The structure of the turbulent flow over a simplified automotive model, the Ahmed body (S. R. Ahmed and G. Ramm, SAE Paper No. 8403001, 1984) with a 25° slanted back face, is investigated using high-order large-eddy simulations (LESs) at Reynolds number $\mathrm{Re}=768000$ . The numerical approach is carried out with a multidomain spectral Chebyshev–Fourier solver and the bluff body is modeled with a pseudopenalization method. The LES capability is implemented thanks to a spectral vanishing viscosity (SVV) technique, with particular attention to the near wall region. Such a SVV-LES approach is extended for the first time to an industrial three-dimensional turbulent flow over a complex geometry. In order to better understand the interactions between flow separations and the dynamic behavior of the released vortex wake, a detailed analysis of the flow structures is provided. The topology of the flow is well captured showing a partial separation of the boundary layer over the slanted face and the occurrence of two strong contrarotating trailing vortices expanding farther in the wake. The interactions of these large vortices with smaller structures reminiscent of horseshoe vortices, within the shear layer over the slanted face, form large helical structures providing strong unsteady phenomena in the wake. Mean velocity fields and turbulence statistics show a global agreement with the reference experiments of Lienhart et al. (DGLR Fach Symposium der AG SRAB, Stuttgart University, 15–17 November 2000). In order to provide a deeper insight into the nature of turbulence, the flow is analyzed using power spectra and the invariant theory of turbulence of Lumley [Adv. Appl. Mech. 18, 123 (1978)].

This article reviews the range of flows that may be created within thin cylindrical or annular cavities due to the rotation of one of the confining disks. At low Reynolds numbers, the rotation gives rise to an axisymmetric, radially outward motion near the rotor with a return flow along the stationary disk. As the Reynolds number is raised, this base flow gives way to a shear flow populated by discrete vortices, whether of cylindrical or spiral form, near both the rotating and stationary disks. At Reynolds numbers high enough for turbulent flow to occur, in the twentieth century both experimental and computational studies treated the flow as axisymmetric and steady. Recent research has shown, however, that complex organized structures also persist in the turbulent regime.

Different instabilities of the boundary layer flows that appear in the cavity between stationary and rotating discs are investigated using three-dimensional direct numerical simulations. The influence of curvature and confinement is studied using two geometrical configurations: (i) a cylindrical cavity including the rotation axis and (ii) an annular cavity radially confined by a shaft and a shroud. The numerical computations are based on a pseudo-spectral Chebyshev–Fourier method for solving the incompressible Navier–Stokes equations written in primitive variables. The high level accuracy of the spectral methods is imperative for the investigation of such instability structures. The basic flow is steady and of the Batchelor type. At a critical rotation rate, stationary axisymmetric and/or three-dimensional structures appear in the Bödewadt and Ekman layers while at higher rotation rates a second transition to unsteady flow is observed. All features of the transitions are documented. A comparison of the wavenumbers, frequencies, and phase velocities of the instabilities with available theoretical and experimental results shows that both type II (or A) and type I (or B) instabilities appear, depending on flow and geometric control parameters. Interesting patterns exhibiting the coexistence of circular and spiral waves are found under certain conditions.