Application of the lattice Boltzmann method to transition in oscillatory channel flow

In this study the applicability of the lattice Boltzmann method to oscillatory channel flow with a zero mean velocity has been evaluated. The model has been compared to exact analytical solutions in the laminar case (Re-delta < 100, where Re-delta is the Reynolds number based on the Stokes layer) for the Womersley parameter 1 < alpha < 31. In this regime, there was good agreement between numerical and exact analytical solutions. The model was then applied to study the primary instability of oscillatory channel flow with a zero mean velocity. For these transitionary flows the parameters were varied in the range 400 < Re-delta < 1000 and 4 < alpha < 16. Disturbances superimposed on the numerical solution triggered the two-dimensional primary instability. This phenomenon has not been numerically evaluated over the range of a or Res currently investigated. The results are consistent with quasi-steady linear stability theories and previous numerical investigations.