Philipp Schlatter, KTH Mechanics

The turbulent flow close to solid walls is a major topic in today's research in fluid dynamics. In nature and technical applications such walls are usually not perfectly flat, and also curved. Thus the mean flow is seldomly exactly two-dimensional, the spatially developing, zero-pressure gradient turbulent boundary layer on a flat plate has emerged as an important canonical flow case for theoretical, numerical as well as experimental studies. In recent years, a number of careful experiments have been conducted featuring accurately controlled experimental conditions. Some of these experiments aim at investigating the flow behaviour at high Reynolds numbers (e.g. high velocities), but there are also some experimental studies that included data points at Reynolds numbers that are accessible to fully-resolved numerical simulations. Two of these studies have actually been performed at KTH, namely the ones by Österlund (1999) and Örlu (2009). These experiments include a few data points below Reθ=6000. This particular Reynolds number, common for boundary layers, is based on the momentum thickness θ and the free-stream velocity U∞.

However, only recently spatially developing turbulent boundary layers have been considered with numerical simulations. 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, also the numerical cost of such spatial simulations is comparably high due to the long domains necessary for the full development of all relevant turbulent scales.

At KTH Mechanics, we have recently peformed a number of direct and large-eddy simulations pertaining to canonical turbulent boundary layers under zero-pressure-gradient. The largest of these simulations, based on a fully spectral discretisation, uses about 10 billion grid points. In that regard this is the largest simulation of such a geometry that has been performed so far; due to the large computational cost such simulations need to be run on large parallel supercomputers; in the present case we could use the SNIC/KAW system Ekman at PDC. The boundary layer is tripped to turbulence close to the numerical inlet at low Reynolds numbers, and thus the flow is allowed to develop over a long streamwise distance. The simulation covers thus a long, wide and high domain starting at Reθ=180 extending up to the (numerically high) value of Reθ=4300. Fully turbulent flow is obtained starting from Reθ=500. Thus, the range of Reynolds numbers is considerably extended compared to previous simulations.

The seminar will summarise some of the basic concepts related to turbulent wall-bounded flow, e.g. scalings and profiles. Then, the difficulties of performing simulations of boundary layers are discussed, also in comparison with channel-flow simulations at similar Reynolds numbers. The last part will give a outline of some of the main results that have been obtained using such simulations. One particularly interesting result is related to the dynamics in wall-bounded flows: How do the actual vortical structures look like, i.e. what are the basic building blocks of wall turbulence, if any? Can the turbulent flow been considered as an ensemble of hairpin-like vortices?