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Experiments on the onset of buoyant instabilities leading to periodic formation of vortical structures in planar buoyant plumes of helium and helium/air mixtures injected into quiescent air are reported for a range of nozzle widths (w=20–70 mm), plume fluid densities (pure helium to that approaching air), and velocities at the nozzle exit. First, the plume parameters corresponding to the onset of the oscillatory instability were experimentally determined by varying the nozzle exit velocity for different nozzle widths and plume fluid densities in two different nozzle configurations. These configurations corresponded to a freestanding rectangular nozzle and a rectangular nozzle surrounded by a flat plate in the plane of the nozzle exit. The observed plume behavior in the near field was characterized as nonoscillatory, transitional, or pulsatile. The onset of pulsations in the near field of these buoyant plumes (within a height of two nozzle widths) was best correlated in terms of the plume source Reynolds number and the plume fluid to ambient density ratio. It was also found that the boundary conditions surrounding the nozzle exit had an influence on the onset of plume instability in the near field. Specifically, at a given plume to the ambient density ratio, the plumes with flat plate surround were found to transition to the oscillatory state at a lower value of the threshold velocity and therefore are less stable than the plumes originating from freestanding nozzles. Subsequently, the plume oscillation frequencies were measured as a function of plume width, plume source velocity, and the density ratio for a range of these parameters. The plume oscillation frequency was found to correlate well in terms of the nondimensional parameters, Strouhal number, S=(fw)/Vp, and Richardson number, Ri=[(ρ∞−ρp)gw]/ρ∞Vp2, yielding a correlation S=0.55Ri0.45 determined for 1<Ri<102. This correlation is somewhat different from that of the axisymmetric buoyant plumes, which can be attributed to the differences in mixing rates and the strength of the local buoyancy flux in planar and axisymmetric plumes. The vortical structures formed in the unstable plumes also exhibit several distinct vortex pair modes. The centers of the formed vortex pairs, in general, do not remain colinear and distort with respect to each other when compared with the axisymmetric plume vortex rings, which are toroidal. The convection speeds of the vortex pair centers were also measured and reported in this study.

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Abstract:Group key management is one of the basic building blocks in collaborative and group-oriented applications in Mobile Ad Hoc Networks (MANETs). Group key establishment involves creating and distributing a common secret for all group members. However, key management for a large and dynamic group is a difficult problem because of scalability and security. Modification of membership requires the group key to be refreshed to ensure backward and forward secrecy. In this paper, we propose a Simple and Efficient Group Key (SEGK) management scheme for MANETs. Group members compute the group key in a distributed manner.