Academic literature on the topic 'Instability and transition'

This paper performs direct numerical simulations of hypersonic boundary layer transition over a Hypersonic Transition Research Vehicle (HyTRV) model lifting body designed by the China Aerodynamic Research and Development Center. Transitions are simulated at four angles of attack: 0°, 3°, 5°, and 7°. The free-stream Mach number is 6, and the unit Reynolds number is 107 m−1. Four distinct transitional regions are identified: the shoulder cross-flow and vortex region and the shoulder vortex region on the leeward side, the windward vortex region and the windward cross-flow region on the windward side. As the angle of attack increases, the transition locations on the leeward side generally move forward and the transition ranges expand, while the transition locations generally move backward and the transition ranges decrease on the windward side. Moreover, the shoulder vortex region moves toward the centerline of the leeward side. At large angles of attack (5° and 7°), the streamwise vortex on the shoulder cross-flow and vortex region will enable the transition region to be divided into the cross-flow instability region on both sides and the streamwise vortex instability region in the middle. In addition, the streamwise vortex also leads to a significant increase in cross-flow instability in their upper region, which can generate a new streamwise vortex instability region between the two transition regions on the leeward side. Furthermore, since the decrease in the intensity and the range for the cross-flow on the windward side, the windward cross-flow region tends to become narrow and ultimately disappears.

A detailed numerical study of the separating and reattaching flow over a square leading-edge plate is presented, examining the instability modes governing transition from two- to three-dimensional flow. Under the influence of background noise, experiments show that the transition scenario typically is incompletely described by either global stability analysis or the transient growth of dominant optimal perturbation modes. Instead two-dimensional transition effectively can be triggered by the convective Kelvin–Helmholtz (KH) shear-layer instability; although it may be possible that this could be described alternatively in terms of higher-order optimal perturbation modes. At least in some experiments, observed transition occurs by either: (i) KH vortices shedding downstream directly and then almost immediately undergoing three-dimensional transition or (ii) at higher Reynolds numbers, larger vortical structures are shed that are also three-dimensionally unstable. These two paths lead to distinctly different three-dimensional arrangements of vortical flow structures. This paper focuses on the mechanisms underlying these three-dimensional transitions. Floquet analysis of weakly periodically forced flow, mimicking the observed two-dimensional quasi-periodic base flow, indicates that the two-dimensional vortex rollers shed from the recirculation region become globally three-dimensionally unstable at a Reynolds number of approximately 380. This transition Reynolds number and the predicted wavelength and flow symmetries match well with those of the experiments. The instability appears to be elliptical in nature with the perturbation field mainly restricted to the cores of the shed rollers and showing the spatial vorticity distribution expected for that instability type. Indeed an estimate of the theoretical predicted wavelength is also a good match to the prediction from Floquet analysis and theoretical estimates indicate the growth rate is positive. Fully three-dimensional simulations are also undertaken to explore the nonlinear development of the three-dimensional instability. These show the development of the characteristic upright hairpins observed in the experimental dye visualisations. The three-dimensional instability that manifests at lower Reynolds numbers is shown to be consistent with an elliptic instability of the KH shear-layer vortices in both symmetry and spanwise wavelength.

Speed-related gait transitions occur in many animals, but it remains unclear what factors trigger gait changes. While the most widely accepted function of gait transitions is that they reduce locomotor costs, there is no obvious metabolic trigger signalling animals when to switch gaits. An alternative approach suggests that gait transitions serve to reduce locomotor instability. While there is evidence supporting this in humans, similar research has not been conducted in other species. This study explores energetics and stride variability during the walk–run transition in mammals and birds. Across nine species, energy savings do not predict the occurrence of a gait transition. Instead, our findings suggest that animals trigger gait transitions to maintain high locomotor rhythmicity and reduce unstable states. Metabolic efficiency is an important benefit of gait transitions, but the reduction in dynamic instability may be the proximate trigger determining when those transitions occur.

The laminar-turbulent transition of three-dimensional boundary layers is critically reviewed for some typical axisymmetric bodies rotating in still fluid or in axial flow. The flow structures of the transition regions are visualized. The transition phenomena are driven by the compound of the Tollmien-Schlichting instability, the crossflow instability, and the centrifugal instability. Experimental evidence is provided relating the critical and transition Reynolds numbers, defined in terms of the local velocity and the boundary layer momentum thickness, to the local rotational speed ratio, defined as the ratio of the circumferential speed to the free-stream velocity at the outer edge of the boundary layer, for the rotating disk, the rotating cone, the rotating sphere and other rotating axisymmetric bodies. It is shown that the cross-sectional structure of spiral vortices appearing in the transition regions and the flow pattern of the following secondary instability in the case of the crossflow instability are clearly different than those in the case of the centrifugal instability.