### 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