Numerical study of sink-flow boundary layers

Direct numerical simulations of sink-flow boundary layers, with acceleration parameters K between 1.5 × 10 −6 and 3.0 × 10 −6 , are presented. The three-dimensional, time-dependent Navier–Stokes equations are solved numerically using a spectral method, with about 10 6 degrees of freedom. The flow is assumed to be statistically steady, and self-similar. A multiple-scale approximation and periodic conditions are applied to the fluctuations. The turbulence is studied using instantaneous and statistical results. Good agreement with the experiments of Jones & Launder is observed. Two effects of the favourable pressure gradient are to extend the logarithmic layer, and to alter the energy balance of the turbulence near the edge of the boundary layer. At low Reynolds number the logarithmic layer is shortened and slightly displaced, but wall-layer streaks are present even at the lowest values of R θ for which turbulence can be sustained. Large quiescent patches appear in the flow. Relaminarization occurs at K = 3.0 × 10 −6 , corresponding to a Reynolds number R θ ≈ 330.