We report first results of an experiment in which explicit information is obtained on the field of velocity derivatives (all the nine components of the tensor ∂ui/∂xj) along with all the three components of velocity fluctuations at Reynolds number as high as Reλ∼104. This includes information on such basic processes as enstrophy and strain production, geometrical statistics, the role of concentrated vorticity and strain, and the reduction of nonlinearity.

This is a report on a field experiment in an atmospheric surface layer at heights between 0.8 and 10 m with the Taylor micro-scale Reynolds number in the range Re λ = 1.6 − 6.6 × 10 3 . Explicit information is obtained on the full set of velocity and temperature derivatives both spatial and temporal, i.e. no use of Taylor hypothesis is made. The report consists of three parts. Part 1 is devoted to the description of facilities, methods and some general results. Certain results are similar to those reported before and give us confidence in both old and new data, since this is the first repetition of this kind of experiment at better data quality. Other results were not obtained before, the typical example being the so-called tear-drop R − Q plot and several others. Part 2 concerns accelerations and related matters. Part 3 is devoted to issues concerning temperature, with the emphasis on joint statistics of temperature and velocity derivatives. The results obtained in this work are similar to those obtained in experiments in laboratory turbulent grid flow and in direct numerical simulations of Navier-Stokes equations at much smaller Reynolds numbers Re λ ∼ 10 2 , and this similarity is not only qualitative, but to a large extent quantitative. This is true of such basic processes as enstrophy and strain production, geometrical statistics, the role of concentrated vorticity and strain, reduction of nonlinearity and non-local effects. The present experiments went far beyond the previous ones in two main respects. (i) All the data were obtained without invoking the Taylor hypothesis, and therefore a variety of results on fluid particle accelerations became possible. (ii) Simultaneous measurements of temperature and its gradients with the emphasis on joint statistics of temperature and velocity derivatives. These are reported in Parts 2 and 3.

We report the first results of an experiment, in which explicit information on all velocity derivatives (the nine spatial derivatives, ∂u i /∂x j , and the three temporal derivatives, ∂u i /∂t) along with the three components of velocity fluctuations at a Reynolds number as high as Re λ ∼ 10 4 is obtained. No use of the Taylor hypothesis was made, and this allowed us to obtain a variety of results concerning acceleration and its different Eulerian components along with vorticity, strain and other smallscale quantities. The field experiments were performed at five heights between 0.8 and 10 m above the ground.The report consists of three parts. Part 1 is devoted to the description of facilities, methods and some general results. Part 2 concerns accelerations and related matters. Part 3 is devoted to the issues concerning temperature with the emphasis on joint statistics of temperature and velocity derivatives. Introductory notesAs the material derivative of the velocity vector, the fluid particle acceleration field in turbulent flow is among the natural physical parameters of special interest in turbulence research for a variety of reasons. Problems in which fluid particle acceleration plays a key role range from studies of basic issues such as finescale intermittency, production of Reynolds stresses, the so-called random Taylor hypothesis and two-phase turbulent flows to applications in turbulent mixing and transport, cloud physics and influence of turbulence on the behaviour of insects. In particular, Lagrangian acceleration statistics are at the core of the kinematic theory and modelling of turbulent dispersion, mixing, particulate transport and combustion. Finally, the acceleration gradient tensor is known to govern the topology of quasi-geostrophic stirring (particle dispersion and tracer gradient evolution) and transport properties in nearly two-dimensional and geostrophic turbulence (Yeung

This is part 3 of our work describing experiments in which explicit information was obtained on all the derivatives, i.e. spatial derivatives, ∂/∂x j , and temporal derivatives, ∂/∂t, of velocity and temperature fields (and all the components of velocity fluctuations and temperature) at the Reynolds number Re λ ∼ 10 4 .This part is devoted to the issues concerning temperature with the emphasis on joint statistics of temperature and velocity derivatives, based on preliminary results from a jet facility and the main results from a field experiment. Apart from a number of conventional results, these contain a variety of results concerning production of temperature gradients, such as role of vorticity and strain, eigencontributions, geometrical statistics such as alignments of the temperature gradient and the eigenframe of the rate-of-strain tensor, tilting of the temperature gradient, comparison of the true production of the temperature gradient with its surrogate. Among the specific results of importance is the essential difference in the behaviour of the production of temperature gradients in regions dominated by vorticity and strain. Namely, the production of temperature gradients is much more intensive in regions dominated by strain, whereas production of temperature gradients is practically independent of the magnitude of vorticity. In contrast, vorticity and strain are contributing equally to the tilting of the vector of temperature gradients.The production of temperature gradients is mainly due to the fluctuative strain, the terms associated with mean fields are unimportant. It was checked directly (by looking at corresponding eigen-contributions and alignments), that the production of the temperature gradients is due to predominant compressing of fluid elements rather than stretching, which is true of other processes in turbulent flows, e.g. turbulent energy production in shear flows. Though the production of the temperature gradient and its surrogate possess similar univariate PDFs (which indicates the tendency to isotropy in small scales by this particular criterion), their joint PDF is not close to a bisector. This means that the true production of the temperature gradient is far from being fully represented by its surrogate. The main technical achievement is demonstrating the possibility of obtaining experimentally joint statistics of velocity and temperature gradients.

We report results of experiments at large Reynolds numbers, confirming the equivalent form of the Kolmogorov 4 / 5 law obtained recently by Hosokawa ͓Prog. Theor. Phys. 118, 169 ͑2007͔͒. This, as well as purely kinematic exact relations, demonstrates one of the important aspects of nonlocality of turbulent flows in the inertial range and stands in contradiction with the sweeping decorrelation hypothesis understood as statistical independence between large and small scales. This letter is provoked by a short paper by Hosokawa 1 concerned mainly with the issues of refined similarity hypothesis. A starting point in his paper is that it is proven that the famous third-order structure function of the velocity in homogeneous isotropic turbulence derived by Kolmogorov implies the statistical interdependence of the difference and sum of the velocities at two points separated by a distance r. 1 In other words, contrary to frequent claims on locality of interactions and similar things, the 4 / 5 law points to an important aspect of nonlocality of turbulent flows understood as direct and bidirectional interaction of large and small scales. 2,3 Before proceeding, we quote the key relations obtained by Hosokawa.The first relation, the most important and equivalent ͑un-der the same assumptions of global isotropy͒ to the 4 / 5 law, reads ͗u + 2 u − ͘ = ͗⑀͘r/30. ͑1͒Here 2u + = u 1 ͑x + r͒ + u 1 ͑x͒, 2u − = u 1 ͑x + r͒ − u 1 ͑x͒; u 1 ͑x͒ is the longitudinal velocity component ͑in our case it will be just the streamwise velocity component͒ and ͗⑀͘ is the mean dissipation. It is noteworthy that though Eq. ͑1͒ contains velocity and not just its increments, it is readily checked that it is still Galilean invariant. We would like to emphasize that the relation ͑1͒-though formally equivalent to the Kolmogorov 4 / 5 law-has an important advantage from purely experimental point of view. Namely, it is linear in velocity increment u − , whereas the 4 / 5 law is cubic in u − . Therefore, the precision requirements for the verification of the relation ͑1͒ are far less stringent than those for the 4 / 5 law. We will return to this point below.The relation ͑1͒ is a consequence of the 4 / 5 law and a purely kinematic relation which is valid under isotropy assumptionwhich is a clear indication of the absence of statistical independence between u + and u − , i.e., between small and large scales.A similar purely kinematic relation is valid for secondorder quantities, 1Thus this is also-as stated by Hosokawa 1 -an elementary signature indicating the necessary statistical relationship between u + and u − , i.e., reflecting the nonlocality even at the level of second-order quantities. One more kinematic relation of third order was obtained by Sabelnikov in 1994,along with another set of kinematic relations involving a one-point quantity u 1 ͑x͒ ͓or u 1 ͑x + r͔͒ instead of u + , which is a two-point quantity. 5 The main purpose of this note is to present direct experimental evidence for the validity of the above relations ͑1͒-͑4͒ at very large Rey...