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Title: Prandtl-Batchelor theorem for three-dimensional flows slowly varying in one direction and its application to vortex breakdown
Author: Sandoval Espinoza, Mario
ISNI:       0000 0004 2702 8396
Awarding Body: Imperial College London
Current Institution: Imperial College London
Date of Award: 2011
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In this work, the Prandtl-Batchelor theorem is extended to three-dimensional flows slowly varying in one direction by using asymptotic techniques, and thus overcoming the problem of having non-closed streamlines for recirculating three-dimensional flows. The derived equations turned out to be an analogue of the quasi-cylindrical equations used for describing behavior of streamwise vortices, rotating jets, vortex breakdown phenomenon and some other problems. Hence, the derived equations may be used for studying similar phenomena in non-axisymmetric cases. In order to apply such a system of equations to particular problems, a computational code was developed and validated by reproducing numerical results available in the literature. This code was constructed in two parts, one part considered the parabolic system of partial differential equations as decoupled from the Poisson equation and the second part solved the nonlinear Poisson equation by using an iterative method. Finally, these two algorithms were joined in order to solve the entire system. Once the code was available, it was used to investigate possible non-axisymmetric effects on the position of vortex breakdown phenomenon. The results of this study suggest that non-axisymmetric effects precipitate the onset of vortex breakdown. From all this work, two articles were written, one article was published in the Journal of Fluid Mechanics (see Appendix D) and the second article will be submitted.
Supervisor: Chernyshenko, Sergei Sponsor: CONACYT (National Council of Science and Technology of Mexico)
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral