Adjoint solutions of the linearized incompressible Navier–Stokes equations are presented for a cross-flow-dominated swept-wing boundary layer. For the first time these have been computed in the region upstream of the swept leading edge and may therefore be used to predict receptivity to any disturbances of the incoming free stream as well as to surface roughness. In this paper we present worst-case scenarios, i.e. those external disturbances yielding maximum receptivity amplitudes of a steady cross-flow disturbance. In the free stream, such an ‘optimal’ disturbance takes the form of a streak which, while being convected downstream, penetrates the boundary layer and smoothly turns into a growing cross-flow mode. The ‘worst-case’ surface roughness has a wavy shape and is distributed in the chordwise direction. It is shown that, under such optimal conditions, the boundary layer is more receptive to surface roughness than to incoming free stream disturbances.

Motivated by the laboratory experiments of Browand & Winant (Geophys. Fluid Dyn., vol. 4, 1972, pp. 29–53), a series of two-dimensional numerical simulations of flow past a cylinder of diameter are run for different values of the approach Froude number between and at . The observed flow is characterized by blocking and upstream influence in front of the cylinder and by relatively thin, fast jets over the top and bottom of the cylinder. This continuously stratified flow can be understood in terms of an inviscid non-diffusive integral inertia–buoyancy balance reminiscent of reduced-gravity single-layer hydraulics, but one where the reduced gravity is coupled to the thickness of the jets. The proposed theoretical framework describes the flow upstream of the obstacle and at its crest. The most important elements of the theory are the inclusion of upstream influence in the form of blocked flow within an energetically constrained depth range and the recognition that the flow well above and well below the active, accelerated layers is dynamically uncoupled. These constraints determine, through continuity, the transport in the accelerated layers. Combining these results with the observation that the flow is asymmetric around the cylinder, i.e. hydraulically controlled, allows us to determine the active layer thicknesses, the effective reduced gravity and thus all of the integral flow properties of the fast layers in good agreement with the numerically computed flows.

The lattice Boltzmann method has become a widely used tool for the numerical simulation of fluid flows and in particular of turbulent flows. In this frame the inclusion of subgrid scale closures is of crucial importance and is not completely understood from the theoretical point of view. Here, we propose a consistent way of introducing subgrid closures in the BGK Boltzmann equation for large eddy simulations of turbulent flows. Based on the Hermite expansion of the velocity distribution function, we construct a hierarchy of subgrid scale terms, which are similar to those obtained for the Navier–Stokes equations, and discuss their inclusion in the lattice Boltzmann method scheme. A link between our approach and the standard way on including eddy viscosity models in the lattice Boltzmann method is established. It is shown that the use of a single modified scalar relaxation time to account for subgrid viscosity effects is not consistent in the compressible case. Finally, we validate the approach in the weakly compressible case by simulating the time developing mixing layer and comparing with experimental results and direct numerical simulations.