Taylor's Hypothesis Research Articles

Spectral description of migrating bed forms and sediment transport

AbstractThis paper considers the problem of spatiotemporal bed topography evolution and sediment transport estimation in rivers with migrating bed forms of different types and sizes, in statistical equilibrium conditions. Instead of resorting to bed form classification, we propose to evaluate the evolution of multiscale bed topography as the integral of unit contributions defined through a space‒time Fourier decomposition of bed elevations. Using joint 2‒D spectra in the frequency and wave number domain, a functional relationship between the length scales and the timescales in which migrating bed forms are decomposed is proposed and developed into a dimensionless expression for scale‒dependent convection velocities. This formulation highlights the violation of Taylor's hypothesis for migrating bed forms, confirming statistically that larger bed forms travel slower as compared to smaller bed forms. This phenomenological description leads to a spectral extension of the Simons et al. (1965) formula for sediment transport to incorporate a range of multiscale migrating features. Both the scaling of convection velocities and the spectral estimate of sediment transport rate were validated through extensive bed elevation data from laboratory experiments conducted at the St. Anthony Falls Laboratory, for a range of Froude numbers 0.2<Fr<0.5, under varying discharge and bed material composition.

Exchange Rate Pass Through in a Small Open Economy: A case study of West African Monetary Zone

The study investigated the magnitude of exchange rate pass through to import prices and domestic prices   (consumer price index) in WAMZ economy using quarterly time-series data between 2000 and 2010 with the aids of Vector autoregressive (VAR) modeling technique supported with Johansen co-integration approach cross country analysis comprising of Gambia, Ghana, Nigeria and Sierra-Leone. The study discovered that transmission of exchange rate to import prices is more when compared with consumer price in the zone while the contributions of exchange rate to import price are not less 13 percent at average in entire zone. Consumer price index was explained by exchange rate pass through with an average of 26 percent in the zone where the pass through to consumer price is less than two percent in Ghanaian economy. The Taylor (2000) hypothesis was observed in the study where Ghana and Nigeria are the outlier economies while Nigeria established a positive relationship between interest rate volatility and exchange rate pass through to import prices.

Very-large-scale coherent structures in the wall pressure field beneath a supersonic turbulent boundary layer

Data have been acquired from a spanwise array of fluctuating wall pressure sensors beneath a wind tunnel wall boundary layer at Mach 2, then invoking Taylor's hypothesis allows the temporal signals to be converted into a spatial map of the wall pressure field. Different frequency ranges of pressure fluctuations may be accessed by bandpass filtering the signals. In all frequency ranges, this reveals signatures of coherent structures where negative pressure events are interspersed amongst positive events, with some degree of alternation in the streamwise direction. Within lower frequency ranges, streaks of instantaneously correlated pressure fluctuations elongated in the streamwise direction exhibit a spanwise meander and show apparent merging of pressure events. Coherent length scales based on single-sensor correlations are artificially shortened by neglecting this meander and merging, but are captured correctly using the sensor array. These measurements are consistent with similar observations by other researchers in the velocity field above the wall, and explain the presence of the flat portion of the wall pressure spectrum at frequencies well below those associated with the boundary layer thickness. However, the pressure data lack the common spanwise alternation of positive and negative events found in velocity data, and conversely demonstrate a weak positive correlation in the spanwise direction at low frequencies.

Experimental test of revised similarity hypotheses without Taylor's hypothesis

The refined similarity hypotheses (RSH) and their extension to passive scalar (RSH-P) are tested experimentally using simultaneous velocity and scalar data in a turbulent jet. Different from the single-point hot-wire probe in a previous experimental test, a combined particle image velocimetry and planar laser induced fluorescence technique enable us to obtain the test data without applying Taylor's hypothesis. RSH is successfully validated with direct examinations of its three hypotheses. RSH-P is partially supported, where the hypothesis of independent behavior of the stochastic variable υ(θ) is not supported. The conditional probability density functions (PDFs) of υ and υ(θ) cannot be described by Gaussian distributions when Re(r)<5 for υ and Re(r)<300 for υ(θ), and their Gaussian peaks converge when Re(r)>100 for υ and Re(r)>1000 for υ(θ). In addition, the bimodal behavior of the PDFs and oscillations at small r in previous experimental tests are not observed in this study.

Dual non-Kolmogorov cascades in a von Kármán flow

The experimental spatial power spectrum of the velocity fluctuations in a von Kármán flow is measured, in a wide range of Reynolds numbers, 102 < Re < 106, for the first time without using the Taylor hypothesis. At high enough Reynolds numbers, the spectra display a clear dual (direct and inverse) cascade. For any Re, the scaling of the direct cascade is steeper than the classical Kolmogorov −5/3 exponent of homogeneous and isotropic 3D turbulence. We then discuss the possibility of dual local and non-local cascades in a 3D turbulent Beltrami (a property satisfied by the von Kármán flow at large scale) flow, with inverse energy cascade and direct helicity cascade, by analogy with 2D turbulence. The corresponding energy spectra are computed in both local and non-local cases, and compared with our experimental results. The inverse cascade scaling is found to be in agreement with the non-local scenario. The direct cascade scaling is close to the non-local scenario for Re ≲ 4.104, and switches towards the local scenario at Re > 105.

Frequency–wavenumber velocity spectra, Taylor's hypothesis, and length scales in a natural gravel bed river

Macroscale turbulent coherent flow structures in a natural fast‐flowing river were examined with a combination of a novel 2 MHz Acoustic Doppler Beam (ADB) and a Maximum Likelihood Estimator (MLE) to characterize the streamwise horizontal length scales and persistence of coherent flow structures by measuring the frequency (f)‐streamwise‐wavenumber (ks) energy density velocity spectrum, E(f, ks), for the first time in natural rivers. The ADB was deployed under a range of Froude numbers (0.1–0.6) at high Reynolds numbers (∼106) based on depth and velocity conditions within a gravel bed reach of the Kootenai River, Idaho. The MLE employed on the ADB data increased our ability to describe river motions with relatively long (&gt;10 m) length scales in ∼1 m water depths. The E(f, ks) spectra fell along a ridge described by V = f/ks, where Vis the mean velocity over depth, consistent with Taylor’s hypothesis. New, consistent length scale measures are defined based on averaged wavelengths of the low‐frequencyE(f, ks) and coherence spectra. Energetic (∼50% of the total spectral energy), low‐frequency (f &lt; 0.05 Hz) streamwise motions were found. Mean length scales,Lm, compared with the depth, h, are significantly larger than previously suggested for macroturbulence with Lm/h∼ 28–118. Although the energy appears as low‐pass white noise, it is streamwise coherent along the length of the array. In fast flows with velocities &gt; 1 m/s,Lmwere found to be significantly longer than their corresponding coherence lengths, suggesting that the turbulent structures evolve rapidly under these conditions. This is attributed to the stretching and concomitant deformation of preexisting macroturbulent motions by the ubiquitous bathymetry‐induced spatial flow accelerations present in a natural gravel bed river.

Agregação temporal e não-linearidade afetam os testes da paridade do poder de compra: evidência a partir de dados brasileiros

Este artigo analisa as séries de câmbio real brasileira calculada a partir de índices de preços ao consumidor para o Brasil e 21 parceiros comerciais no período de 1957 a 2010. O primeiro objetivo deste trabalho será o de avaliar a validade da Paridade do Poder de Compra (PPC) entre Brasil e seus parceiros comerciais através de diversos testes de raiz unitária (ADF, PP, KPSS, Kapetanios et alii (2003) e Bierens (1997)). O segundo objetivo consiste em investigar a hipótese de Taylor (2001) de que a meia-vida é superestimada quando os dados das séries são construídos a partir de um mecanismo de agregação temporal pela média e cujo processo gerador dos dados é linear. O trabalho apresenta elementos para confirmar o argumento de Taylor (2001) de que agregação temporal causa sérias distorções na estimação da meia-vida dos choques da PPC. Os resultados dos testes de raiz unitária lineares (PP e ADF) são desfavoráveis a PPC. Já o teste KPSS, de Kapetanios et alii (2003) e, de Bierens (1997) aplicados a base sem agregação temporal sugerem um cenário bem mais favorável a PPC.

Spectral structure of mesoscale winds over the water

AbstractStandard meteorological measurements from a number of masts around two Danish offshore wind farms have been used to study the spectral structure of the mesoscale winds, including the power spectrum, the co‐ and quadrature spectrum and the coherence. When average conditions are considered, the power spectra show universal characteristics, in agreement with the findings in literature, including the energy amplitude and the −5/3 spectral slope in the mesoscale range transitioning to a slope of −3 for synoptic and planetary scales. The integral time‐scale of the local weather is found to be useful to describe the spectral slope transition as well as the limit for application of the Taylor hypothesis. The stability parameter calculated from point measurements, the bulk Richardson number, is found insufficient to represent the various atmospheric structures that have their own spectral behaviours under different stability conditions, such as open cells and gravity waves. For stationary conditions, the mesoscale turbulence is found to bear some characteristics of two‐dimensional isotropy, including (1) very minor vertical variation of spectra; (2) similar spectral behaviour for the along‐ and across‐wind components; and (3) the along‐ and across‐wind components at one point are not correlated. Copyright © 2012 Royal Meteorological Society

Reconstructing Ontong Java Nui: Implications for Pacific absolute plate motion, hotspot drift and true polar wander

The Taylor (2006) hypothesis suggesting a common origin for the Ontong Java, Manihiki, and Hikurangi large igneous provinces provides an opportunity for a quantitative reconstruction and reassessment of the Ontong Java–Louisville hotspot connection. Our plate tectonic reconstructions of the three plateaus into Ontong Java Nui, or greater Ontong Java, combined with models for Pacific absolute plate motion (APM), allow an analysis of this connection. A new survey of the central Ellice Basin confirms easterly fracture zones, northerly abyssal hill fabric, as well as an area of sigmoidally-southeast-trending fracture zones associated with a late-stage spreading reorientation. From the fracture zone trends we derive new rotation poles for a two-stage model of Ellice Basin opening between the Ontong Java and Manihiki Plateaus. We use these and a single stage pole for separation of the Manihiki and Hikurangi Plateaus, together with three different Pacific APMs, to reconstruct the Ontong Java Nui super plateau back to 123Ma and compare its predicted location with paleolatitude data obtained from the Ontong Java and Manihiki plateaus. Discrepancies between our Ontong Java Nui reconstructions and Ontong Java and Manihiki paleolatitudes are largest for the fixed Pacific hotspot APM. Assuming a Louisville hotspot source for Ontong Java Nui, remaining disparity between Ontong Java Nui's paleo-location at 123Ma and published paleomagnetic latitudes for Ontong Java plateau imply that 8°–19° of Louisville hotspot drift or true polar wander may have occurred since the formation of Ontong Java Nui. However, the older portions of the Pacific APMs could easily be biased by a similar amount, making a firm identification of the dominant source of misfit difficult. Prior studies required a combined 26° of hotspot drift, octupole bias effects, and true polar wander just to link the Ontong Java Plateau to Louisville. Consequently, we suggest the super plateau hypothesis and our new reconstructions have considerably strengthened the case for a Louisville plume origin for Ontong Java Nui.

Elasto-plasticity Behavior of IF Steel Sheet with Planar Anisotropy and Its Macro-meso Modeling

Elasto-plasticity behavior of an IF steel sheet was investigated by performing uniaxial tension tests in three directions (0°, 45° and 90° to the rolling direction of the sheet), in-plane cyclic tension compression test and bi-axial tension test. The sheet has strong planar anisotropy (r0 = 2.15, r45 = 2.12 and r90 = 2.89) but very weak flow stress directionality. Equi-biaxial flow stress is as large as 1.23 times of the uniaxial flow stress. These elasto-plasticity deformation characteristics, as well as the Bauschinger effect and cyclic hardening behavior, are well described by a macro-plasticity model (Yoshida-Uemori model incorporating with the 4th-order anisotropic yield function). Further, the simulation of elasto-plasticity stress strain responses of the sheet were conducted by two types of crystal plasticity models, i.e., Taylor hypothesis based model and CPFEM, using the crystallographic orientation distribution data measured by neutron diffraction method. The models capture most of the above-mentioned deformation characteristics qualitatively, but the predicted anisotropy and the Bauschinger effect are weaker than those of the real material. The CPFEM gives more realistic results than the Taylor model.

Experimental investigation of small scale geometries in a turbulent round jet

In the present work, we present a method to gather highly accurate three-dimensional measurements of a scalar field in order to experimentally validate the theory of dissipation elements as developped by Wang & Peters (2006, 2008). Combining a two-dimensional high-speed Rayleigh scattering technique with Taylor's hypothesis allows to resolve the concentration field of gaseous propane discharging into ambient air from a turbulent round jet at a Reynolds number (based on nozzle diameter and exit velocity) of 2,800 down to the Kolmogorov scale in every spatial direction. Based on the acquired data, the normalized probability density function of the length of dissipation elements P̃(l̃) is investigated at various downstream positions x/d = 15 − 40 and an excellent agreement with the theoretically derived model equation is obtained.

Nonaxisymmetric Anisotropy of Solar Wind Turbulence

A key prediction of turbulence theories is frame-invariance, and in magnetohydrodynamic (MHD) turbulence, axisymmetry of fluctuations with respect to the background magnetic field. Paradoxically the power in fluctuations in the turbulent solar wind are observed to be ordered with respect to the bulk macroscopic flow as well as the background magnetic field. Here, nonaxisymmetry across the inertial and dissipation ranges is quantified using in situ observations from Cluster. The observed inertial range nonaxisymmetry is reproduced by a "fly through" sampling of a direct numerical simulation of MHD turbulence. Furthermore, fly through sampling of a linear superposition of transverse waves with axisymmetric fluctuations generates the trend in nonaxisymmetry with power spectral exponent. The observed nonaxisymmetric anisotropy may thus simply arise as a sampling effect related to Taylor's hypothesis and is not related to the plasma dynamics itself.

Quantifying variance due to temporal and spatial difference between ship and satellite winds

[1] Ocean vector winds measured by SeaWinds can be validated with comparison in situ data that are within a certain time and space range to the satellite overpass. The total amount of random observational error is composed of two primary components, which are quantified in this study: the uncertainty associated with the data sets and the uncertainty associated with the temporal and/or spatial difference between two observations. The variance associated with a temporal difference, which can be translated into a spatial difference using Taylor's hypothesis, between two observations is initially examined in an idealized case that includes only Shipboard Automated Meteorological and Oceanographic System (SAMOS) 1 min data. The results show that the amount of variance in wind speed and direction increases as the time difference increases, while the amount of variance in wind speed increases and direction decreases with larger wind speeds. Collocated SeaWinds and SAMOS observations are used to determine the total amount of variance associated with a temporal (equivalent) difference from 0 to 60 min. For combined differences less than 25 min (equivalent) and the selected wind speed bins, the variance associated with the temporal and spatial difference is dominated by small changes in the wind speed distribution, and the sum of the observational errors is approximately 1.0 m2 s−2 (12 deg2) and 1.5 m2 s−2 (10 deg2) for wind speeds between 4 and 7 m s−1 and 7–12 m s−1. For larger combined differences, the observational error variance is no longer the dominant term; therefore, the total variance is seen to gradually increase with increasing time differences.

Taylor’s hypothesis convection velocities from mass conservation equation

We propose to use the continuity equation to calculate convection velocities provided by the Taylor hypothesis for flow structures crossing a measurement plane. This is carried out in Fourier space to identify a velocity associated to each frequency. High-speed PIV experimental data of an axisymmetric mixing layer is used to implement the method. We show that as expected the Taylor hypothesis fails for the lowest frequencies and predicts the convection velocity to be close to the mean velocity for the higher ones. The method is compared to one of the definitions proposed by Del Álamo and Jiménez [J. Fluid Mech. 640, 5 (2009)].

Experimental measurement of large-scale three-dimensional structures in a turbulent boundary layer. Part 2. Long structures

Three-dimensional (3D) measurements of a turbulent boundary layer have been made using high-speed particle image velocimetry (PIV) coupled with Taylor's hypothesis, with the objective of characterising the very long streamwise structures that have been observed previously. The measurements show the 3D character of both low- and high-speed structures over very long volumes. The statistics of these structures are considered, as is their relationship to the important turbulence quantities. In particular, the length of the structures and their wall-normal extent have been considered and their relationship to the other components of the velocity fluctuations and the instantaneous stress.

A case‐study of mesoscale spectra of wind and temperature, observed and simulated

AbstractThe spectra of the zonal and meridional winds and temperature over the mesoscale range of length‐scales (10−5&lt;k&lt;10−3rad m−1, with k the radian wave number) are examined through a case‐study using measurements and simulations. The measurements include 1 s and 10 min average winds and temperature, from which the temporal spectra are obtained by Fourier transform. The mesoscale Weather Research and Forecasting (WRF) model is used to simulate the weather for four days when gravity waves are observed. The four‐day dataset also includes a period with unstable conditions and free of gravity waves. The simulation provides a possibility to study the spatial spectra and, together with the measurements, it provides an opportunity to examine the validity of the Taylor hypothesis for transforming between temporal and spatial spectra. We examined these issues under stable and unstable conditions, both in the absence and presence of gravity waves. It was found that, in the absence of gravity waves, the spectral behaviour of wind and temperature (in terms of the form of the spectra and the energy distribution) is similar to the literature, and the Taylor hypothesis is valid. When the gravity waves are present, it was found that the Doppler‐shifted frequency has to be taken into account when converting the spectra between time and space. The simulation suggests that, in the presence of gravity waves, the kinetic energy is not evenly distributed between the zonal and meridional winds, rather the wind component along the main wave propagation direction contains larger variance. Copyright © 2011 Royal Meteorological Society

Elasto–plasticity Behavior of IF Steel Sheet with Planar Anisotropy and Its Macro–Meso Modeling

Elasto–plasticity behavior of a IF steel sheet was investigated by performing uniaxial tension tests in three directions (0°, 45° and 90‚ to the rolling direction of the sheet), in-plane cyclic tension–compression test and bi-axial tension test. The sheet has strong planar r-value anisotropy (r0=2.15, r45=2.12 and r90=2.89) but very weak flow stress directionality. Equi-biaxial flow stress is as large as 1.23 times of the uniaxial flow stress. These elasto–plasticity deformation characteristics, as well as the Bauschinger effect and cyclic hardening behavior, are well described by a macro–plasticity model (Yoshida–Uemori model incorpolating with the 4th-order anisotropic yield function). Further, the simulation of elasto–plasticity stress–strain responses of the sheet were conducted by two types of crystal plasticity models, i.e., Taylor hypothesis based model and CPFEM, using the crystallographic orientation distribution data measured by neutron diffraction method. The models capture most of the above-mentioned deformation characteristics qualitatively, but the predicted anisotropy and the Bauschinger effect are weaker than those of the real material. The CPFEM gives more realistic results than the Taylor model.

InSAR atmospheric distortions mitigation: GPS observations and NCEP FNL data

Atmospheric delay variations can cause problems for the interpretation of interferograms. In this paper, we propose a method to mitigate the atmospheric distortions of the interferometric synthetic aperture radar (InSAR) interferogram by integrating GPS observations and operational global analysis data from the National Centers for Environmental Prediction Final (NCEP FNL). Mean wind is extracted from NCEP FNL to implement the Taylor's frozen-flow hypothesis, which increases the density of GPS derived wet delay control points. The results indicate that the integration of GPS observations and NCEP FNL data can effectively identify and mitigate ENVISAT Advanced Synthetic Aperture Radar (ASAR) interferogram atmospheric distortions. Furthermore, it is also shown that it is possible to implement Taylor’s frozen-flow hypothesis and obtain a denser network of wet delay of control points to mitigate the InSAR atmospheric delay.

Stratified Inertial Subrange Inferred from In Situ Measurements in the Bottom Boundary Layer of the Rockall Channel

Abstract Deep-ocean high-resolution moored temperature data are analyzed with a focus on superbuoyant frequencies. A local Taylor hypothesis based on the horizontal velocity averaged over 2 h is used to infer horizontal wavenumber spectra of temperature variance. The inertial subrange extends over fairly low horizontal wavenumbers, typically within 2 × 10−3 and 2 × 10−1 cycles per minute (cpm). It is therefore interpreted as a stratified inertial subrange for most of this wavenumber interval, whereas in some cases the convective inertial subrange is resolved as well. Kinetic energy dissipation rate ε is inferred using theoretical expressions for the stratified inertial subrange. A wide range of values within 10−9 and 4 × 10−7 m2 s−3 is obtained for time periods either dominated by semidiurnal tides or by significant subinertial variability. A scaling for ε that depends on the potential energy within the inertio-gravity waves (IGW) frequency band PEIGW and the buoyancy frequency N is proposed for these two cases. When semidiurnal tides dominate, ε ≃ (PEIGWN)3/2, whereas ε ≃ PEIGWN in the presence of significant subinertial variability. This result is obtained for energy levels ranging from 1 to 30 times the Garrett–Munk energy level and is in contrast with classical finescale parameterization in which ε ∼ (PEIGW)2 that applies far from energy sources. The specificities of the stratified bottom boundary layer, namely a weak stratification, may account for this difference.

Wave vector analysis methods using multi-point measurements

Abstract. Recent developments of multi-point measurements in space provide a means to analyze spacecraft data directly in the wave vector domain. For turbulence study this means that we are able to estimate energy, helicity, and higher order moments in the wave vector domain without assuming Taylor's hypothesis or axisymmetry around the mean magnetic field. The methods of the wave vector analysis are presented and applied to four-point data of Cluster in the solar wind.