Solitary wave structure of transitional flow in the wake of a sphere

The soliton-like coherent structure (SCS), which has been verified to exist in both transitional and turbulent boundary layers [Y. S. Kachanov, “Physical mechanisms of laminar-boundary-layer transition,” Annu. Rev. Fluid Mech. 26, 411–482 (1994); C. Lee, “New features of CS solitons and the formation of vortices,” Phys. Lett. A 247, 397–402 (1998); C. Lee and J. Z. Wu, “Transition in wall-bounded flows,” Appl. Mech. Rev. 61, 030802 (2008); and C. Lee and X. Jiang, “Flow structures in transitional and turbulent boundary layers,” Phys. Fluids 31, 111301 (2019)], still poses a challenge in the understanding of its formation and behavior. In our previous study [Niu et al., “Turbulence generation in the transitional wake flow behind a sphere,” Phys. Fluids 36, 034127 (2024)], the SCS was also found to exist in the transitional wake flow behind a sphere. In the present study, the formation and evolution of the SCS is further investigated at various Reynolds numbers by numerical simulation. The results show that at the early stage of the turbulence transition, the SCS appears as a form of wave packet during the Tollmien–Schlichting (T–S) wave stage. With the increase in the Reynolds number, the SCS reaches its maximum amplitude downstream where the velocity discontinuity occurs. This position is located after the breakdown of the T–S wave and the three-dimensional structure is formed. Then, the SCS conserves its shape and amplitude over a long distance downstream. The relationships among the SCS, the spikes, the vortex structures, and the high-shear layers are further analyzed. It is found that the SCS in the wake flow has similarities to the phenomena observed in boundary layer flows during the turbulent transition. The vortex structures and high-shear layers mostly wrap around the border of the SCS. The vortex structure is considered to be a consequence of the development of the SCS rather than its cause.