Turbulence generation in the transitional wake flow behind a sphere

Abstract

Turbulence generation in the transitional flow in the wake behind a sphere is studied with numerical simulations. The filtered Navier–Stokes equation and the large eddy simulation method are employed as the governing equation and the numerical method, respectively. The ΩR̃ vortex identification method is used to trace the evolution of vortices in the wake flow. The energy gradient theory is used to analyze the spike formation in the wake flow. The simulation results show that the vortex structure in the wake flow is the type of hairpin vortices, which is similar to that in a boundary layer flow. Ejection and sweep motions exist around the hairpin vortices. There are two most unstable regions in the wake where turbulence “burst” is first produced, one is near the center of the vortex head and the other is between the two vortex legs. There is a high-pressure zone above the vortex head due to the decrease in the streamwise velocity, and a soliton-like coherent structure exists in this area. The mechanism of turbulence generation in the wake is the discontinuity of the streamwise velocity, which makes the Navier–Stokes equation be singular. This singularity leads to the formation of the “negative spike” in the streamwise velocity. The amplitude of the “negative spike” reaches up to 60% of the incoming velocity, which is close to the situation in a boundary layer flow on a flat plate. It is concluded that the mechanism of turbulence generation in the wake flow is the same as that in the boundary layer flow.