Numerical simulation of Tollmien-Schlichting waves by use of a modified vortex particle-in-cell method

Tollmien-Schlichting (TS) wave motion was numerically simulated by a modified vortex-particle-in-cell method, in which a relative vorticity strength concept is introduced to define a continuous vorticity for better simulation of TS waves. The method is based on the exact Navier-Stokes equation for the disturbance, rather than its linearized version: therefore it may be used, in principle, to simulate the whole laminar-turbulent transition process from the initial unstability in the final breakdown. In the small disturbance region, the predicted wave velocity of TS waves corresponds to the eigenfunction of the Orr-Sommerfeld equation used to specify the initial disturbance distribution.