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- ItemSchneefernerhaus as a mountain research station for clouds and turbulence(München : European Geopyhsical Union, 2015) Risius, S.; Xu, H.; Di Lorenzo, F.; Xi, H.; Siebert, H.; Shaw, R.A.; Bodenschatz, E.Cloud measurements are usually carried out with airborne campaigns, which are expensive and are limited by temporal duration and weather conditions. Ground-based measurements at high-altitude research stations therefore play a complementary role in cloud study. Using the meteorological data (wind speed, direction, temperature, humidity, visibility, etc.) collected by the German Weather Service (DWD) from 2000 to 2012 and turbulence measurements recorded by multiple ultrasonic sensors (sampled at 10 Hz) in 2010, we show that the Umweltforschungsstation Schneefernerhaus (UFS) located just below the peak of Zugspitze in the German Alps, at a height of 2650 m, is a well-suited station for cloud–turbulence research. The wind at UFS is dominantly in the east–west direction and nearly horizontal. During the summertime (July and August) the UFS is immersed in warm clouds about 25 % of the time. The clouds are either from convection originating in the valley in the east, or associated with synoptic-scale weather systems typically advected from the west. Air turbulence, as measured from the second- and third-order velocity structure functions that exhibit well-developed inertial ranges, possesses Taylor microscale Reynolds numbers up to 104, with the most probable value at ~ 3000. In spite of the complex topography, the turbulence appears to be nearly as isotropic as many laboratory flows when evaluated on the "Lumley triangle".
- ItemQuasiconvexity equals rank-one convexity for isotropic sets of 2 x 2 matrices(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2011) Heinz, SebastianLet K be a given compact set of real 2x2 matrices that is isotropic, meaning invariant under the left and right action of the special orthogonal group. Then we show that the quasiconvex hull of K coincides with the rank-one convex hull (and even with the lamination convex hull of order 2). In particular, there is no difference between quasiconvexity and rank-one convexity for K. This is a generalization of a known result for connected sets.