S. T. Thoroddsen

Evolution of the fingering pattern of an impacting drop

The impact of a drop on a solid surface generates a rapidly expanding thin jet traveling along the surface. We study the evolution of the fingering pattern at the edge of this jet during the impact of a water drop on a glass plate. Multiple-flash photography shows that systematic changes in frontal shapes take place during the expansion. The initial fingers widen and split in two. This splitting is in many cases limited to the development of a double peak on each finger. The subsequent interaction of two such adjacent undulations often results in merging which produces three pronounced fingers. Despite the significant changes in the frontal shapes, the number of fundamental undulations remains approximately constant during the expansion. The progenitors of these azimuthal disturbances are observed right at first contact. Some heuristic arguments based on capillary waves are put forth to explain the splitting and merging. The main focus of this study is on impacts having Reynolds numbers of about 15 000, b...

The coalescence cascade of a drop

When a drop is deposited gently onto the surface of a layer of the same liquid, it sits momentarily before coalescing into the bottom layer. High-speed video imaging reveals that the coalescence process is not instantaneous, but rather takes place in a cascade where each step generates a smaller drop. This cascade is self-similar and we have observed up to six steps. The time associated with each partial coalescence scales with the surface tension time scale. The cascade will, however, not proceed ad infinitum due to viscous effects, as the Reynolds number of the process is proportional to the square root of the drop diameter. Viscous effects will therefore begin to be important for the very smallest drops. This cascade is very similar to the one observed previously by Charles and Mason [J. Colloid Sci. 15, 105 (1960)] for two immiscible liquids, where one of the liquids replaces the air in our setup.

SCALING OF THE FINGERING PATTERN OF AN IMPACTING DROP

We have studied experimentally the fingered splatter left behind after a liquid drop impacts a solid surface at high values of the Reynolds and Weber numbers. The viscosity and surface tension of the liquid was varied by using several different fluid mixtures. The surface chosen was a thick paper sheet, on which the drop left a clear signature of the impact pattern. The maximum spreading of the fluid and the number of fingers seem to scale with an Impact Reynolds number, U(π2ρD3/16σ)1/4/ν1/2, where U is the impact velocity, ν the kinematic viscosity of the fluid, ρ the fluid density, σ the surface tension and D the drop diameter. The number of fingers is weakly dependent on the surface tension and depends primarily on the inertial‐viscous interaction.

Experimental evidence supporting Kolmogorov’s refined similarity hypothesis

In a recent Letter, Hosokawa and Yamamoto [Phys. Fluids A 3, 457 (1992)] have provided evidence against Kolmogorov’s refined similarity hypothesis based on the results of direct numerical simulations of isotropic turbulence [J. Phys. Soc. Jpn. 60, 1852 (1991)] with Reλ close to 100. Here experimental results are presented from a wind‐tunnel study of a cylinder wake, at Reλ of 550, which in spirit confirm the hypothesis, especially for the smaller scales in the inertial range. The present experimental velocity spectra contain one and one‐half decades of inertial range. The apparent basic disagreement between the numerical simulations and the experiments may be due to the difference in Reλ, or may be symptomatic of a more subtle problem.

The influence of stable stratification on small‐scale anisotropy and dissipation in turbulence

Small-scale turbulence measurements in stably stratified grid-generated turbulence show that strong stable stratification induces large anisotropies in the mean-square strain rates ∂v/∂x and ∂w/∂x, relative to ∂u/∂x. This effect is magnified with increased strength of stratification. Froude number scaling is partially successful in collapsing the data. Anisotropies of the strain rates associated with the small scales are found to develop relatively faster than the anisotropy of the large-scale energy containing eddies. The mean-square magnitude of the ∂w/∂x strain rate is up to 4 times lower than the level predicted from ∂u/∂x based on isotropy. These results cast doubt on the accuracy of employing conventional dissipation estimates based on the assumption of local isotropy in stratified turbulence, at least for the low Reynolds numbers characterizing these experiments. These results are especially relevant to ocean microscale measurements, as buoyancy affected turbulence with similar dynamical character, i.e., e/νN2 of similar magnitudes, has been observed in the thermocline (see Gregg and Sanford, 1988; Yamazaki, 1990). Estimates of dissipation rates based on the formulations of Stillinger et al. (1983) and Yamazaki and Osborn (1990) are shown to disagree by as large as a factor of 2. The measurements also show that stable stratification induces anisotropy in the lateral horizontal rms velocity component in addition to the well-known vertical anisotropy. The lateral anisotropy is about half of the vertical anisotropy. Measured spectral relations between the stream wise and lateral velocity components in the horizontal plane were compared with relations predicted by the two- and three-dimensional (2-D and 3-D) isotropic theories. Comparison of measured and calculated lateral spectra indicate no tendency toward the development of 2-D turbulence in the range of Froude numbers studied.

Reevaluation of the experimental support for the Kolmogorov refined similarity hypothesis

Experiments in high Reynolds number turbulence call into question the experimental verification of Kolmogorov’s refined similarity hypothesis. Previous experimental support for the hypothesis is shown to be distorted by the severe simplifications used in estimating the turbulence energy dissipation, which has invariably been based only on the streamwise gradient of the streamwise velocity component. However, when the dissipation is estimated by the streamwise gradient of a transverse velocity component the dependence between ‖Δur‖ and (rer*)1/3 all but disappears. These results suggest that previous experimental support for the hypothesis may have been premature.

Qualitative flow visualization using colored lights and reflective flakes

We present a novel flow-visualization technique utilizing reflective flakes in combination with color illumination. Three differently colored columated light beams are used to illuminate the flow, each color being directed from a separate direction. In this way, the color of the light reflected from the flakes gives an indication of the local flake orientation. The flake orientation in complex three-dimensional (3-D) flow is in general a complicated function of the local velocity gradient tensor, but can be calculated if the underlying velocity field is known. This has recently been demonstrated by Gauthier et al. [Phys. Fluids. 10, 2147 (1998)] using monochome light. In complex flow fields the distribution of flakes may, however, be rearranged by the motion, thus making the local intensity of reflection depend on both orientation and flake concentration. The color is, however, immune to the local number density of flakes inside the flow, making quantitative information possible. This technique is demonst...

Wave patterns in a thin layer of sand within a rotating horizontal cylinder

A variety of wave patterns are found to form in a thin layer of sand inside a cylinder rotated about its horizontal axis of symmetry at constant angular velocity. In particular, we observe a spanwise instability characterized by serrated frontal shapes remarkably similar to those seen in Newtonian fluids. Within a certain parameter range, an accompanying spatial pattern forms on the rising side of the cylinder and travels along the cylinder span. The associated phase velocity is relatively constant, whereas the relevant wavelength increases quadratically with angular rotation speed. Standing waves appear at a critical rotation rate. Further, in some cases, a propagating cellular pattern forms on the surface of the medium.

Experiments on density-gradient anisotropies and scalar dissipation of turbulence in a stably stratified fluid

The anisotropic behaviour of density-gradient fluctuations in stably stratified grid turbulence and the consequences for simplified (isotropic) estimates of scalar dissipation rates χ were experimentally studied in a thermally stratified wind tunnel at moderate Reynolds numbers (Re λ ≃ 20). Strong stable stratifications were attained, with Brunt-Vaisala frequency N as high as 4 rad s -1 . The correlation method was used to estimate the mean-square cross-stream and streamwise density gradients. Cross-stream gradients were measured using two cold wires. The mean-square vertical gradients were found to become larger than the streamwise gradients by as much as a factor of 2.2 for the largest dimensionless buoyancy times (Nt = 7). This corresponds to a 40% error in the scalar dissipation estimates based on ∂θ/∂x alone, and assuming the validity of the isotropic relations. Gradient spectral relations show that this buoyancy-induced anisotropy persists at all length scales. Better closure of the scalar variance balance was attained than in previously reported measurements by other researchers. This is attributed to our use of cold-wire temperature sensors having larger length-to-diameter ratio than used in the previous measurements.

Marangoni instability of two liquids mixing at a free surface

The impact of a water drop on a thin layer of glycerin leads to the formation of an intricate flower-like pattern. We show that these leaf-like forms are generated by a surface-tension instability at the air–liquid interface along which there exists variable concentration of glycerin and water. Spatial variations of surface tension drive intense vortices inside the water layer, which interact with the glycerin–water concentration at the surface. Horizontal bending of these vortices is reinforced by the resulting enhancement of the surface-tension gradients.