DNS Study of Transient Disturbance Growth and Bypass Transition*

Direct numerical simulation was used to investigate the detailed flow past a periodic array of cylindrical roughness elements. The problem was constructed as channel flow over a flat plate surface with roughness elements formed using an immersed boundary technique with a spectral method approach. Solutions were obtained for two roughness heights corresponding to Reynolds numbers (Re$_{k})$ of 189 and 350, and results are presented for both cases. Cylindrical roughness elements with Re$_{k}$=189 produced minimal disturbances and the flow remained laminar in the wake downstream of the roughness elements. Flow past cylindrical roughness elements corresponding to Re$_{k}$=350 was found to transition as soon as 2-3 cylinder diameters downstream and had developed into fully turbulent flow by the end of the domain. Results were found to compare reasonably well with a similar set of DNS computations by Rizzetta and Visbal using a sixth-order-accurate centered compact finite difference scheme as well as experimental results obtained by Ergin and White using time-averaged hotwire measurements of the velocity components.