ALBERT

Notes: The scattering of high vibrationally excited sodium molecules Na2(v=31) with Ne atoms at 180 meV collision energy is investigated in a crossed molecular beam arrangement using laser optical methods. Angularly resolved rotationally inelastic and vibrationally elastic cross sections ji→jf are measured for ji =5, 7, and 9≤jf ≤25. Pronounced rotational rainbow maxima are observed, the angular position of which indicates a significantly larger anisotropy of the interaction potential compared to that of Na2(v=0)–Ne. Except for the increase of the anisotropy the vibrational excitation has little effect on the dynamics of rotational energy transfer. Good agreement with a new semiempirical Na2–Ne potential surface V(r,R,γ) is found.

Notes: The orientational order–disorder and melting transition temperatures for quasi two-dimensional islands of N2 molecules deposited on graphite are calculated for sizes 1≤N≤256 molecules, using a Monte Carlo procedure with free surface boundary conditions. These transition temperatures are strong functions of N, and the values for 256 molecules are close to those measured experimentally for fractional macroscopic monolayers. Calculated results show that the two sublattice herringbone orientational structure persists up to the orientational transition temperature, above which hindered planar rotation occurs. The registered (square root of)3×(square root of)3 mass center structure exists until melting, where the islands disassociate. These features are consistent with experiment. Below melting, the root mean square fluctuations of the mass centers away from their (square root of)3×(square root of)3 equilibrium values are substantially larger than for bulk N2 or for small three-dimensional rare gas clusters. The fluctuations are also substantially larger for edge molecules than for those in the center.

Notes: Oscillations in the chattering region in plots of final action and collision time as a function of the initial vibrational phase of the diatom in collinear He+H+2(ni=0) collisions are shown to have characteristics of fractals with a capacity dimension 1.38–1.68 over a wide range of translational energies. For energies above the reaction threshold, the fractal zones are shown to occur between reactive and nonreactive bands and are related to known quantal reactive scattering resonances.

Notes: The properties of F2 monolayers on graphite are calculated using both a constant pressure and constant density Monte Carlo procedure with deformable periodic boundary conditions. A wide range of thermodynamic quantities and order parameters are determined over the temperature range 0≤T≤35 K. The ground state is found to be an incommensurate, centered rectangular structure with molecules oriented in the plane of the substrate in a herringbone arrangement. At T=19 K, a phase change occurs into a triangular structure, accompanied by an orientational transition. Details of the phases and the transition are given.

Notes: The structural features of turbulence at the free surface of a channel flow have been experimentally investigated. The experiments were conducted in a horizontal channel of large aspect ratio in the (depth based) Reynolds number range of 2800–8800. The results indicate that the persistent structures on the free surface can be classified as upwellings, downdrafts, and spiral eddies. Upwellings are shown to be related to the bursts originating in the sheared region at the channel bottom and the eddies are seen to be generated at the edges of the upwellings. The eddies often merge if rotating in the same direction, and form "pairs" if rotating in opposite directions—though there are occasional mergers of such counter-rotating ones. The spiral eddies decay slowly and are sometimes annihilated by fresh upwellings. The population densities and the persistence times of the various structures were measured for different flow conditions. The resulting data show that the physical parameters characterizing the structures at the interface, scale with a mix of inner (wall shear stress and viscosity) and outer variables. Measurement of the streamwise and spanwise velocities at the free-surface were made by particle imaging velocimetry (PIV) and the surface normal velocity near the free-surface estimated by continuity. The results indicate that the upwellings and spiral eddy regions would be expected to dominate scalar transport rates at high Prandtl/Schmidt numbers. The one-dimensional energy spectra of the flow field at the free-surface compare well with direct numerical simulations and show a region with −5/3 slope at low wave numbers. This experimentally confirms a previous result regarding the two-dimensionality of turbulence near the free surface, based on numerical simulations by Pan and Banerjee [Phys. Fluids 7, 1649 (1995)]. © 1998 American Institute of Physics.

Notes: A method for particle image velocimetry (PIV) is presented which improves upon the accuracy, computational efficiency and dynamic range (i.e., the difference between the largest and smallest resolvable particle displacement vectors) of conventional PIV techniques. The technique is applied to free-surface turbulence to resolve energy spectra for motions with a wide dynamic range. The methodology—based on multi-grid image processing algorithms for rigid body motion analysis, estimates the displacement vectors at discrete particle locations. The essence of this technique is to estimate large scale motions from image intensity patterns of low spatial frequencies and small scale motions from intensity patterns of high spatial frequencies. Cross-correlation between a pair of time separated particle images is implemented by the hierarchical computational scheme of Burt ["Fast filter transforms for image processing," Int. J. Comput. Vision 16, 20 (1981)]. Each image is convolved with a series of band-pass filters and subsampled to obtain a set of images progressively decreasing in resolution and size. A coarse estimate of the displacement field obtained from pairs of lower resolution images are used to obtain more accurate estimates at the next (finer) level. Processing starts at the level of lowest resolution and stops at the highest resolution level, which contains the original image pair. Due to subsampling of low resolution images, the match template size can be kept constant for all stages of computation, thus eliminating the dependence of the largest resolvable displacement on the size of match template. In the present work, the search area at each level is kept constant at 3×3 pixels and the match template size at 5×5 pixels for all levels of computation. The algorithm has been implemented using simple thresholding based on the confidence level of an estimated displacement vector, as suggested by Anandan ["A computational framework and an algorithm for measurement of visual motion," Int. J. Comput. Vision, 2, 283, (1987)]. However, the confidence-level-based smoothing technique for rigid body motions (continuous velocity fields) could not be applied to displacement estimates obtained at discrete points i.e., the particle locations. Instead, smoothing was performed over the area covered by each particle. The algorithm has been tested against direct numerical simulations of turbulent flows when the flow field is known and particle images have been generated from these with the addition of noise. Both the accuracy of motion estimation and the computation time are seen to improve as compared to conventional PIV methods. Finally, video images taken of particle motion on the free-surface of a channel flow have been used to determine the capabilities of the technique in an experimental study. The resulting spectra show a quasi-two-dimensional character of the free-surface turbulent flow field, which corresponds well with the direct numerical simulations. © 1998 American Institute of Physics.