By David R. Morrison, Janos Kolla Summer Research Institute on Algebraic Geometry
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Additional info for Algebraic Geometry Santa Cruz 1995: Summer Research Institute on Algebraic Geometry, July 9-29, 1995, University of California, Santa Cruz (Proceedings of Symposia in Pure Mathematics) (Pt. 2)
In order to avoid possible misunderstandings: we are now working on the derivation of a metric that includes the gradients of the extensive variables from the outset; this metric will be much better suited to deal with non-uniform flows than the one considered in the present work. 1 Corresponding author; e-mail: pasmante@knmi. nl 39 T. Kambe et al. ), /UTAM Symposium on Geometry and Statistics ofTurbulence, 39-46. © 2001 Kluwer Academic Publishers. 40 2 Metric of a gas in thermal equilibrium In [] we constructed a natural metric tensor in the configuration space of a compressible fluid in local thermal equilibrium and in uniform motion.
56, 427 (1997). 1. 2. 3. 4. 5. 6. 7. 8. Trying a metric on atmospheric flows Ruben A. Pasmanter 1 and Xue-Li Wang KNMI, P. , in a space with (p, T, il) = (density, temperature, velocity) as coordinates. , between two positions with coordinates (Pl. T1, ill) and (p2, T2, il2) respectively; neither is it possible to talk of "the norm" of the vector formed by the rate of change of the dynamical variables (dpjdt,dT/dt,diljdt); it is not possible to consider the angle between two such vectors; there is no volume element defined in configuration space, therefore, it does not make sense to talk about "the density" of a distribution of points in that space; etc.
The experimental data do not seem however to encounter this behavior. Mathematically, the Nusselt number represents the maximum (among all possible invariant measures) of the expected value of the diameter of the global attractor in the energy dissipation norm. The functions on the attractor are not arbitrary, and may have certain properties that explain the experimentally observed bounds (). In this paper we showed that if the ratio n N 30 is small then the Nusselt number dependence on Rayleigh is depleted.