Taylor's Hypothesis Research Articles

Experimental measurements of spectral subgrid-scale Prandtl number in a heated turbulent wake flow, EDQNM predictions and 4/3-law

For turbulent flows including scalar transport, the spectral diffusivity as well as the spectral Prandtl number characterizes the scalar-variance transfer rate from any wavenumber κ to all scales smaller than a specified filter scale. Classical theories predict a plateau behavior at inertial-range wavenumbers with deviations of the diffusivity at scales close to the cutoff wavenumber. However, to date these quantities have not been measured in high Reynolds number flows. To examine realistic turbulence at a moderately high Reynolds number, in this study an experimental measurement technique previously applied to obtain spectral eddy viscosities (Cerutti et al. 2000 Journal of Fluid Mechanics 421 307–338) is extended and applied to the case of scalar eddy diffusivity. We show that the subgrid-scale (SGS) dissipation spectrum of scalar variance can be expressed as the co-spectrum of negative SGS scalar flux and filtered scalar gradient. Using local isotropy, the result is expressed in terms of the streamwise components of the SGS scalar flux and filtered scalar gradient that can be measured in experiments. Using an array of four X-type hot-wire and four I-type cold-wire probes, two-dimensional box-filtered velocities and temperatures in the streamwise (invoking Taylor's hypothesis) and cross-stream directions are obtained at the centerline of a heated wake flow, at a Taylor-scale Reynolds number of 350. From the radial dissipation spectra, the spectral eddy viscosity and Prandtl number are evaluated. The measured spectral eddy viscosity, diffusivity and Prandtl number (the ratio of the spectral eddy viscosity to diffusivity) decrease near the filter scale. They also decrease with decreasing wavenumber near the integral scale of turbulence. Measurement results are compared with predictions from a classical two-point closure (eddy-damped quasi-normal Markovian, EDQNM) applied with a Gaussian filter and finite integral scale. Measurement and predictions are in qualitative agreement (decreasing trends observed near the filter wavenumber), but the details differ especially in the low wavenumber limit. This could be due to the assumption of isotropy which does not hold for the experiment at large scales. We also find significant sensitivity of the EDQNM predictions to free parameters of the eddy-damping term. Analysis in physical space shows that the two-point correlation between the SGS scalar flux and filtered scalar plays an important role to predict a mixed third-order structure function in the von Kármán–Howarth–Kolmogorov equation for the resolved scalar field (the LES equivalent of the 4/3-law).

Effect of Streamwise Vortices on Characteristics of Jets

The interaction of streamwise and axisymmetric vortices in an axisymmetric jet is studied by flow visualization and velocity measurement. The jet is excited by azimuthal and axial perturbations to enhance streamwise and axisymmetric vortices. The three-dimensional views of the jet-boundary surface and streamwise vortices are constructed by applying the Taylor hypothesis to the jet cross-sectional images, and the interaction model of streamwise and axisymmetric vortices is proposed. The interaction of spanwise and streamwise vortices in a plane jet is also studied by velocity measurement. The experiment is carried out under conditions similar to those of the axisymmetric jet. The vortical structure is discussed on the basis of the three-dimensional views of phase-averaged vorticities. It is confirmed that the interacting vortical structure is similar to that in an axisymmetric jet. The entrainment mechanism is also discussed in relation to the vortical structure.

Validity of the Taylor hypothesis in a random spatially smooth flow

The validity of the Taylor frozen flow hypothesis in a chaotic flow of a dilute polymer solution in a regime of elastic turbulence is investigated experimentally. By accurate time-dependent measurements of the flow field we study the velocity coherence between pairs of points displaced both in time and space and quantify the degree of applicability of the Taylor hypothesis. Alternatively, the frozen flow assumption is assessed by comparison of the measured velocity structure functions with the ones derived by a frozen flow assumption. The breakdown of the Taylor hypothesis is further discussed in both the context of strong velocity fluctuations and long-range spatial correlations, which are the result of the flow smoothness and lack of scale separation. Different choices of the advection velocity are tested and discussed.

On the Taylor hypothesis in forced unsteady wall flows

Experiments on the modulation characteristics of the wall shear stress τ′-longitudinal velocity u′ and u′−u′ space–time correlations are reported in a forced turbulent channel flow in a wide range of imposed frequencies. The resulting integral and Taylor scale properties are discussed in detail in the low buffer layer under steady and unsteady flow conditions. It is shown that the small-scale turbulence is sensitive to the imposed unsteadiness since the amplitude and phase of the Taylor length scale vary considerably in the imposed frequency range investigated here. The Taylor hypothesis is acceptably valid in steady and unsteady wall layers just above the low buffer layer. Production and instantaneous pressure gradients are mostly responsible for the deviation of the frozen turbulence-state in the viscous and low buffer sublayers.

Spatiotemporal Intermittency Measurements in a Gas-Phase Near-Isotropic Turbulence Using High-Speed Dpiv and Wavelet Analysis

AbstractRecently, Shy and his co-workers developed a new turbulent flow system that used a pair of counter-rotating fans and perforated plates to generate stationary near-isotropic turbulence, as verified by LDV measurements, for the study of premixed turbulent combustion processes. This paper evaluates for the first time the correlations between spatial and temporal properties of small-scale intermittency in such a fan-stirred near-isotropic turbulence. These spatiotemporal properties are obtained simultaneously via high-speed digital particle image velocimetry together with wavelet analyses. It is found that the wavelet energy spectra in the inertial range of near-isotropic region all exhibit a slope of nearly −5/3 which spans at least from 3Hz to 100Hz. Characteristic scales, including the integral time and length scales, Taylor microscales, and viscous dissipation scales, are identified without the use of Taylor hypothesis. Thus, a direct evaluation of Taylor hypothesis in near-isotropic turbulence with zero mean velocity can be made. From variations of the flatness factor, equivalent to the 4th order velocity structure function, in the spatial and time domains, it is found that the characteristic spatial and temporal intermittent scales of intense vorticity structures in the dissipation range of the fan-stirred near-isotropic turbulence occur around 5 ∼ 8η and τk, respectively, where η and τk are the Kolmogorov length and time scales. These results are useful for further study of particle settling in turbulence, a problem of both engineering and geophysical interest.

Flames with Realistic Thermal Expansion in a Time-Dependent Turbulent Flow

The propagation velocity of turbulent premixed flames with real thermal expansion in a time-dependent external flow is studied for an infinitely thin flame front and for flames of small but finite thickness. It is shown that the influence of temporal pulsations is usually small and can be neglected for reasonable values of the pulsation frequency. The role of pulsations is even smaller for realistic thermal expansion in comparison with the artificial case of zero thermal expansion studied previously. The results obtained indicate that the Taylor hypothesis of “ stationary” turbulence is a good approximation for turbulent flames. The role of pulsations is substantial only if the integral turbulent length scale is close to the cut-off wavelength of the Darrieus-Landau instability. In this particular case, temporal pulsations can be important for explaining recent experiments on turbulent burning.

Advective velocity and energy dissipation rate in an oscillatory flow

Characterizing the transport processes at the sediment-water interface along sloping boundaries in lakes and reservoirs is of fundamental interest in lake and reservoir water quality management. The turbulent bottom boundary layer (TBBL) along a slope, induced by the breaking of internal waves in a linearly stratified fluid, was investigated through laboratory measurements. Fast response micro-scale conductivity and temperature probes in conjunction with laser-Doppler velocimetry were used to measure the time series of salinity, temperature, and velocity along a sloping boundary. Turbulent energy spectra were computed from the velocity data using a time-dependent advective velocity and Taylor's hypothesis. The energy spectra were used to estimate the energy dissipation rate at different positions in the TBBL. The advective velocity in this near-zero mean shear flow is based on an integral time scale (T(int)). The integral time scale is related to the average frequency of the spectral energy density of the flow velocity. The energy dissipation rate estimated from the variable advective velocity with an averaging time window equal to the integral time scale (T=T(int)) was 43% higher than the energy dissipation rate estimated from a constant advective velocity. The estimated dissipation rates with T=T(int) were comparable to values obtained by curve-fitting a theoretical Batchelor spectrum for the temperature gradient spectra. This study proposes the integral time scale to be used for the oscillatory flows as (a) a time-averaging window to estimate the advective velocity and associated energy dissipation level, and (b) a normalizing parameter in the energy spectrum.

Experimental investigation of the grid-generated turbulence features in a free surface flow

The present study aims to investigate the features of a grid-generated turbulence occurring in a current flow with a free surface flow. The interest is focused on the length and time scales of the turbulence. These are the macro, the micro and the Kolmogorov scales. To analyze the flow, a 2D LDV system has been used to measure U ¯ , W ¯ , u′ and w′. This non-intrusive and optical technique is really accurate (in terms of space and time resolution). Furthermore, it does not disturb the flow and provides a high data rate. Both horizontal and vertical velocities are recorded at the same time according to a coincidence window ( τ cw). Bias measurements are avoided by using a filtering technique during data processing. The improved homogeneity and isotropy of the turbulence downstream of the grid allows the use of the Taylor hypothesis. Thus, all length and time scales of the flow can be estimated. Results are discussed as well as the influence of the upcoming mean velocity ( U ¯ ) on the turbulence properties.

PIV Measurement and Turbulence Scale in Turbulent Combustion

We have investigated a turbulent combustion by PIV (Particle Image Velocimetry) technique. Comparing with LDV data, the validity of PIV measurement has been confirmed. Especially, the conditions of sampling number and spatial resolution have been revealed to obtain reliable data by PIV. Based on the velocity fields in cold flow and combustion, the interaction between flame and flow has been discussed. It is observed that the flow field is changed by combustion and the turbulence is reduced. For determining statistic quantities such as mean velocity and rms of velocity fluctuation, the sampling number of 1000 is needed. Moreover, the velocity correlation coefficient is evaluated to obtain the integral length scale of the flow. For both cold flow and combustion, the estimated scale by PIV is very close to that by LDV based on the assumption of Taylor's hypothesis. Resultantly, the special resolution in this study is about 6 times smaller than the integral length scale.

C304 位相平均変動静圧測定による噴流中の三次元渦構造の抽出

Measurements of fluctuating static-pressure in a rectangular jet were conducted to educe three-dimensional vortical structure with phase-averaging technique. The experiments were performed for the air issuing from a sharp-edged rectangular orifice. The jet was excited at the interaction mode, where the stable interaction of vortices was generated. For phase-averaging processing, the reference signals were detected by a single normal hot-wire probe fixed at a downstream station whose distance from the jet exit corresponded to an equivalent diameter of the exit, and fluctuating static-pressure were measured over the flow field by a static pressure probe. Phase-average incoherent fluctuating static-pressure, which is related to jittering motions of vortices and is defined in phase-averaging, and adequacy of Taylor hypothesis to obtain three-dimensional structure were discussed. The results suggested that interaction and stretching of vortices contributes to generation of the incoherent vortex motions, and the use of a constant convection velocity in the hypothesis is acceptable for qualitative consideration.

Temperature Microstructure beneath Surface Gravity Waves

Abstract Oceanic turbulence very near the water surface controls heat, momentum, energy, and mass transfer at the air–sea interface. This study examines the use of a rising temperature microstructure profiler for determination of the rate of turbulent energy dissipation ε beneath a water surface dominated by wind-driven surface gravity waves. Under short-fetch wind waves there is sufficient turbulent energy to generate an inertial-convective subrange. Thus, as well as the conventional Batchelor spectrum fitting approach, ε can be estimated using the temperature spectrum at lower wavenumbers. The inertial-convective subrange-derived turbulent energy dissipation rate εi compares well with the Batchelor spectrum method εb for higher dissipation rates. Sensor limitations mean that these estimates will be a lower bound. The highest dissipation rate estimates were in the uppermost data bin, indicating the importance of resolving right to the surface. Velocimeter results show that the surface waves modulate the rise velocity of the profiler, with variations reaching 75% of the deep water profiler speed. This increases the uncertainty in the transformation of spectra from frequency to wavenumber space using Taylor's frozen-field hypothesis. The use of an inertial convective structure-function-derived energy dissipation rate avoids this transformation. However, the structure function results are not encouraging as they provide a very poor estimate due to the sensitivity of the calculations and the low signal-to-noise ratio in the data. Repeated profiling illustrates the variability of turbulence intensity near the surface and also enables a reliable estimate of the background temperature gradient to be derived. This provides an improved estimate of vertical diffusion of heat.

Anisotropic fluctuations in turbulent shear flows

An experimental analysis of small-scale anisotropic fluctuations has been performed in two different flows in order to assess possible universal features of shear dominated turbulence, such as the decay rate of anisotropy at small scales and the recovery of isotropy. The two data sets—a homogeneous shear flow and a turbulent boundary layer—are characterized by turbulent Reynolds numbers in the range Reλ=230−330. The measurements in the logarithmic region of the turbulent boundary layer extend from y+=90 up to y+=350. The explicit use of the Taylor hypothesis is avoided by resorting to two-point measurements, with separation in the spanwise direction, z. Streamwise (u) and wall-normal (v) velocity components are simultaneously measured in both positions by means of cross-wire probes. This procedure allows the construction of the mixed transverse structure functions, here addressed up to order 6. According to the SO(3) formalism, the observables we selected are free of any isotropic contribution, thus allowing a direct measurement of the fully anisotropic component of the field. The results are consistent with the “exponent-only” scenario for universality, i.e., all experimental data can be fitted by fixing the same set of anisotropic scaling exponents by changing only the prefactors, for different shear intensities and boundary conditions.

MEAN-FIELD AND FLUCTUATION ANALYSIS OF A FORCED TURBULENCE SIMULATED BY THE LATTICE BOLTZMANN METHOD

On the basis of the lattice Boltzmann method for the Navier–Stokes equation, we have done a numerical experiment of a forced turbulence in real space and time. Our new findings are summarized into two points. Firstly, in the analysis of the mean-field behavior of the velocity field using the exit-time statistics, we have verified Kolmogorov's scaling and Taylor's hypothesis at the same time. Secondly, in the analysis of the intermittent velocity fluctuations using a non-equilibrium probability distribution function and the wavelet denoising, we have clarified that the coherent vortices sustain the power-law velocity correlation in the non-equilibrium state.

Instantaneous measurement of velocity fields in developed thermal turbulence in mercury.

Using ultrasonic velocimetry we measured the vertical profile of the velocity fluctuation in high-Rayleigh-number thermal convection in a cell with aspect ratio of 0.5, filled with a low-Prandtl-number fluid, mercury. The intriguing fluctuating dynamics of the mean flow and universal nature of the kinetic energy cascade are elucidated utilizing spectral decomposition and reconstruction. The scaling properties of the structure functions and the energy spectrum are directly calculated without the use of Taylor's frozen-flow hypothesis. Despite the complex nature of the mean flow, it is found that the energy cascade process exhibits universal laws in thermal turbulence.

Local and global statistics of clear‐air Doppler radar signals

A refined theoretical analysis of the clear‐air Doppler radar (CDR) measurement process is presented. The refined theory builds on the Fresnel‐approximated (as opposed to Fraunhofer‐approximated) radio wave propagation theory, and turbulence statistics like locally averaged velocities, local velocity variances, local dissipation rates, and local structure parameters are allowed to vary randomly within the radar's sampling volume and during the dwell time. A local version of the moments theorem and the random Taylor hypothesis are used to derive first‐principle formulations of all higher moments of the Doppler cross‐spectrum. The mth moment is written as a convolution integral of a spectral sampling function and a generalized, mth‐order refractive‐index spectrum or, alternatively, as a convolution integral of a lag‐space sampling function and a spatial cross‐covariance function of the local refractive‐index fluctuations and their local mth‐order time derivatives. Closed‐form expressions of the first three moments (i.e., m = 0, 1, 2) of the Doppler spectrum for the monostatic, single‐signal case are derived. This refined theory, or “local sampling theory,” enables one to correctly interpret CDR observations that are collected under conditions where the applicability of the traditional “global sampling theory” is questionable. The commonly used global sampling assumptions (Bragg‐isotropy, homogeneity, and stationarity of all turbulence statistics within the sampling volume and during the dwell time) may be invalid for small‐scale intermittency in the mixed layer, for refractive‐index sheets corrugated by gravity waves or instabilities, and for layered turbulence in the stably stratified atmosphere.

Spatial Correlation Measurements in Flow over a Rectangular Cube by Means of LDA and PIV.

Spatial correlation measurements of velocity fluctuations in turbulent flow over a rectangular cube are presented. Direct measurement of spatial correlation requires simultaneous measurement of velocities at two or multi-points in the flow. Therefore this study is carried out by means of a particle image velocimetry (PIV) or two LDAs (laser Doppler anemometer) composed by He-Ne and Ar+ lasers. The cube is set on the floor of the wind tunnel. At the inlet, the mean flow velocity and the relative turbulence intensity are 4.0m/s and 1.5%, respectively in both experiments. Under this condition, the flow Reynolds number based on the rectangular cube height and the mean velocity is about 8 800. Firstly, comparisons are made for longitudinal and transversal spatial correlation coefficients measured by LDA. Secondly, distributions of integral length scales distributions acquired by LDA and PIV have been discussed. In addition, the validities of integral length scale calculated by Taylor's hypothesis are evaluated in the flow.

A231 二次元噴流初期領域における渦構造とエントレインメントの関連性

The relation of the vortical structure and the entrainment in the initial region of a plane jet was investigated under the four conditions of vortex generators by vorticity measurements. The vortices were enhanced and stabilized by streamwise and spanwise disturbances. The three-dimensional views of the vortices were constructed by applying the Taylor hypothesis to the phase-average vorticities, and the entrainment was discussed in relation to the vortical structures. The result reveals the enhancement of entrainment by the interaction of spanwise and streamwise vortices

Interaction of Vortex Rings and Streamwise Vortices in an Axisymmetric Jet

The interaction of vortex rings and streamwise vortices in an axisymmetric jet is studied by flow visualization and velocity measurement. The jet is excited by axial and azimuthal perturbations to stabilize and enhance axisymmetric and streamwise vortices. A laser fluorescent dye and a laser light sheet are used to visualize the jet. The three-dimensional views of jet-boundary surface and streamwise vortices are constructed by applying the Taylor hypothesis to the jet cross-sectional images. From the three-dimensional views, the interaction model of axisymmetric and streamwise vortices is proposed. The characteristics of the flow field and the entrainment of the jet are also discussed in relation to the vortical structure.

Coordinate-free description of corrugated flames with realistic density drop at the front.

The complete set of hydrodynamic equations for a corrugated flame front is reduced to a system of coordinate-free equations at the front using the fact that the vorticity effects remain relatively weak even for corrugated flames. It is demonstrated how small but finite flame thickness may be taken into account in the equations. Similar equations are obtained for turbulent burning in the flamelet regime. The equations for a turbulent corrugated flame are consistent with the Taylor hypothesis of "stationary" external turbulence.

Heterogeneous deformation and texture development in halite polycrystals: comparison of different modeling approaches and experimental data

Modeling the plastic deformation and texture evolution in halite is challenging due to its high plastic anisotropy at the single crystal level and to the influence this exerts on the heterogeneity of deformation over halite polycrystals. Three different assumptions for averaging the single crystal responses over the polycrystal were used: a Taylor hypothesis, a self-consistent viscoplastic model, and a finite element methodology. The three modeling approaches employ the same single crystal relations, but construct the polycrystal response differently. The results are compared with experimental data for extension at two temperatures: 20 and 100 °C. These comparisons provide new insights of how the interplay of compatibility and local equilibrium affects the overall plastic behavior and the texture development in highly anisotropic polycrystalline materials. Neither formulation is able to completely simulate the texture development of halite polycrystals while, at the same time, giving sound predictions of microstructural evolution. Results obtained using the finite element methodology are promising, although they point to the need for greater resolution of the individual crystals to capture the full impact of deformation heterogeneities.