Evolution of unstable system.

Abstract

Scenario of appearance and development of instability in problem of a flow around a solid sphere at rest is discussed. The scenario was created by solutions to the multimoment hydrodynamics equations, which were applied to investigate the unstable phenomena. These solutions allow interpreting Stokes flow, periodic pulsations of the recirculating zone in the wake behind the sphere, the phenomenon of vortex shedding observed experimentally. In accordance with the scenario, system loses its stability when entropy outflow through surface confining the system cannot be compensated by entropy produced within the system. The system does not find a new stable position after losing its stability, that is, the system remains further unstable. As Reynolds number grows, one unstable flow regime is replaced by another. The replacement is governed tendency of the system to discover fastest path to depart from the state of statistical equilibrium. This striving, however, does not lead the system to disintegration. Periodically, reverse solutions to the multimoment hydrodynamics equations change the nature of evolution and guide the unstable system in a highly unlikely direction. In case of unstable system, unlikely path meets the direction of approaching the state of statistical equilibrium. Such behavior of the system contradicts the scenario created by solutions to the classic hydrodynamics equations. Unstable solutions to the classic hydrodynamics equations are not fairly prolonged along time to interpret experiment. Stable solutions satisfactorily reproduce all observed stable medium states. As Reynolds number grows one stable solution is replaced by another. They are, however, incapable of reproducing any of unstable regimes recorded experimentally. In particular, stable solutions to the classic hydrodynamics equations cannot put anything in correspondence to any of observed vortex shedding modes. In accordance with our interpretation, the reason for this isthe classic hydrodynamics equations themselves.

About the Transition to Turbulence Through Chaotic Distortion of Vortex Shedding

“…The system loses its stability when entropy produced in the system can not compensate entropy outflow through the surface confining the system. Such interpretation follows directly from the principle of retention and loss of the open system stability formulated in [25], [26]. In accordance with solutions to the multimoment hydrodynamics equations, the system, when loses its stability, remains further unstable.…”

“…The replacement of one unstable regime by another is governed the tendency of the system to discover the fastest path to depart from the state of statistical equilibrium. This striving follows directly from the evolution criterion formulated in [25], [26]. Thus, the evolution of solutions in any way does not follow the Landau-Hopf bifurcation scenario on the Re scale.…”

“…Therefore, the instability development through the development of large-scale stochastic fluctuations provides a faster path to depart from the state of statistical equilibrium compared to instability development through the development of small-scale stochastic fluctuations. Then, in accordance with the evolution criterion [25], [26], the system will go along the instability development path contained large-scale stochastic fluctuations. Moreover, before large-scale fluctuations arrive at the periphery of recirculating zone at the instant of separation, they may experience some periods of sharp increase in the recirculating zone ( Fig.…”