Numerical simulations of vortex lines in transitional pipe flow*

Concentrated vortex lines appear in many flows, such as aerodynamics, turbulence, and weather systems. Although significant past work has focused on understanding the behavior of isolated vortices, the interaction of vortices with walls and shear flows also plays an important role in many systems. To study these interactions, we have developed tools to simulate an experiment which generates streamwise vortices in pipe flow at the laminar/turbulent transition regime. Our simulations employ a second-order projection method with adaptive octree grids and supra-convergent finite difference schemes to solve the incompressible Navier-Stokes equations across a wide range of Reynolds numbers. We use a level-set formulation and efficient tree-traversal algorithms to represent the realistic solid obstructions that are used in these experiments. A key feature of our simulation toolbox is the ability to augment and fine-tune the solver to match the experimental apparatus, allowing us to visualize and compare our results with experimental data easily.