The full set of velocity derivatives, $\partial u_{i}/\partial x_{j}$, is measured experimentally in a Lagrangian way in quasi-homogeneous isotropic turbulence. This is achieved by applying the three-dimensional particle tracking velocimetry (3D-PTV) technique to an electromagnetically forced flow with $\hbox{\it Re}_{\lambda}\,{\thickapprox}\,50$. Checks based on precise kinematic relations show that the technique presented measures the velocity derivatives with good accuracy. In a study on vorticity, characteristic properties of turbulent flows known from direct numerical simulations are reproduced. These are the positive skewness of the intermediate eigenvalue of the rate of strain tensor, $s_{ij}$, $\langle \Lambda_{2}\rangle \,{>}\,0$, the predominance of vortex stretching over vortex compression, $\langle \omega_{i}\omega_{j}s_{ij}\rangle \,{>}\,0$ and the predominant alignment of vorticity, ${\bm \omega}$, with the intermediate principal axis of strain, ${\bm \lambda}_{2}$. Results on the evolution in time of material lines, ${\bm l}$, compared to vortex lines, ${\bm \omega}$, are presented. They show that the nonlinear interaction of vorticity with the surrounding flow assists viscosity in maintaining this predominant ${\bm \lambda}_{2}$-alignment of vorticity. Lagrangian measurements of enstrophy budget terms suggest that there is no pointwise balancing of production and viscous reduction of enstrophy and that the role played by viscosity is of great importance.

We present results of experiments on a turbulent grid flow and a few results on measurements in the outer region of a boundary layer over a smooth plate. The air flow measurements included three velocity components and their nine gradients. This was done by a twelve-wire hot-wire probe (3 arrays × 4 wires), produced for this purpose using specially made equipment (micromanipulators and some other auxiliary special equipment), calibration unit and calibration procedure. The probe had no common prongs and the calibration procedure was based on constructing a calibration function for each combination of three wires in each array (total 12) as a three-dimensional Chebishev polynomial of fourth order. A variety of checks were made in order to estimate the reliability of the results.Among the results the most prominent are the experimental confirmation of the strong tendency for alignment between vorticity and the intermediate eigenvector of the rate-of-strain tensor, the positiveness of the total enstrophy-generating term ωiωjsij (sij = ½(∂ui/∂xj+∂uj/∂xi), ωi = εijk∂uj/∂xk) even for rather short records and the tendency for alignment in the strict sense between vorticity and the vortex stretching vector Wi = ωjsij. An emphasis is put on the necessity to measure invariant quantities, i.e. independent of the choice of the system of reference (e.g. sijsij and ωiωjsij) as the most appropriate to describe physical processes. From the methodological point of view the main result is that the multi-hot-wire technique can be successfully used for measurements of all the nine velocity derivatives in turbulent flows, at least at moderate Reynolds numbers.

Annu. Rev. Fluid Mech. 1992.24:281-312. Downloaded from www.annualreviews.org Access provided by University of Toronto Library on 02/06/15. For personal use only. Quick links to online content Further ANNUAL REVIEWS Annu. Rev. Fluid Mech. 1992.24:281-312. Downloaded from www.annualreviews.org Access provided by University of Toronto Library on 02/06/15. For personal use only.

The work reported below is a first of its kind study of the properties of turbulent flow without strong mean shear in a Newtonian fluid in proximity of the turbulent/non-turbulent interface, with emphasis on the small scale aspects. The main tools used are a three-dimensional particle tracking system (3D-PTV) allowing to measure and follow in a Lagrangian manner the field of velocity derivatives and direct numerical simulations (DNS). The comparison of flow properties in the turbulent (A), intermediate (B) and non-turbulent (C) regions in the proximity of the interface allows for direct observation of the key physical processes underlying the entrainment phenomenon. The differences between small scale strain and enstrophy are striking and point to the definite scenario of turbulent entrainment via the viscous forces originating in strain.