The Saffman-Taylor problem on a sphere

The Saffman-Taylor problem addresses the morphological instability of an interface separating two immiscible, viscous fluids when they move in a narrow gap between two flat parallel plates (Hele-Shaw cell). In this work, we extend the classic Saffman-Taylor situation, by considering the flow between two curved, closely spaced, concentric spheres (spherical Hele-Shaw cell). We derive the mode-coupling differential equation for the interface perturbation amplitudes and study both linear and nonlinear flow regimes. The effect of the spherical cell (positive) spatial curvature on the shape of the interfacial patterns is investigated. We show that stability properties of the fluid-fluid interface are sensitive to the curvature of the surface. In particular, it is found that positive spatial curvature inhibits finger tip-splitting. Hele-Shaw flow on weakly negative, curved surfaces is briefly discussed.Comment: 26 pages, 4 figures, RevTex, accepted for publication in Phys. Rev.

Towards In-Flight Measurements of Helicopter Blade Tip Vortices

In the framework of the AIM project the near field of the blade tip vortex of a full-scale helicopter in simulated hover flight was investigated by combining three-component Particle Image Velocimetry and Background Oriented Schlieren measurements. The velocity field measurements in the range of wake ages of 1° to 30° in azimuth provided a reference for a quantitative analysis of the Schlieren results yielding vortex core density estimates. Ongoing vortex roll-up was observed at 1° while considerable aperiodicity was persistent thereafter. The vortex parameters for vortices older than 1° were consistent with the Scully vortex model. However, the particular challenges of full-scale, outdoor testing, especially the limited spatial resolution and aperiodicity effects, yielded a higher level of measurement uncertainty as compared to sub-scale experiments

G.: Topology based flow analysis and superposition effects

Summary. Using topology for feature analysis in flow fields faces several problems. First of all, not all features can be detected using topology based methods. Second, while in flow feature analysis the user is interested in a quantification of feature parameters like position, size, shape, radial velocity and other parameters of feature models, many of these parameters can not be determined using topology based methods alone. Additionally, in some applications it is advantageous to regard the vector field as a superposition of several, possibly simple, features. As topology based methods are quite sensitive to superposition effects, their precision and usability is limited in these cases. In this paper, topology based analysis and visualization of flow fields is estimated and compared to other feature based approaches demonstrating these problems.