Effect of the number of vortices on the torque scaling in Taylor-Couette flow

Torque measurements in Taylor-Couette flow, with large radius ratio and large aspect ratio, over a range of velocities up to a Reynolds number of 24 000 are presented. Following a specific procedure, nine states with distinct number of vortices along the axis were found and the aspect ratio of the vortices were measured. The relationship between the speed and the torque for a given number of vortices is reported. In the turbulent Taylor vortex flow regime, at relatively high Reynolds number, a change in behaviour is observed corresponding to intersections of the torque-speed curves for different states. Before each intersection, the torque for a state with larger number of vortices is higher. After each intersection, the torque for a state with larger number of vortices is lower. The exponent, from the scaling laws of the torque, always depends on the aspect ratio of the vortices. When the Reynolds number is rescaled using the mean aspect ratio of the vortices, only a partial collapse of the exponent data is found.Comment: 11 pages, 6 figure

Spinors in Higher Dimensional and Locally Anisotropic Spaces

The theory of spinors is developed for locally anisotropic (la) spaces, in brief la-spaces, which in general are modeled as vector bundles provided with nonlinear and distinguished connections and metric structures (such la-spaces contain as particular cases the Lagrange, Finsler and, for trivial nonlinear connections, Kaluza-Klein spaces). The la-spinor differential geometry is constructed. The distinguished spinor connections are studied and compared with similar ones on la-spaces. We derive the la-spinor expressions of curvatures and torsions and analyze the conditions when the distinguished torsion and nonmetricity tensors can be generated from distinguished spinor connections. The dynamical equations for gravitational and matter field la-interactions are formulated.Comment: 54 pages, Revtex, an extension of the paper published in J. Math. Phys. 37 (1996), 508--52

Matrix exponential via Clifford algebras

We use isomorphism $\varphi$ between matrix algebras and simple orthogonal Clifford algebras \cl(Q) to compute matrix exponential ${e}^{A}$ of a real, complex, and quaternionic matrix A. The isomorphic image $p=\varphi(A)$ in \cl(Q), where the quadratic form $Q$ has a suitable signature $(p,q),$ is exponentiated modulo a minimal polynomial of $p$ using Clifford exponential. Elements of \cl(Q) are treated as symbolic multivariate polynomials in Grassmann monomials. Computations in \cl(Q) are performed with a Maple package `CLIFFORD'. Three examples of matrix exponentiation are given

Mixing of dust aerosols into a mesoscale convective system: Generation, filtering and possible feedbacks on ice anvils

International audienceDuring the second Specific Observing Period (SOP) of the African Monsoon Multidisplinary Analyses (AMMA) campaign, several intense mesoscale convective systems (MCS) developed over Niger. An examination of a particular convective storm simulated with a mesoscale model near Banizoumbou, Niger, on 1 July, 2006, shows that this MCS generates a strong emission of dust particles at the leading edge of its density current. A fraction of these dust aerosols are uplifted by the convective core of the system and redistributed by aqueous processes. Aerosol impaction scavenging is the main process by which particles are deposited within the mesoscale convective system. However, small particles (smaller than 1 μm) that are not efficiently scavenged, are able to reach the upper troposphere at a concentration of 6 particles per cm3. This suggests that deep convection over semi-arid regions is able to create its own ice nuclei in high concentrations. This leads to the question: can deep convection over semi-arid regions affect particular ice properties such as ice anvil extension or induce possible feedbacks of dust on precipitation through ice sedimentation