Production mechanisms of intense events
Ferguson, Andrew Neil
The Restricted Euler equations, taken from the Vieillefosse model for the\ud velocity gradient tensor, are re-investigated using data from direct numerical\ud simulations of an intense event, rather than using data from forced simulations\ud of homogeneous, isotropic turbulence. The goal is to develop ideas for extensions\ud to turbulence models based on the RE equations that can handle these\ud intense events. With this goal in mind, the new numerical data is compared\ud against the evolution of the RE equations towards a finite time limit and its\ud predictions on how ratios of the RE moments converge. The analysis starts by\ud looking at distributions of the invariants in the R-Q phase space. From this,\ud the analysis then compares the Vieillefosse equations to the full equations and\ud notes that there is a significant change in behaviour around t = 0:5. It is\ud suggested that this is associated with a change in \ud ow topology due to the\ud reconnection of vortex tubes in the \ud flow field. To build a higher-order model,\ud more terms from the full RE equations should be used, which is investigated\ud by looking at the co-evolution of the second invariant Q and the third-order\ud moments, Rw and Rs.
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