Hairpin Vortices Singularities And Transition To Turbulence In Three Dimensional Shear Flows

Download or read book Hairpin Vortices, Singularities, and Transition to Turbulence in Three-dimensional Shear Flows written by and published by . This book was released on 1990 with total page 17 pages. Available in PDF, EPUB and Kindle. Book excerpt: We study the evolution of a transversely perturbed co-flowing jet in a triply periodic box by means of a second-order projection method for the three-dimensional Euler equations. Advection-diffusion equations are solved without enforcing the incompressibility constraint, and the resulting velocity field is projected onto a divergence-free subspace. The method is unique in its treatment of nonlinear advection; it incorporates a second-order, upstream-centered differencing procedure that provides a robust treatment of nonsmooth data without introducing spurious oscillations, even in the limit of vanishing viscosity. The flow is visualized by following the evolution of a tracer function initialized on the surface of the tube. We also carry out a volume rendering of the vorticity field with an opacity profile and color map which shows that hairpin vortices abound and that vorticity intensifies greatly at their tips. We present strong numerical evidence that the vorticity becomes unbounded, and show that accompanying the onset of the singularity is a decay in the mean kinetic energy. Following the onset, a Kolmogorov (k−53) range emerges in the energy spectrum.