Near-field flow structures and transient growth due to subcritical surface roughness

An immersed boundary spectral method is used to simulate laminar boundary layer flow over a periodic array of cylindrical surface roughness elements. Direct comparisons are made with experiments by using a roughness-based Reynolds number Re[subscript k] of 216 and a diameter to spanwise spacing ratio d/[lamda] of 1/3. Near-field differences between three similar studies are presented and addressed. The shear layer developed over the roughness element produces the downstream velocity deficit region while splitting of the vortex sheet shed the trailing edge forms its lateral modes. Additional geometrical configurations are simulated for comparisons with experimental results and future analysis by linear stability theory. Total disturbance energy E[subscript rms] is fairly consistent with experimental results while spanwise energy components vary significantly. Physical relaxation of the disturbance wake is found to remain a prominent issue for this simulation technique.