Hairpin vortices, singularities, and transition to turbulence in three-dimensional shear flows
Abstract
The evolution of a transversely perturbed co-flowing jet was studied 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. 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 was performed. Strong numerical evidence was presented that the vorticity becomes unbounded, and that accompanying the onset of the singularity is a decay in the mean kinetic energy. Following the onset, a Kolmogorov (k exp -5/3) range emerges in the energy spectrum.
- Publication:
-
AIAA, Space Programs and Technologies Conference
- Pub Date:
- October 1990
- Bibcode:
- 1990aiaa.confR..24M
- Keywords:
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- Computerized Simulation;
- Fluid Flow;
- Horseshoe Vortices;
- Shear Flow;
- Singularity (Mathematics);
- Three Dimensional Flow;
- Three Dimensional Motion;
- Transition Flow;
- Adjoints;
- Advection;
- Reynolds Number;
- Turbulence;
- Fluid Mechanics and Heat Transfer