy‐containing scale to the integral scale, which determines the sharpness of the ‘spectral knee’, varies considerably from one parameter to another, and sometimes with altitude. This demonstrates that a single unique parametrization cannot be defined for turbulence spectra. As a consequence, the eddy‐exchange coefficients, which depend on a characteristic length‐scale, should vary from one parameter to another. This would then have to be taken into account in model parametrization based on mixing length‐scales.

Rainfall downscaling in a space‐time multifractal framework

A space‐time multifractal analysis on radar rainfall sequences selected from the Global Atmospheric Research Program Atlantic Tropical Experiment database is presented. It is shown that space‐time rainfall can be considered with a good approximation to be a self‐similar multifractal process, so that a multifractal analysis can be carried out assuming Taylor's hypothesis to hold for rainfall over a wide range of spatial and temporal scales. The advection velocity needed to rescale the time dimension is estimated using different tracking techniques. On each selected rainfall sequence, a very good scaling is observed for spatial scales ranging from 4 to 256 km and for timescales from 15 min to 16 hours. A recently developed scale‐covariant multifractal model is then reformulated for numerical simulation of space‐time rainfall fields. The two parameters of the log‐Poisson distribution used as cascade generator within the model are systematically estimated from each selected rainfall sequence, and the dependence of one of these parameters on the large‐scale rain rate is highlighted. The model is then applied to disaggregate large‐scale rainfall, and some comparisons between synthetically downscaled and observed rainfall are discussed.

Turbulent length-scales in the marine atmospheric mixed layer

The spectra of turbulence signals can be characterized by several independent scales. To provide a parametrization of these spectra requires knowledge of the relationships between these scales. This paper focuses on three independent scales: the integral scale (which is influenced by the low-frequency behaviour of the spectra); the wavelength of the spectrum peak (which characterizes the energy-containing domain); and the dissipation scale (which is relevant for the inertial subrange). First, we present definitions of these various scales, and the possible relationships between them. The profiles of the scales were computed from airborne measurements made in the atmospheric mixed layer over the open ocean, in a region where horizontal homogeneity can be assumed, at least for several tens of km. Furthermore, the diurnal cycle being very weak in this oceanic area, and aircraft moving at high speed through the air mass, stationarity is well verified on the runs, and Taylor's hypothesis may be used. The meteorological conditions correspond to a slightly unstable mixed layer, with weak to moderate winds. In a first part, we analyse the integral scales of various parameters on a 180-km run and demonstrate that these parameters cannot be computed with any soundness from horizontal-wind, temperature and moisture signals, because of the continuous increase in the spectral energy when moving towards lower frequencies. For the same reasons, the spectrum peak and the corresponding wavelength cannot be determined for these parameters. The computation of the integral and energy-containing scale is therefore restricted to the vertical velocity, and to the various covariances. The turbulence field is characterized by a stretching of the eddies along the mean wind direction which results in greater integral and energy-containing scales (but not in greater dissipation scales) when computed for along-wind runs than for the cross-wind runs. The profiles of the various scales increase with altitude and are well defined in the lower half of the mixed layer, but are much more scattered in the upper half. This behaviour is related to the source of turbulence, which lies in the surface buoyancy flux in the lower half of the mixed layer, and comes from higher altitude sources in the upper half. The integral scales have values comparable with those found in previous work, except for parameters related to temperature fluctuations, which have lower values. The ratio of the energy-containing scale to the integral scale, which determines the sharpness of the ‘spectral knee’, varies considerably from one parameter to another, and sometimes with altitude. This demonstrates that a single unique parametrization cannot be defined for turbulence spectra. As a consequence, the eddy-exchange coefficients, which depend on a characteristic length-scale, should vary from one parameter to another. This would then have to be taken into account in model parametrization based on mixing length-scales.

Gas-flow measurements in a jet flame using cross-correlation ofhigh-speed-particle images

Temporal variations of a two-dimensional distribution of velocitiesin a nitrogen jet and a methane-jet flame are measured by cross-correlationparticle-image velocimetry (PIV). Two different approaches to investigatingthe turbulence characteristics are demonstrated. One gives the distribution ofensemble-averaged velocities and turbulence intensities by means of repetitivePIV measurements using a double-pulse laser for a longer period. The otherprovides the detailed motion of velocity profiles for a shorter duration,allowing one to analyse the characteristic scale of turbulence using ahigh-power continuous laser.The accuracy of measurements of the time-averaged velocity and turbulenceintensity is quantitatively assessed on the basis of the agreement with theresults from hot-wire-anemometry (HWA) measurement. This indicates thefeasibility of the PIV measurement, which may supply information aboutturbulence characteristics. From the measured results for a jet and a jettingflame, it is shown that the velocity gradient in the shear layer in thereacting zone is increased due to the local acceleration caused by buoyancy,resulting in higher turbulence intensities than those in a non-reacting jet.Also, from the change in the distribution of velocity vectors with time, it isclear that the turbulence eddies are carried downstream along the gas motionwith little transformation. The time scale of turbulence at each location inthe flow is obtained from the autocorrelation function of the velocityfluctuations. Furthermore, this can afford an estimate of the turbulencelength scale if one assumes that the Taylor hypothesis is valid and multipliesthe time scale and the time-average velocity. It is shown that thecharacteristic length scales of a flaming jet are about 1.5 times greater thanthose of a non-flaming jet. The effects of combustion on the turbulence in aflaming jet are discussed in detail on the basis of these experimentalresults.

Plumes in Stellar Convection Zones

Abstract: All numerical simulations of compressible convection reveal the presence of strong downward directed flows. Thanks to helioseismology, such plumes have now also been detected at the top of the solar convection zone, on supergranular scales. Their properties may be crudely described by adopting Taylor's turbulent entrainment hypothesis, whose validity is well established under various conditions. Using this model, one finds that the strong density stratification does not prevent the plumes from traversing the whole convection zone, and that they carry upward a net energy flux. They penetrate to some extent in the adjacent stable region, where they establish an almost adiabatic stratification when there is little radiative diffusion. These plumes have a strong impact on the dynamics of stellar convection zones, and they probably play a key role in the dynamo mechanism.

Probability distribution functions of derivatives and increments for decaying burgers turbulence

A Lagrangian method is used to show that the power law with a -7/2 exponent in the negative tail of the probability distribution function (PDF) of the velocity gradient and of velocity increments, predicted by E et al. [Phys. Rev. Lett. 78, 1904 (1997)] for forced Burgers turbulence, is also present in the unforced case. The theory is extended to the second-order space derivative whose PDF has power-law tails with exponent -2 at both large positive and negative values and to the time derivatives. PDF's of space and time derivatives have the same (asymptotic) functional forms. This is interpreted in terms of a random Taylor hypothesis.

266成層流体中を曳航する円柱後流中の渦列の3次元渦構造

Flow visualization experiments were conducted to clarify 3D vortex structure of the vortex streets in the wake of a circular cylinder. The cylinder was towed in a liner salt stratification fluid or in a homogeneous fluid filled in a translucent tank. Main observation of the flows was made for the streaklines visualized by fluorescent dye issuing from the surface of the cylinder. The patterns depicted by the streaklines are intimately related to the vortex structure since the vorticities are generated only on the surface of the cylinder. Three-dimensional streakline patterns contain excess information to understand the vortex structure. Based on Taylor hypothesis we propose the procedures to compose a 3D image or a superposed image rendering the concise vortex structure from a series of video pictures of the streaklines passing through the cross section of the wake. The stratification effects on the vortex structure observed in a homogeneous fluid were investigated with the 3D images and the superposed images as well as the video pictures of the flows.

1916 円形噴流の三次元渦構造の可視化

The three-dimensional vortical structure of a circular water jet was investigated by a flow visualization technique. The jet was excited by axial and azimuthal perturbations to stabilize and enhance axisymmetric and streamwise vortices. A laser florescent dye and a laser light sheet were used to visualize the jet. The three-dimensional view of vortical structure was constructed by applying the Taylor hypothesis to the jet cross-sectional images. The view reveals the details of the complicated structure. From the three-dimensional view, the area of jet boundary surface was estimated to discuss jet mixing. The result suggests that the enhancement of axisymmetric and streamwise vortices is very effective to increase mixing.

A102三次元画像解析による円形噴流の渦構造と混合機構に関する研究

The three-dimensional vortical structure of a circular water jet was investigated by a flow visualization technique. The jet was excited by axial and azimuthal perturbations to stabilize and enhance axisymmetric and streamwise vortices. A laser florescent dye and a laser light sheet were used to visualize the jet. The three-dimensional view of vortical structure was constructed by applying the Taylor hypothesis to the jet cross-sectional images. The view reveals the details of the complicated structure. From the three-dimensional view, the area of jet boundary surface was estimated to discuss jet mixing. The result suggests that the enhancement of axisymmetric and streamwise vortices is very effective to increase mixing.

Texture gradient simulations for extrusion and reversible rolling of FCC metals

A texture simulation method is described for some complex plane strain deformation paths during hot shaping of FCC metals. The method employs both finite element calculations and a polycrystal plasticity model based on the Relaxed-Constraints (RC) Taylor hypothesis and a viscoplastic constitutive law. We have considered the {111}<110> slip systems and the {100}, {110}, {112} <110> non-octahedral slip systems. The finite element codes simulate the strain paths of material flow during a shaping process. The local velocity gradients, expressed in the macroscopic reference coordinates, are rewritten in the local flow line coordinates using a kinematic analysis for steady-state flow. Secondly, for the different deformation paths, the RC polycrystal plasticity model is used to numerically simulate the local deformation texture evolutions as a function of depth. Texture simulations are carried out for two deformation processes combining hot compression and shear: extrusion and reversible rolling. For extrusion, the simulated pole figures and ODFs show the typical texture variations through the thickness of an extruded 6082 aluminium alloys, i.e. (β-fibre in the centre and a TD rotated copper component near the surface. It is shown that hot reversible rolling should develop a strong pure shear texture {001}<110> near the surface.

The analysis of energy and ozone flux data from the LANDES 94 experiment

Parametrisation of vertical fluxes of matter and energy at the biosphere–atmosphere interface requires precise measurements over different periods of the plant growth cycle. Accuracy is related to the validation of Taylor's hypothesis and the stationarity and homogeneity of the turbulent scales characteristic of transfers. To allow for systematisation of measurements, we present an approach for calculation of turbulent fluxes based on searching for data selection criteria (noise criterion, statistical validation of the wind vertical fluctuations criterion and stationarity criteria) thus enabling rejection of a certain number of samples. This approach was applied to calculate vertical flux of ozone at the vegetation–atmosphere interface of a coniferous forest in southwest France. Out of 1474 turbulent samples, 35% that did not comply with the basic assumptions for calculation of fluxes were rejected on the basis of the criteria. After application of the criteria, the variation of non-dimensionalised standard deviations for ozone in relation to the Monin–Obukhov stability criterion complied with the forecasts of the surface layer similarity theory.

A Submersible Particle Image Velocimetry System for Turbulence Measurements in the Bottom Boundary Layer

Abstract This paper introduces an oceanic particle image velocimetry (PIV) system that has been under development at The Johns Hopkins University over the past three years. PIV maps two components of the instantaneous velocity distribution within a selected sample area by recording the motion of microscopic tracer particles illuminated by a pulsed laser sheet. The primary purpose of this instrument, in its current configuration, is to directly measure the Reynolds stresses, velocity profile, vorticity, and turbulent spectra in the bottom boundary layer of the coastal ocean. Due to the basic principles of PIV, the validity of these measurements is independent of any of the usual assumptions about the nature of the flow, such as the existence of a log layer in the velocity profile, a constant stress layer, or an inertial subrange in the turbulence spectra. In addition, at scales up to those of a single image, the analysis does not require the use of the Taylor hypothesis. The primary focus of this paper is ...

Evolution of a wave packet into vortex loops in a laminar separation bubble

A laminar boundary layer develops in a favourable pressure gradient where the velocity profiles asymptote to the Falkner &amp; Skan similarity solution. Flying-hot-wire measurements show that the layer separates just downstream of a subsequent region of adverse pressure gradient, leading to the formation of a thin separation bubble. In an effort to gain insight into the nature of the instability mechanisms, a small-magnitude impulsive disturbance is introduced through a hole in the test surface at the pressure minimum. The facility and all operating procedures are totally automated and phase-averaged data are acquired on unprecedently large and spatially dense measurement grids. The evolution of the disturbance is tracked all the way into the reattachment region and beyond into the fully turbulent boundary layer. The spatial resolution of the data provides a level of detail that is usually associated with computations.Initially, a wave packet develops which maintains the same bounded shape and form, while the amplitude decays exponentially with streamwise distance. Following separation, the rate of decay diminishes and a point of minimum amplitude is reached, where the wave packet begins to exhibit dispersive characteristics. The amplitude then grows exponentially and there is an increase in the number of waves within the packet. The region leading up to and including the reattachment has been measured with a cross-wire probe and contours of spanwise vorticity in the centreline plane clearly show that the wave packet is associated with the cat's eye pattern that is a characteristic of Kelvin–Helmholtz instability. Further streamwise development leads to the formation of roll-ups and contour surfaces of vorticity magnitude show that they are three-dimensional. Beyond this point, the behaviour is nonlinear and the roll-ups evolve into a group of large-scale vortex loops in the vicinity of the reattachment. Closely spaced cross-wire measurements are continued in the downstream turbulent boundary layer and Taylor's hypothesis is applied to data on spanwise planes to generate three-dimensional velocity fields. The derived vorticity magnitude distribution demonstrates that the second vortex loop, which emerges in the reattachment region, retains its identity in the turbulent boundary layer and it persists until the end of the test section.

Temporal surrogates of spatial turbulent statistics: the Taylor hypothesis revisited.

The Taylor hypothesis, which allows surrogating spatial measurements requiring many experimental probes by time series from one or two probes, is examined on the basis of a simple analytic model of turbulent statistics. The main points are as follows: (i) The Taylor hypothesis introduces systematic errors in the evaluation of scaling exponents. (ii) When the mean wind V0 is not infinitely larger than the root-mean-square longitudinal turbulent fluctuations v(T), the effective Taylor advection velocity V(ad) should take the latter into account. (iii) When two or more probes are employed the application of the Taylor hypothesis and the optimal choice of the effective advecting wind V(ad) need extra care. We present practical considerations for minimizing the errors incurred in experiments using one or two probes. (iv) Analysis of the Taylor hypothesis when different probes experience different mean winds is offered.

Corrective measures in turbulent pipe flows and extended self-similarity

Significant statistical bias in LDA measurements and how to adequately deal with it is a subtle problem when dealing with turbulent flows. In order to attempt a clarification we have performed measurements on a non-standard “grid experiment” where a clear bias effect is found. We have investigated the effect of several corrective measures and find that best results, in the sense of having the first moment converge to zero, are obtained when using the time between events as statistical weights. The corrected time series have been used to check for extended self-similarity (ESS). Even though no scaling regime is seen for the third moment and the flow certainly is neither isotropic nor homogeneous, perfect ESS scaling based on the absolute third moment is observed up to the twelfth moment, extending into a time domain regime where the Taylor hypothesis of frozen turbulence is obviously violated. Reversing the argument this indicates that the correction scheme needed can be experimentally decided on using the criterion stated above and especially so if ESS is to be expected. Finally we have used the corrected data to quantify the deviations from Gaussian behavior of the velocity difference probability density function for a weakly turbulent flow. Through comparison with results on the Gaussian-Lorentzian distribution we find that the even part of the experimental distribution can be reproduced quite well by a single-parameter family of distributions with second moment equal unity.

Large-Scale Motions in the Marine Atmospheric Surface Layer

Multi-level turbulent wind data from the Riso Air-Sea Experiments (RASEX) were used to examine the structure of large-scale motions in the marine atmospheric surface layer. The quadrant technique was used to identify flux events (ejections/sweeps). Ejections, which appear to occur in groups, are seen to occur first at the upper level, moving successively to lower levels with small time delays. A strong correlation between events at different heights suggests that they may all be part of a single large structure. Cross-correlation between velocity signals was used to estimate orientation of the structure using Taylor's hypothesis. The inclination of this structure is shallow (≃ 15°) near the surface and increases with height. Spatial representations of the fluctuating wind vectors show a structure that is strikingly similar to conceptual models of transverse vortices and shear layers seen in laboratory flows and direct numerical simulation (DNS) of low Reynolds number flows. Spatial visualization of velocity fluctuations during other time periods and conditions clearly shows the existence of shear layers, transverse vortices, plumes, and downdrafts of various sizes and strengths. A quantitative analysis shows an increase in the frequency of shear related events with increasing wind speed.

High-order structure functions of turbulence

The scaling behaviour of high-order structure functions Gp(r) =〈(u(x+r)−u(x))p〉 is studied in a variety of laboratory turbulent flows. The statistical accuracy of the structure function benefits from novel instrumentation for its real-time measurement. The nature of statistical errors is discussed extensively. It is argued that integration times must increase for decreasing separations r. Based on the statistical properties of probability density functions we derive a simple estimate of the required integration time for moments of a given order. We further give a way for improving this accuracy through careful extrapolation of probability density functions of velocity differences.Structure functions are studied in two different kinematical situations. The (standard) longitudinal structure functions are measured using Taylor's hypothesis. In the transverse case an array of probes is used and no recourse to Taylor's hypothesis is needed. The measured scaling exponents deviate from Kolmogorov's (1941) prediction, more strongly so for the transverse exponents.The experimental results are discussed in the light of the multifractal model that explains intermittency in a geometrical framework. We discuss a prediction of this model for the form of the structure function at scales where viscosity becomes of importance.