Persistence of small-scale anisotropy of magnetic turbulence as observed in the solar wind

The anisotropy of magnetophydrodynamic turbulence is investigated by using solar wind data from the Helios 2 spacecraft. We investigate the behaviour of the complete high-order moment tensors of magnetic field increments and we compare the usual longitudinal structure functions which have both isotropic and anisotropic contributions, to the fully anisotropic contribution. Scaling exponents have been extracted by an interpolation scaling function. Unlike the usual turbulence in fluid flows, small-scale magnetic fluctuations remain anisotropic. We discuss the radial dependence of both anisotropy and intermittency and their relationship.Comment: 7 pages, 2 figures, in press on Europhys. Let

Dynamical equations for high-order structure functions, and a comparison of a mean field theory with experiments in three-dimensional turbulence

Two recent publications [V. Yakhot, Phys. Rev. E {\bf 63}, 026307, (2001) and R.J. Hill, J. Fluid Mech. {\bf 434}, 379, (2001)] derive, through two different approaches that have the Navier-Stokes equations as the common starting point, a set of steady-state dynamic equations for structure functions of arbitrary order in hydrodynamic turbulence. These equations are not closed. Yakhot proposed a "mean field theory" to close the equations for locally isotropic turbulence, and obtained scaling exponents of structure functions and an expression for the tails of the probability density function of transverse velocity increments. At high Reynolds numbers, we present some relevant experimental data on pressure and dissipation terms that are needed to provide closure, as well as on aspects predicted by the theory. Comparison between the theory and the data shows varying levels of agreement, and reveals gaps inherent to the implementation of the theory.Comment: 16 pages, 23 figure

The Scaling Structure of the Velocity Statistics in Atmospheric Boundary Layer

The statistical objects characterizing turbulence in real turbulent flows differ from those of the ideal homogeneous isotropic model.They containcontributions from various 2d and 3d aspects, and from the superposition ofinhomogeneous and anisotropic contributions. We employ the recently introduceddecomposition of statistical tensor objects into irreducible representations of theSO(3) symmetry group (characterized by $j$ and $m$ indices), to disentangle someof these contributions, separating the universal and the asymptotic from the specific aspects of the flow. The different $j$ contributions transform differently under rotations and so form a complete basis in which to represent the tensor objects under study. The experimental data arerecorded with hot-wire probes placed at various heights in the atmospheric surfacelayer. Time series data from single probes and from pairs of probes are analyzed to compute the amplitudes and exponents of different contributions to the second order statistical objects characterized by $j=0$, $j=1$ and $j=2$. The analysis shows the need to make a careful distinction between long-lived quasi 2d turbulent motions (close to the ground) and relatively short-lived 3d motions. We demonstrate that the leading scaling exponents in the three leading sectors ($j = 0, 1, 2$) appear to be different butuniversal, independent of the positions of the probe, and the large scaleproperties. The measured values of the exponent are $\zeta^{(j=0)}_2=0.68 \pm 0.01$, $\zeta^{(j=1)}_2=1.0\pm 0.15$ and $\zeta^{(j=2)}_2=1.38 \pm 0.10$. We present theoretical arguments for the values of these exponents usingthe Clebsch representation of the Euler equations; neglecting anomalous corrections, the values obtained are 2/3, 1 and 4/3 respectively.Comment: PRE, submitted. RevTex, 38 pages, 8 figures included . Online (HTML) version of this paper is avaliable at http://lvov.weizmann.ac.il

Yakhot's model of strong turbulence: A generalization of scaling models of turbulence

We report on some implications of the theory of turbulence developed by V. Yakhot [V. Yakhot, Phys. Rev. E {\bf 57}(2) (1998)]. In particular we focus on the expression for the scaling exponents $\zeta_{n}$. We show that Yakhot's result contains three well known scaling models as special cases, namely K41, K62 and the theory by V. L'vov and I. Procaccia [V. L'vov & I. Procaccia, Phys. Rev. E {\bf 62}(6) (2000)]. The model furthermore yields a theoretical justification for the method of extended self--similarity (ESS).Comment: 8 page

Remote sensing data acquisition, platforms and sensor requirements

Although data available from various earth observation systems have been routinely used in many resource applications, however there have been gaps, and data needs of applications at different levels of details have not been met. There is a growing demand for availability of data at higher repetivity, at higher spatial resolution, in more and narrower spectral bands etc. Some of the thrust areas of applications particularly in the Indian context are; - Management of natural resources to ensure sustainable increase in agricultural production, - Study the state of the environment, its monitoring and assessment of the impact of. various development actions on the environment, - Updating and generation of large scale topographical maps. - Exploration/exploitation of marine and mineral resources and - Operational meteorology and studying various land and oceanic processes to understand/predict global climate changes. Each of these thrust area of application has many components, related to basic resource areas such as agriculture, forestry, water resources, minerals, marine resources etc. and the field of cartography. Observational requirements for major applications have been summarized as under. Monitoring vegetation health from space remains the most important observational parameter with applications, in agriculture, forestry, environment, hydrology etc. Vegetation extent, quantity and temporal changes are the three main requirements which are not fully realized with RS data available. Vegetation productivity, forest biomass, canopy moisture status, canopy biogeochemistry are some examples. Crop production forecasting is an important application area. Remotely sensed data has been used for identification of crops and their acreage estimation. Fragmented holdings, large spread in crop calendars and different management practices continue to pose a challenge lo remote sensing. Remotely sensed data at much higher spatial resolution than hitherto available as well as at greater repetivity are required to meet this need. Non-availability of cloud-free data in the kharif season is one of the serious problems in operational use of remote sensing for crop inventory. Synthetic aperture radar data al X & Ku bands is necessary to meet this demand. Nutrient stress/disease detection requires observations in narrow spectral bands. In case of forestry applications, multispectral data at high spatial resolution of the order of 5 to 10 metres is required to make working plans at forest compartment level. Observations from space for deriving tree height are required for volume estimation. Observations in the middle infrared region would greatly enhance capability of satellite remote sensing in forest fire detection. Temporal, spatial and spectral observational requirements in various applications on vegetation viewing are diverse, as they address processes at different spatial and time scales. Hence, it would be worthwhile to address this issue in three broad categories. a) Full coverage, moderate spatial resolution with high repetivity (drought, large scale deforestation, forest phenology....). b) Full coverage, moderate to high spatial resolution and high repetivity (crop forecasting, vegetation productivity). c) Selected viewing at high spatial resolution, moderate to high repetivity and with new dimensions to imaging (narrow spectral bands, different viewing angles). A host of agrometeorological parameters are needed to be measured from space for their effective use in development of yield models. Estimation of root-zone soil moisture is an important area requiring radar measurements from space. Surface meteorological observations from space at the desired spatial and temporal distributions has not developed because of heavy demands placed on the sensor as well as analytical operational models. Agrometeorology not only provides quantitative inputs to other applications such as crop forecasting, hydrological models but also could be used for farmer advisory services by local bodies. Mineral exploration requires information on geological structures, geomorphology and lithology. Surface manifestation over localized regions requires large scale mapping while the lithology can be deciphered from specific narrow bands in visible. NIR, MIR and TIR regions. Sensors identified for mapping/cartography in conjunction with imaging spectrometer would seem to cover requirements of this application. Narrow spectral bands in the short regions which provide diagnostics of relevant geological phenomenon are necessary for mineral exploration. Thermal inertia measurements help in better discrimination of different rock units. Measurements from synthetic aperture data which would provide information on geological structures and geomorphology are necessary for mineral exploration. The applications related to marine environment fall in three major areas: (i) Ocean colour and productivity, biological resources; (ii) Land-ocean interface, this includes coastal landforms, bathymetry, littoral transport processes, etc. and; (iii) Physical oceanography, sea surface temperature, winds, wave spectra, energy and mass exchange between atmosphere and ocean. Measurement of chlorophyll concentration accurately on daily basis, sea surface temperature with an accuracy of 0.5 °K. and information on current patterns arc required for developing better fishery forecast models. Improved spatial resolution data are desirable for studying sediment and other coastal processes. Cartography is another important application area. The major problems encountered in relation to topographic map updation are location and geometric accuracy and information content. Two most important requirements for such an application are high spatial resolution data of 1 to 2 metre and stereo capability to provide vertical resolution of 1 metre. This requirement places stringent demands on the sensor specifications, geometric processing, platform stability and automated digital cartography. The requirements for the future earth observation systems based on different application needs can be summarized as follows: • Moderate spatial resolution (l50-300m), high repetivity (2 Days), minimum set of spectral bands (VIS, NIR, MIR. TIR) full coverage. • Moderate to high spatial resolution (20-40m), high repetivity (4-6 Days), spectral bands (VIS, MR, MIR, TIR) full coverage. • High spatial resolution (5-10m) muitispectral data with provision for selecting specific narrow bands (VIS, N1R. MIR), viewing from different angles. • Synthetic aperture radar operating in at least two frequencies (C, X, Ku), two incidence angles/polarizations, moderate to high spatial resolution (20-40m), high repetivity (4-6 Days). • Very high spatial resolution (1-2m) data in panchromatic band to provide terrain details at cadastral level (1:10,000). • Stereo capability (1-2m height resolution) to help planning/execution of development plans. • Moderate resolution sensor operating in VIS, NIR, MIR on a geostationary platform for observations at different sun angles necessary for the development of canopy reflectance inversion models. • Diurnal (at least two i.e. pre-dawn and noon) temperature measurements of the earth surface. • Ocean colour monitor with daily coverage. • Multi-frequency microwave radiometer, scatterometer. altimeter, atmospheric sounder, etc

Universal behaviour of entrainment due to coherent structures in turbulent shear flow

I suggest a solution to a persistent mystery in the physics of turbulent shear flows: cumulus clouds rise to towering heights, practically without entraining the ambient medium, while apparently similar turbulent jets in general lose their identity within a small distance through entrainment and mixing. From dynamical systems computations on a model chaotic vortical flow, I show that entrainment and mixing due to coherent structures depend sensitively on the relative speeds of different portions of the flow. A small change in these speeds, effected for example by heating, drastically alters the sizes of the KAM tori and the chaotic mixing region. The entrainment rate and, hence, the lifetime of a turbulent shear flow, shows a universal, non-monotone dependence on the heating.Comment: Preprint replaced in order to add the following comment: accepted for publication in Phys. Rev. Let

Strong Universality in Forced and Decaying Turbulence

The weak version of universality in turbulence refers to the independence of the scaling exponents of the $n$th order strcuture functions from the statistics of the forcing. The strong version includes universality of the coefficients of the structure functions in the isotropic sector, once normalized by the mean energy flux. We demonstrate that shell models of turbulence exhibit strong universality for both forced and decaying turbulence. The exponents {\em and} the normalized coefficients are time independent in decaying turbulence, forcing independent in forced turbulence, and equal for decaying and forced turbulence. We conjecture that this is also the case for Navier-Stokes turbulence.Comment: RevTex 4, 10 pages, 5 Figures (included), 1 Table; PRE, submitte

Hyperviscosity, Galerkin truncation and bottlenecks in turbulence

It is shown that the use of a high power $\alpha$ of the Laplacian in the dissipative term of hydrodynamical equations leads asymptotically to truncated inviscid \textit{conservative} dynamics with a finite range of spatial Fourier modes. Those at large wavenumbers thermalize, whereas modes at small wavenumbers obey ordinary viscous dynamics [C. Cichowlas et al. Phys. Rev. Lett. 95, 264502 (2005)]. The energy bottleneck observed for finite $\alpha$ may be interpreted as incomplete thermalization. Artifacts arising from models with $\alpha > 1$ are discussed.Comment: 4 pages, 2 figures, Phys. Rev. Lett. in pres

Turbulence anisotropy and the SO(3) description

We study strongly turbulent windtunnel flows with controlled anisotropy. Using a recent formalism based on angular momentum and the irreducible representations of the SO(3) rotation group, we attempt to extract this anisotropy from the angular dependence of second-order structure functions. Our instrumentation allows a measurement of both the separation and the angle dependence of the structure function. In axisymmetric turbulence which has a weak anisotropy, this more extended information produces ambiguous results. In more strongly anisotropic shear turbulence, the SO(3) description enables one to find the anisotropy scaling exponent. The key quality of the SO(3) description is that structure functions are a mixture of algebraic functions of the scale with exponents ordered such that the contribution of anisotropies diminishes at small scales. However, we find that in third-order structure functions of homogeneous shear turbulence the anisotropic contribution is always large and of the same order of magnitude as the isotropic part. Our results concern the minimum instrumentation needed to determine the parameters of the SO(3) description, and raise several questions about its ability to describe the angle dependence of high-order structure functions