A dynamic multi-scale approach for turbulent inflow boundary conditions in spatially developing flows

A dynamic method for prescribing realistic inflow boundary conditions is presented for simulations of spatially developing turbulent boundary layers. The approach is based on the rescaling-recycling method proposed by Lund, Wu & Squires (J. Comput. Phys, vol. 140, 1998, pp. 233-258) and the multi-scale method developed by Araya, Jansen & Castillo (J. Turbul., vol. 10, no. 36, 2009, pp. 1-33). The rescaling process requires prior knowledge about how the velocity and length scales are related between the inlet and recycle stations. Here a dynamic approach is proposed in which such information is deduced dynamically by involving an additional plane, the so-called test plane located between the inlet and recycle stations. The approach distinguishes between the inner and outer regions of the boundary layer and enables the use of multiple velocity scales. This flexibility allows applications to boundary layer flows with pressure gradients and avoids the need to prescribe empirically the friction velocity and other flow parameters at the inlet of the domain. The dynamic method is tested in direct numerical simulations of zero, favourable and adverse pressure gradient flows. The dynamically obtained scaling exponents for the downstream evolution of boundary layer parameters are found to fluctuate in time, but on average they agree with the expected values for zero, favourable and adverse pressure gradient flows. Comparisons of the results with data from experiments, and from other direct numerical simulations that use much longer computational domains to capture laminar-to-turbulence transition, demonstrate the suitability of the proposed dynamic method.