Numerical simulation of Moffatt Vortices in a V-shaped notch

A numerical study for low-Reynolds-number incompressible viscous fluid flow near a V-shaped notch by boundary element method is presented. The numerically simulated velocity field shows that rolling a cylinder over the V-shaped notch can form Moffatt vortices. Comparison of the simulated velocity fields with Taneda’s experimental results shows good agreement. The numerical results indicate that the fluid flow in the wedge-shaped region consists of an infinite sequence of vortices of rapidly diminishing strength. It is also found that the maximum n is 4 for y n+1 = y n /2, Y n + 1 = Y n /2 of a V-shaped notch with θ = 28.5° and h = 5 cm, because the strength of fourth vortex is 10 − 4 . In particular, the method is very effective in researching and solving the problem of fluid flow near a V-shaped notch with variable θ and h, as well as in finding the condition for the appearance Moffatt vortices.