Search

In any crisis, there is a great deal of uncertainty, often geographical uncertainty or, more precisely, spatiotemporal uncertainty. Examples include the spread of contamination from an industrial accident, drifting volcanic ash, and the path of a hurricane. Estimating spatiotemporal probabilities is usually a difficult task, but that is not our primary concern. Rather, we ask how analysts can communicate spatiotemporal uncertainty to those handling the crisis. We comment on the somewhat limited literature on the representation of spatial uncertainty on maps. We note that many cognitive issues arise and that the potential for confusion is high. We note that in the early stages of handling a crisis, the uncertainties involved may be deep, i.e., difficult or impossible to quantify in the time available. In such circumstance, we suggest the idea of presenting multiple scenarios.

The transient behaviour of natural convection within a horizontal cylindrical enclosure, subjected to a uniform and constant wall temperature, is investigated numerically and experimentally. Numerically the two dimensional instantaneous governing equations are solved through Chebyshev-Fourier spatial approximation. Two boundary condition configurations have been examined. In the first, considered to be an idealised configuration, the enclosure wall is neglected and the constant boundary temperature applied at the solid/fluid interface. The second, applies constant temperature boundary conditions on the outer surface of the enclosure wall, giving a conjugate configuration, as is the case in the experimental study. Numerically, both boundary conditions are considered over the Rayleigh number range of 10 4 < Ra < 108 for Prandtl numbers Pr - 0.71, 7.1 and 100. This is extended to Ra = 109 for Pr = 7.1 and 100 for the ideal and for Pr = 7.1 for the conjugate case. Experimental results are obtained for Ra = 1.4 x 1010 at Pr = 5.6. In order to achieve greater insight, of the transient features, extensive use is made of visualisation techniques both numerically and experimentally. The flows evolution for the ideal boundary condition case is found to be divisible into two time regimes. The early regime, extending over the conduction time period, scales as Ra-1/2 L2/α. The later regime, encompassing the convective flow, scales as Ra-0.24 L2/α. The magnitude of the average Nusselt number scales like Ra1/4. For the conjugate case the thermal conductivity of the wall limits the maximum heat transfer rate into the cylinder for all Ra. The time evolution of the conjugate boundary condition case has no simple scaling. For both boundary conditions, the flow structure demonstrates an asymptotic behaviour with increasing Pr. It is shown that the boundary layer possesses a two layer structure only over the very early time period. This is quickly superseded by a single layer, where both the thermal and dynamic boundary layers are the same thickness. For the ideal boundary condition case this single layer structure scales as Ra1/4. At large Ra, the transients within the core of the enclosure are found to evolve in an oscillatory manner due to internal wave motion. The structure of these waves is Pr dependant.