Stream-wise Periodic Direct Numerical Simulations of an Incompressible, Flat-Plate Boundary Layer: Validations and Analysis

Direct numerical simulations of an incompressible, flat-plate, turbulent boundary layer were performed via a novel simulation method, inspired by Spalart (J. Fluid Mech., vol. 187, 1988, p. 61-98) and his further simplifications on inflow recycling (Int. J. Heat Fluid Fl., vol. 27, 2006, p. 902-910). The new method is stream-wise periodic and uses normalized wall-normal coordinates and overcomes key limitations of Spalart’s original method while still retaining statistical stationarity. The Reynolds number was varied in the range of Re_θ = 670-5500 with shape factor values and skin friction values within 1% and 2%, respectively, of the DNS values given by Orlu et al. (P. Exp Fluids, vol. 54, 2013). Validations were further performed on the higher order moments of velocity profiles as well as energy spectra. Simulations were also run to investigate the effects of stream-wise extent of very-large-scale motions (VLSMs) on boundary layer dynamics. Lastly, a linear stability analysis was conducted on the new stream-wise periodic system to highlight how this new framework can develop insight into boundary layer transition and turbulence.