Subgrid-scale (SGS) modelling is formulated using a local transport of spectral kinetic energy estimated by a wavelet multiresolution analysis. Using a spectrally and spatially local decomposition by wavelet, the unresolved inter-scale energy transfer and modelled SGS dissipation are evaluated to enforce explicitly and optimally their balance a priori over a range of large-eddy simulation (LES) filter widths. The formulation determines SGS model constants that optimally describe the spectral energy balance between the resolved and unresolved scales at a given cutoff scale. The formulation is tested for incompressible homogeneous isotropic turbulence (HIT). One-parameter Smagorinsky- and Vreman-type eddy-viscosity closures are optimised for their model constants. The algorithm discovers the theoretical prediction of Lilly (The representation of small-scale turbulence in numerical simulation experiments. In Proceedings of the IBM Scientific Computing Symposium on Environmental Sciences, pp. 195–210) at a filter cutoff scale in the inertial subrange, whereas the discovered constants deviate from the theoretical value at other cutoff scales so that the spectral optimum is achieved. The dynamic Smagorinsky model used a posteriori shows a suboptimal behaviour at filter scales larger than those in the inertial subrange. A two-parameter Clark-type closure model is optimised. The optimised constants provide evidence that the nonlinear gradient model of Clark et al. (J. Fluid Mech., vol. 91, issue 1, 1979, pp. 1–16) is prone to numerical instability due to its model form, and combining the pure gradient model with a dissipative model such as the classic Smagorinsky model enhances numerical stability but the standard mixed model is not optimal in terms of spectral energy transfer. A posteriori analysis shows that the optimised SGS models produce accurate LES results.

Efforts to reduce the noise from turbulent jets at fixed flow conditions, with aircraft noise as the principal technological motivation, have generally involved some degree of parametric empiricism often based upon a series of trial-and-error testing. As a result, it is unclear if the modest reductions found, in rare cases that do not greatly affect the flow field or incur prohibitive losses, are near the limit of what can be accomplished or if there are undiscovered opportunities for more substantive reductions with better designs or active control. We assess this using an adjoint-based optimization procedure in conjunction with an experimentally validated large-eddy simulation of a Mach 1.3 turbulent jet. The adjoint solution provides a definitive direction in which to adjust a model control actuation in order to reduce noise, providing guidance that seems lacking by any other current means. It is found that three conjugate-gradient iterations in the control space provide ∼3.5 dB of reduction, comparable to other reductions found empirically. The control seems to work by disrupting the coherence of acoustically efficient axisymmetric flow structures. The control and noise-reduction mechanisms are informative, but also suggest that any significantly quieter state would not be a simple perturbation from the uncontrolled jet. Additional iterations might reduce noise more significantly, but there might be only modest opportunities to reduce the sound from simple round turbulent jets without radical changes or relatively sophisticated controls. Though it is difficult to prove any behaviour in a global space of actuations, there does not seem to be a direct route based upon a local sensitivity gradient to substantially quieting a jet, even with an unrealistically flexible actuation. More complex jets or other noisy flows may be more amenable to control, in which case the adjoint-based optimization procedure demonstrated here could provide invaluable engineering guidance.

In this paper, we present a new passive control device for form-drag reduction in flow over a two-dimensional bluff body with a blunt trailing edge. The device consists of small tabs attached to the upper and lower trailing edges of a bluff body to effectively perturb a two-dimensional wake. Both a wind-tunnel experiment and large-eddy simulation are carried out to examine its drag-reduction performance. Extensive parametric studies are performed experimentally by varying the height and width of the tab and the spanwise spacing between the adjacent tabs at three Reynolds numbers of $\hbox{\it Re}\,{=}\,u_\infty h/\nu\,{=}\,20\,000$, 40 000 and 80 000, where $u_\infty$ is the free-stream velocity and $h$ is the body height. For a wide parameter range, the base pressure increases (i.e. drag reduces) at all three Reynolds numbers. Furthermore, a significant increase in the base pressure by more than 30% is obtained for the optimum tab configuration. Numerical simulations are performed at much lower Reynolds numbers of $\hbox{\it Re}\,{=}\,320$ and 4200 to investigate the mechanism responsible for the base-pressure increase by the tab. Results from the velocity measurement and numerical simulations show that the tab introduces the spanwise mismatch in the vortex-shedding process, resulting in a substantial reduction of the vortical strength in the wake and significant increases in the vortex formation length and wake width.