Construction of initial vortex-surface fields and Clebsch potentials for flows with high-symmetry using first integrals

Pengyu He, Yue Yang
2016 Physics of Fluids  
Gliding arc in tornado using a reverse vortex flow Rev. Sci. Instrum. 76, 025110 (2005); 10.1063/1.1854215 Vortex ring pinchoff in the presence of simultaneously initiated uniform background co-flow Phys. Fluids 15, L49 (2003); We report a systematic study on the construction of the explicit, general form of vortex-surface fields (VSFs) and Clebsch potentials in the initial fields with the zero helicity density and high symmetry. The construction methodology is based on finding independent
more » ... ng independent first integrals of the characteristic equation of a given threedimensional velocity-vorticity field. In particular, we derive the analytical VSFs and Clebsch potentials for the initial field with the Kida-Pelz symmetry. These analytical results can be useful for the evolution of VSFs to study vortical structures in transitional flows. Moreover, the generality of the construction method is discussed with the synthetic initial fields and the initial Taylor-Green field with multiple wavenumbers. C 2016 AIP Publishing LLC. [http://dx.
doi:10.1063/1.4943368 fatcat:vocilbfdfngk7nl7x675mtdlku