Here we have demonstrated the possibility of very high performance in the implementation of a global spectral methodology on a massively parallel architec ture with distributed memory. Spectral simulations of channel flow and thermal convection in a three-dimen sional Cartesian geometry have yielded a very high performance—up to 26 Gflops/s on a 512-node CM5. In general, implementation of spectral methodology in parallel processors with distributed memory requires nonlocal interprocessor data transfer that is not re stricted to being between nearest neighbors. In spite of their increased communication overhead, better per formance is possible in global methodologies owing to their dense matrix operations and organized data com munication. In this paper we outline a general method ology for the data-parallel implementation of spectral methods on massively parallel machines with distrib uted memory. Following the steps presented here, very high performance can be obtained on a wide vari ety of massively parallel architectures.
Thermal plumes in Rayleigh–Bénard convection have been observed to occur with strong vertical component of vorticity, resulting in spiraling hot updrafts and cold downdrafts. Results from two different simulations at Rayleigh numbers 9800 and 33 000 times the critical Rayleigh number close to the boundaries show rapid increase in the conditional averages of vertical velocity and temperature perturbation at large values of vertical vorticity. This result along with the spatial distribution of vertical vorticity indicates a strong correlation between narrow regions of upmoving hot fluid (or downmoving cold fluid) and local vertical vorticity. The horizontal dimension of these vortical plumes is an order of magnitude smaller than the layer depth, but they extend up to half the convective layer in the vertical direction.
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