A series of LDA measurements and visual observations of confined turbulent vortex flow are described. The experiments were performed with water as the fluid medium in a vortex tube of length-to-diameter ratio L/D = 3.8 for a range of exit diameters De between De/D = 1 and 0.18. The experiments reveal a remarkable change in the vortex structure as De is reduced: from a thick core with an axial-velocity defect in the centre, and even reversed flow, to a thin annular jet-like core with a peak axial velocity more than an order of magnitude greater than the average value and again a central velocity deficit. The corresponding swirl profiles are not remarkable and are well-represented under all conditions by the solution of Burgers (1948), albeit with a velocity maximum which is strongly dependent upon De.

In this paper we find conditions which guarantee that a given flow $\Phi$ on a compact metric space X admits a Lyapunov 1-form $\omega$ lying in a prescribed Čech cohomology class $\xi\in\check H^1(X;\mathbb{R})$. These conditions are formulated in terms of the restriction of $\xi$ to the chain recurrent set of $\Phi$. The result of the paper may be viewed as a generalization of a well-known theorem by Conley about the existence of Lyapunov functions.

We studied on a nanometer scale the tribological properties of thin silicon carbide films on Si(100) wafers and stainless steel. The coatings were fabricated from a sintered SiC target by pulsed ArF laser deposition at substrate temperatures between 20 °C and 1000 °C. Amorphous films resulted at low deposition temperatures while nanocrystalline structures developed at high deposition temperatures. An atomic force/lateral force microscope was employed to characterize the film topography and the friction behavior. The microhardness was determined from measurements utilizing a depth-sensing nanoindentation instrument. The SiC films on Si(100) exhibit a smooth surface with an average roughness Ra of a few nanometer, the amorphous films being even an order of magnitude smoother. No appreciable differences were found in microhardness and friction coefficient between amorphous and nanocrystalline films. On stainless steel, amorphous SiC coatings were obtained for deposition temperatures up to 500 °C. Their surface relief portrayed the grain boundaries of the underlying steel substrate, reflecting the ballistic nature of the deposition process. No stoichiometric films were obtained above 500 °C as the silicon from the growing film quickly dissolved in the steel substrate.