Abstract
The equations for the pair distribution functions are derived directly from the second equation of the Bogolyubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy. The derivation is fulfilled within the frameworks of the multiscale method. The equations for the pair distribution functions are the kinetic foundation for the multimoment hydrodynamics equations. Solutions to the equations for the pair distribution functions predetermine the possibility of constructing the hydrodynamics equations with an arbitrary number of principle hydrodynamic values specified beforehand. The tendency to increase the number of principal hydrodynamic values is caused by the necessity of interpreting the behavior of the system after the loss of stability. Solutions to the classic hydrodynamics equations constructed for only three principle hydrodynamic values are unable to predict the direction of instability evolution. Solutions to the multimoment hydrodynamics equations are capable of reproducing correctly the phenomenon of emergence and development of instability.
Highlights
Possibility to study the unstable phenomena by means of the direct numerical integration of the Navier-Stokes equations became feasible comparatively recently
Equation (2.20), these integrals are (ξ1 ) different from 1, ξ1 and ξ12 are not zero [3]. It follows that, when we pass to the hydrodynamic stage from the phase space of one particle, such hydrodynamics equations cannot be constructed using more than three lower principal hydrodynamic values corresponding to the 1, ξ1, ξ12 particle properties
In accordance with the interpretation of [1]-[3], the reason for their failure is the lack of the main hydrodynamic values used in constructing the equations of classic hydrodynamics
Summary
Possibility to study the unstable phenomena by means of the direct numerical integration of the Navier-Stokes equations became feasible comparatively recently. Non-stationary solutions exist only at a critical value of the Reynolds number These solutions cannot be put in correspondence to observed periodic vortex shedding modes exceedingly prolonged along the. The idea of bringing the stable solution to interpret the six observed vortex shedding modes and the pulsation mode in the range Re∗∗ < Re < Re∗∗∗ initially seems to have no prospects. This idea is not able to resolve the encountered discrepancies when evaluating the results of the direct numerical integration of the Navier-Stokes equations against experiment.
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