The leading-edge vortex (LEV) is known to produce transient high lift in a wide variety of circumstances. The underlying physics of LEV formation, growth, and shedding are explored for a set of canonical wing motions including wing translation, rotation, and pitching. A review of the literature reveals that, while there are many similarities in the LEV physics of these motions, the resulting force histories can be dramatically different. In two-dimensional motions (translation and pitch), the LEV sheds soon after its formation; lift drops as the LEV moves away from the wing. Wing rotation, in contrast, incites a spanwise flow that, through Coriolis tilting, balances the streamwise vorticity fluxes to produce an LEV that remains attached to much of the wing and thus sustains high lift. The state of the art of vortex-based modeling to capture both the flow field and corresponding forces of these motions is reviewed, including closure conditions at the leading edge and approaches for data-driven strategies.

The effectiveness of a cylindrical perforated liner with mean bias flow in its absorption of planar acoustic waves in a duct is investigated. The liner converts acoustic energy into flow energy through the excitation of vorticity fluctuations at the rims of the liner apertures. A one-dimensional model that embodies this absorption mechanism is developed. It utilizes a homogeneous liner compliance adapted from the Rayleigh conductivity of a single aperture with mean flow. The model is evaluated by comparing with experimental results, with excellent agreement. We show that such a system can absorb a large fraction of incoming energy, and can prevent all of the energy produced by an upstream source in certain frequency ranges from reflecting back. Moreover, the bandwidth of this strong absorption can be increased by appropriate placement of the liner system in the duct. An analysis of the acoustic energy flux is performed, revealing that local differences in fluctuating stagnation enthalpy, distributed over a finite length of duct, are responsible for absorption, and that both liners in a double-liner system are absorbant. A reduction of the model equations in the limit of long wavelength compared to liner length reveals an important parameter grouping, enabling the optimal design of liner systems.

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We report on axisymmetric numerical simulations of rapidly rotating spherical shells in which the axial rotation rate of the outer shell is modulated in time. This allows us to model planetary bodies undergoing forced longitudinal libration. In this study we systematically vary the Ekman number, 10 −7 Յ E Շ 10 −4 , which characterizes the ratio of viscous to Coriolis forces in the fluid, and the libration amplitude, ⌬. For libration amplitudes above a certain threshold, Taylor-Görtler vortices form near the outer librating boundary, in agreement with the previous laboratory experiments of Noir et al. ͓Phys. Earth Planet. Inter. 173, 141 ͑2009͔͒. At the lowest Ekman numbers investigated, we find that the instabilities remain spatially localized at onset in the equatorial region. In addition, nonzero time-averaged azimuthal ͑zonal͒ velocities are observed for all parameters studied. The zonal flow is characterized by predominantly retrograde flow in the interior, with a stronger prograde jet in the outer equatorial region. The magnitude of the zonal flow scales as the square of the librational forcing, ⑀ 2 , where ⑀ = ⌬f and f is the dimensionless libration frequency defined as the ratio between the libration frequency and the mean angular rotation rate. In addition, the zonal flow is primarily independent of the Ekman number, implying that the zonal flow does not depend on the viscosity of the fluid. The simulations show that the zonal flow is driven by nonlinearities in the Ekman boundary layer; it is not driven by Taylor-Görtler vortices or by inertial waves in the fluid interior. Application of our results suggests that many librating bodies in the solar system are above the onset for centrifugal instabilities, with values up to ϳ30 times supercritical. However, the spatial localization of the instabilities at onset in our simulations suggests that their effects are limited on the global dynamics of librating bodies. We find that the zonal flows driven by libration in axisymmetric spherical shells are unlikely to produce significant planetary magnetic fields, but will likely generate nonzero mean torques on the bounding surfaces.