Large‐eddy simulations (LESs) of thermally stratified atmospheric boundary layers (ABLs) typically involve imposed heating or cooling at the ground surface, leading to slowly varying temperature distributions in the domain. While for some applications an interpretation of the resulting fields as quasi‐stationary is possible, there are certain applications for which the slow temporal variations are a serious drawback. An example occurs when using LES for a systematic analysis of effects of large wind farms on atmospheric heat fluxes, where analysis of stationary statistics greatly facilitates understanding. In order to obtain statistically stationary temperature fields in LES of thermally stratified boundary layers, in this article we introduce a control algorithm, and test its effectiveness for various levels of surface heating and cooling. The method uses a ‘proportional‐integral’ (PI) control algorithm, designed to keep constant the horizontally averaged temperature in a computational fringe layer placed above the ABL region of interest. For flows driven by a geostrophic wind, another controller is used to adjust the mean flow angle within the ABL at a specified height to achieve a prescribed direction. This is done by controlling a source term (in the form of an additional Coriolis force) in the momentum equations. This term is deactivated once the statistics become stationary and the flow aligns with the desired direction. Together, these two control schemes enable very long‐time simulations of thermally stratified heated or cooled boundary layers displaying fully stationary distributions of mean velocity and temperature.

We investigate flows interacting with square and fractal shape multi-scale structures in the compressible regime for Mach numbers under subsonic and supersonic upstream conditions using large-eddy simulations. We also aim at identifying similarities and differences that these interactions have with the corresponding interactions in the canonical incompressible flow problem. To account for the geometrical complexity associated with the fractal structures, we apply an immersed boundary method to model the no-slip boundary condition at the solid surfaces, with adequate mesh resolution in the vicinity of the small fractal features. We validate the numerical results through extensive comparisons with experimental wind tunnel measurements at a low Mach number. Similar to the incompressible flow case results, we find a breakup of the flow structures by the fractal plate and an increase in turbulent mixing in the downstream direction. As the Mach number increases, we observe noticeable wake meandering and higher spread rate of the wake in the lateral direction perpendicular to the streamwise–spanwise plane. Although not significant, we quantify the difference between the square and the fractal plates using two-point velocity correlations across the Mach number range. The wakes generated by the fractal plate in the compressible regime showed lower turbulent kinetic energy and energy spectra levels compared to those of the square case. Moreover, results in terms of the near-field pressure spectra seem to indicate that the fractal plate has the potential to reduce the aerodynamic noise.

Noise measurements of heated axisymmetric jets at a fixed supersonic acoustic Mach number indicate that the acoustic spectrum reduces when the temperature ratio increases. The “spectral quietening” effect has been observed both experimentally and computationally using large Eddy simulations. It was explained by Afsar, Goldstein, and Fagan [AIAA J. 49, 2522 (2011)] through the cancellation introduced by the enthalpy flux/momentum flux coupling term using the generalized acoustic analogy formulation. But the parallel flow assumption is known to give inaccurate predictions at high jet speeds. In this paper, we therefore extend the nonparallel flow asymptotic theory of Goldstein, Sescu, and Afsar [J. Fluid Mech. 695, 199 (2012)] for the vector Green’s function of the adjoint linearized Euler equations in the analogy. Using the steady Reynolds averaged Navier Stokes calculation for the jet mean flow, we find that the coupling term propagator is positive-definite and asymptotically subdominant at low frequencies corresponding to the peak jet noise when nonparallel flow effects are taken into account and self-consistent approximations for the turbulence structure are made. We then assess the validity of the non-parallel flow-based acoustic analogy model by computing the overall sound pressure level (OASPL) at various observation angles. Interpretation of the latter allows a more rational explanation of the quietening effect. In general, our noise predictions are in very good agreement with acoustic data beyond the peak frequency.