Numerical Simulation of Vortex Breakdown

Vortex Models and Boundary Layer Instability

“…One of the major conclusions from the experimental data in Klebanoff et al, [23] is that the perturbed flow is periodic in the transverse direction (i.e., y direction). It is therefore natural to consider in three dimensions equations (11) with the added periodicity conditions (13) u(x, y +q, z) u(x, y, z), (x, y + q, z) 2(x, y, z), etc. Furthermore, from Klebanoff et al (1962) we conclude that q is roughly equal to the streamwise wave length of the first unstable Tollmien-Schlichting waves; roughly, q 0.1 in our units.…”

“…Furthermore, from Klebanoff et al (1962) we conclude that q is roughly equal to the streamwise wave length of the first unstable Tollmien-Schlichting waves; roughly, q 0.1 in our units. We shall therefore be solving equations (11) with the boundary conditions (12) and (13), and q 0.1. The numerical methods in three dimensions.…”

“…In earlier three dimensional calculations (Leonard, [26], [27], Del Prete [13], Chorin, (unpublished)), the vorticity field was represented as a sum of vortex filaments. The difficulties with this approach are: (i) a huge amount of bookkeeping is required to keep track of the changing vortex configurations; (ii) there is no obvious way to generate the filaments at the boundary in a consistent manner.…”