TITLE:
About the Prospects for Passage to Instability
AUTHORS:
I. V. Lebed
KEYWORDS:
Instability; Classic Hydrodynamics; Multimoment Hydrodynamics
JOURNAL NAME:
Open Journal of Fluid Dynamics,
Vol.3 No.3,
September
18,
2013
ABSTRACT:
The results of the direct numerical integration
of the Navier-Stokes equations are evaluated against experimental data for problem
on a flow around bluff bodies in an unstable regime. Experiment records several
stable medium states for flow past a body. Evolution of each of these states, after
losing the stability, inevitably goes by periodic vortex shedding modes. Calculations
based on the Navier-Stokes equations satisfactorily reproduced all observed stable
medium states. They were, however, incapable of reproducing any of a vortex shedding
modes recorded experimentally. The solutions to the classic hydrodynamics equations
successfully reach the boundary of instability field. However, classic solutions
are unable to cross this boundary. Most likely, the reason for this is the Navier-Stokes
equations themselves. The classic hydrodynamics equations directly follow from the
Boltzmann equation and naturally contain the error involved in the derivation of
classic kinetic equation. Just the Boltzmann
hypothesis, which closed kinetic equation, allowed us to con- struct classic hydrodynamics on only three lower
principal hydrodynamic values. The use of the Boltzmann hypothesis excludes higher
principal hydrodynamic values from the participation in the formation of classic
hydrodynamics equations. The multimoment hydrodynamics
equations are constructed using seven lower principal hydrodynamic values. The numerical
integration of the multimoment hydrodynamics equations in the problem on flow around
a sphere shows that the solutions to these equations cross the boundary and enter
the instability field. The boundary crossing is accompanied by appearance of very uncommon acts in scenario of system
evolution.