Hidden dynamical variables in rotational flow of barotropic fluid

Yuri A. Rylov

Institute for Problems in Mechanics, Russian Academy of Sciences 
 101-1 ,Vernadskii Ave., Moscow, 119526, Russia 
 email: rylov@ipmnet.ru 
 Web site: http://gas-dyn.ipmnet.ru/~rylov/yrylov.htm

Updated December 22, 2017


Inviscid barotropic fluid is investigated as a dynamical system by means of variational methods. Conventional description in terms of variables: (density ρ, velocity v, and labelling of stream lines ξ) appears to be ineffective for vortical flows, because dynamic equations for ξ contain idefinite parameter. It is possible complete description of barotropic fluid in terms of complex wave function ψ_{α}, α=1,2. At returning to description in terms of ρ,v an additional dynamic variables: spin s=(s,s,s) appear. Spin describes additional vorticity incorporated into fluid. Appearance of additional variable s (instead of ξ) is essential at description of turbulent phenomena.

There is text of the paper in English pdf     and in Russian pdf