Taylor Transformation Research Articles

Spatial distribution of four freshwater gastropod species in a ditch near Orsay, France

The distribution (both specific and individual) of four pulmonate gastropods was studied in a ditch near Orsay, France, from April 1987 to August 1988. Physa fontinalis L. and Anisus albus (Muller) were restricted to the part of the ditch which never dries up and positively associated with the hydrophytes Ceratophyllum submersum L. and Callitriche hamulata Kuntz. On the other hand, Anisus rotundatus (Poiret), which is drought resistant, was abundant in the shallowest part of the ditch and was positively associated with helophytes while Lymnaea palustris (Muller) was ubiquitous and present throughout the ditch. Plant morphology appears to be a major factor determining snail-plant relationships. Within their respective habitats, each species presented an aggregated distribution; their variances were stabilized by logarithmic transformation for L. palustris, Downing's transformation for P. fontinalis and Taylor's transformation for the two remaining species.

Taylor transformation of 2D NMR τm series from time dimension to polynomial dimension

Taylor transformation of 2D NMR τm series from time dimension to polynomial dimension

Analysis and parameter identification of scaled systems via polynomial series

The scaled Taylor operational and transformation matrices of polynomial series are introduced for analysing and approximating the solution of the functional differential equation of a scaled system with a constant scale. The parameter identification problem of the scaled system is also tackled. Illustrative examples with satisfactory results are given. The results are in accordance with exact solutions.

Theoretical Interpretation of Atmospheric Wavenumber Spectra of Wind and Temperature Observed by Commercial Aircraft During GASP

Abstract This paper contains a theoretical interpretation of the wavenumber spectra of wind and temperature obtained from an analysis of data from over 6900 flights during the Global Atmospheric Sampling Program. The spectra cover scales ranging from 3 km to nearly 10 000 km. Major features of the observed spectra are found to be in general agreement with expectations from theoretical models of quasi two-dimensional turbulence. Kinetic energy spectra are remarkably universal, and temperature spectra adjust as required for equipartition between the two horizontal components of kinetic energy and potential energy. The observed wavenumber spectra agree closely in magnitude and shape with frequency spectra obtained independently, and this agreement supports the validity of the Taylor transformation; conversely, because the Taylor transformation works, it suggests the disturbances are turbulence rather than dispersive waves. The GASP spectra are compared in a general way with recently proposed internal wave sp...

Variance spectra of observed winds and initialized wind fields at the 500 mblevel over europe

AbstractTwo‐dimensional scale (variance spectrum) analyses were made of the wind field at 500 mb over Europe and western Asia. Seven separate 20‐ to 30‐day periods, four in winter and three in summer, were investigated. On all occasions actual unmodified measured winds were used; on two of them the same techniques were applied to the interpolated and initialized data on a regular grid used by the National Weather Service in prognostic models. Standard analytical spectral analysis cannot be used on the unmodified observations; the method used involved iterative adjustment of a first guess spectrum to fit calculated variance and covariance functions.Some conclusions are: Our examination of the data does not unambiguously establish an ‘inertial range’ in the spectrum. the Taylor transformation of frequency to wavenumber is not reliable at scales more than about 1000 km. There are significant diurnal changes; in the summer periods they are not confined to the small unresolved scales.The Weather Service initialization‐interpolation procedure quantitatively removes variance at less than twice the grid scale, but also affects the spectrum in the resolved scales to a degree which might be significant in prognostic models.On two occasions there was evidence of widespread and persistent variance on a scale of about 350 km.

Low frequency two dimensional flows through a sparse array of bodies

A low frequency and weak interaction theory is developed to study certain types of unsteady two-dimensional flows through an array of bodies. The results, together with the Taylor transformation, provide a simple and systematic yet powerful technique for obtaining solutions for an important, but otherwise extremely difficult, class of problems. The general results are applied to two specific examples in order to illustrate the approach and to produce some interesting results.

Turbulence Spectra in the Upper Troposphere and Lower Stratosphere at Periods Between 2 Hours and 40 Days

Abstract Zonal and meridional wind measurements made with the Poker Flat MST radar over a 40-day period are used to calculate the frequency power spectra at heights between 5.99 and 14.69 km. The winds used in the analysis are 1 h averages of samples taken every 4 min. We find that the spectra follow an f−5/3 power law in the range of periods from 2 to 50 h. If the Taylor transformation is valid in this frequency range, this would imply a k−5/3 wavenumber spectrum, corresponding to an inertial subrange for two-dimensional turbulence at the atmospheric mesoscale. These observations support and extend earlier studies which also show a −5/3 power law behavior in the atmospheric mesoscale.

The Variance Spectrum of Tropospheric Winds over Eastern Europe

Daily values of the 500 mb wind at 72 radiosonde stations in eastern Europe during July 1966 are analyzed. Variance is extracted for groups of contiguous stations occupying increasingly large areas, and for the whole set of stations over increasing time periods. Covariance over the month is computed for all possible station pairs as a function of length and direction of the separation vector and for observations at the same station as a function of separation in time. Efforts to extract variance spectra by direct inversion or transformation of these statistics fail, and they are, therefore, compared with those appropriate to several hypothetical variance spectra. In the spatial-scale range 500–2500 km, the data are consistent with a k5/3 spectrum which implies a dissipation rate of 1.5–2 ergs g−1, if interpreted as an energy-cascading inertial range. More variance is associated with this scale range than can reasonably he explained on the hypothesis of a k−3 spectrum. Within this scale range, spatial and temporal statistics are found to transform linearly by application of a mean wind speed (Taylor transformation). All results are compatible with an analysis, previously published by other authors, of a 2 h series of observations taken over the same month at a single station central to the group of 72. Because the analysis differs in some important respects from that used by previous workers, particularly in the use of transforms appropriate to a two-dimensional vector field, elementary derivations are given of the methods used.