Structure of a turbulent boundary layer studied by DNS

Abstract

Turbulent boundary layers constitute one of the basic building blocks for understanding turbulence, particularly relevant for industrial applications. Although the geometries in technical but also geophysical applications are complicated and usually feature curved surfaces, the flow case of a canonical boundary layer developing on a flat surface has emerged as an important setup for studying wall turbulence, both via experimental and numerical studies. However, only recently spatially developing turbulent boundary layers have become accessible via direct numerical simulations (DNS). The difficulties of such setups are mainly related to the specification of proper inflow conditions, the triggering of turbulence and a careful control of the free-stream pressure gradient. In addition, the numerical cost of such spatial simulations is high due to the long, wide and high domains necessary for the full development of all relevant turbulent scales. We consider a canonical turbulent boundary layer under zero-pressure-gradient via large-scale DNS. The boundary layer is allowed to develop and grow in space. The inflow is a laminar Blasius boundary layer, in which laminar-turbulent transition is triggered by a random volume force shortly downstream of the inflow. This trip force, similar to a disturbance strip in an experiment (Schlatter and Örlü, 2010; Schlatter et al., 2009), is located at a low Reynolds number to allow the flow to develop over a long distance. The simulation covers thus a long, wide and high domain starting at Re _θ =180 extending up to the (numerically high) value of Re _θ =4300, based on momentum thickness θ and free-stream velocity U _∞. Fully turbulent flow is obtained from Re _θ ≈500. The numerical resolution for the fully spectral numerical method (Chevalier et al., 2007) is in the wall-parallel directions Δx ⁺=9 and Δz ⁺=4, resolving the relevant scales of motion. The simulation domain requires a total of 8⋅10⁹ grid points in physical space, and was thus run massively parallel with 4096 processors.