Development of instability in the problem of flow around a sphere

Abstract

Multimoment hydrodynamics equations are used to solve the problem of flow around a quiescent solid sphere. The solutions to the multimoment hydrodynamics equations are found, which enable to interpret of the phenomenon of vortex shedding. The solutions give a pattern of instability development that qualitatively reproduces experimental data over a wide range of Reynolds numbers. The replacement of one unstable flow mode by another unstable mode is governed the tendency of the system to find the fastest way to depart from the state of statistical equilibrium. After stability loss, the system does not reach a new stable state. Such a scenario is at odds with the ideas of classical hydrodynamics, which interprets the development of instability in terms of a bifurcation transition from one stable state to another. This picture presented shows the direction of solving the problems faced by classical hydrodynamics in the interpretation of the phenomenon of vortex shedding.