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 Octoer 4, 2015

abstract

It is shown that for inviscid barotropic fluid the dynamic variables, namely the density $\rho $, the velocity $\mathbf{v}$ and the labelling of stream lines $\mathbf{\xi }$ form the complete system of dynamic variables only for irrotational flow. For vortical flow the complex fluid potential $\psi _{\alpha },$ $\alpha =1,2,..n$ (wave function) forms a complete set of dynamic variables for inviscid barotropic fluid. Initial values of variables $\rho ,\mathbf{v,}$and $\mathbf{\xi }$ do not determine initial values of $\psi $. For vortical flows solution of the Cauchy problem is unique only in the case, when the fluid is described in terms of complex fluid potential (wave function). Variables $\rho ,\mathbf{v,}$ and $\mathbf{\xi }$ are observable quantities, whereas the complex fluid potential $\psi $ is not an observable quantity. It generates some problems for description of the barotropic fluid in terms of observable dynamic variables..

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