The temporal boundary layer under the action of decaying free-stream turbulence

The problem of the turbulent boundary layer under decaying free-stream turbulence is numerically investigated using the temporal boundary layer framework. This tool is particularly suited to the problem since the evolution of homogeneous isotropic turbulence is classically described by temporal decay. This study focuses on the interaction between the fully turbulent boundary layer and free-stream turbulence, which has so far received little attention compared to the behaviour of the transitional boundary layer subject to free-stream turbulence. The bulk of our simulations were completed by seeding the free-stream of boundary layers ‘pre-grown’ to a desired thickness with homogeneous isotropic turbulence from a precursor simulation. This strategy allowed us to test different combinations of the turbulence intensity and largeeddy lengthscale of the free-stream turbulence with respect to the velocity- and large-eddy length-scales of the boundary layer; such a parametric investigation would remain otherwise inaccessible given available computing resources. Additionally, the present strategy permits assessment of the direct effect of the locally present free-stream disturbances, as opposed to a ‘downstream’ effect from free-stream disturbances far ‘upstream’. The relative large-eddy turnover timescale between the free-stream turbulence and the boundary layer emerges as an important parameter in predicting if the free-stream turbulence and boundary layer interaction will be ‘strong’ or ‘weak’ before the free-stream turbulence eventually fades away. For a ‘strong’ interaction, the main action of the free-stream turbulence on the boundary layer is to cause increased spreading of the boundary layer away from the wall, which then permits incursions of free-stream fluid deep within it, changing the boundary layer velocity profiles in the outer part of the flow. This has the important effect of increasing the boundary layer thickness _ by flattening the intermittency profile.