About the Transition to Turbulence Through Chaotic Distortion of Vortex Shedding

Abstract

The results of direct numerical integration of the Navier-Stokes equations are evaluated against experimental data for the problem of flow around a hard sphere at rest. The evaluation is performed for both the sequence of vortex shedding regimes, replacing stable modes after the loss of stability, and the regime of turbulence replacing vortex shedding modes as Reynolds number Re increases. The evaluation demonstrates the unsuitability of classic hydrodynamics equations to interpret the phenomenon of vortex shedding. Moreover, the attainment of critical value of Re is accompanied by loss of the direction of instability development. Wrong direction of instability development results in the attainment of multiperiodic, that is, essentially chaotic, solution. Insurmountable discrepancies between calculation results and experimental data show that the chaotic deterministic solution to the Navier-Stokes equation is not suitable for interpretation of turbulence. An analogy is revealed between the sequence of modes observed in flow around a sphere as Re increases and sequence of modes in shear layer behind a cylinder with paraboloidal nose recorded while moving downstream along the contour of streamlined body. The conclusions are as follows. The turbulence of shear flow is regular unstable vortex shedding regime distorted by chaotic fluctuations. Solutions to the classic hydrodynamics equations are incapable of interpreting both regular and chaotic turbulence component. Multimoment hydrodynamics seeks for decision of these problems along the way toward an increase in the number of principle hydrodynamic values.