Experimental investigations of laminar swirling jets had revealed a new form of vortex breakdown, named conical vortex breakdown, in addition to the commonly observed bubble form. The present study explores these breakdown states that develop for the Maxworthy profile (a model of swirling jets) at inflow, from streamwise-invariant initial conditions, with direct numerical simulations. For a constant Reynolds number based on jet radius and a centreline velocity of 200, various flow states were observed as the inflow profile’s swirl parameter $S$ (scaled centreline radial derivative of azimuthal velocity) was varied up to 2. At low swirl ( $S=1$ ) a helical mode of azimuthal wavenumber $m=-2$ (co-winding, counter-rotating mode) was observed. A ‘swelling’ appeared at $S=1.38$ , and a steady bubble breakdown at $S=1.4$ . On further increase to $S=1.5$ , a helical, self-excited global mode ( $m=+1$ , counter-winding and co-rotating) was observed, originating in the bubble’s wake but with little effect on the bubble itself – a bubble vortex breakdown with a spiral tail. Local and global stability analyses revealed this to arise from a linear instability mechanism, distinct from that for the spiral breakdown which has been studied using Grabowski profile (a model of wing-tip vortices). At still higher swirl ( $S=1.55$ ), a pulsating type of bubble breakdown occurred, followed by conical breakdown at 1.6. The latter consists of a large toroidal vortex confined by a radially expanding conical sheet, and a weaker vortex core downstream. For the highest swirls, the sheet was no longer conical, but curved away from the axis as a wide-open breakdown. The applicability of two classical inviscid theories for vortex breakdown – transition to a conjugate state, and the dominance of negative azimuthal vorticity – was assessed for the conical form. As required by the former, the flow transitioned from a supercritical to subcritical state in the vicinity of the stagnation point. The deviations from the predictions of the latter model were considerable.

Transonic buffet refers to the self-sustained periodic motion of shock waves observed in transonic flows over wings and can limit the flight envelope of aircraft. Based on the boundary layer characteristics at the shock foot, buffet has been classified as laminar or turbulent and the mechanisms underlying the two have been proposed to be different (Dandois et al., J. Fluid Mech., vol. 18, 2018, pp. 156–178). The effect of various flow parameters (freestream Mach and Reynolds numbers and sweep and incidence angles) on laminar transonic buffet on an infinite wing (Dassault Aviation's supercritical V2C aerofoil) is reported here by performing large-eddy simulations (LES) for a wide range of parameters. A spectral proper orthogonal decomposition identified the presence of a low-frequency mode associated with buffet and high-frequency wake modes related to vortex shedding. A flow reconstruction based only on the former shows periodic boundary-layer separation and reattachment accompanying shock wave motion. A modal reconstruction based only on the wake mode suggests that the separation bubble breathing phenomenon reported by Dandois et al. is due to this mode. Together, these results indicate that the physical mechanisms governing laminar and turbulent buffet are the same. Buffet was also simulated at zero incidence. Shock waves appear on both aerofoil surfaces and oscillate out of phase with each other indicating the occurrence of a Type I buffet (Giannelis et al., Aerosp. Sci. Technol., vol. 18, 2018, pp. 89–101) on a supercritical aerofoil. These results suggest that the mechanisms underlying different buffet types are the same.

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Transonic buffet is commonly associated with self-sustained flow unsteadiness involving shock-wave/boundary-layer interaction over airfoils and wings. The phenomenon has been classified as either laminar or turbulent based on the state of the boundary layer immediately upstream of the shock foot, and distinct mechanisms for the two types have been suggested. The turbulent case is known to be associated with a global linear instability. Herein, large-eddy simulations are used for the first time to make direct comparisons of the two types by examining free- and forced-transition conditions. Corresponding simulations based on the Reynolds-averaged Navier–Stokes equations for the forced-transition case are also performed for comparison with the scale-resolving approach and for linking the findings with existing literature. Coherent flow features are scrutinized using both data-based spectral proper orthogonal decomposition of the time-marched results and operator-based global linear stability and resolvent analyses within the Reynolds-averaged Navier–Stokes framework. It is demonstrated that the essential dynamic features remain the same for the two buffet types (and for the two levels of the aerodynamic modeling hierarchy), suggesting that both types arise due to the same fundamental mechanism.

Transonic buffet is an unsteady flow phenomenon that limits the safe flight envelope of modern aircraft. Scale-resolving simulations with span-periodic boundary conditions are capable of providing new insights into its flow physics. The present contribution shows the co-existence of multiple modes of flow unsteadiness over an unswept laminar-flow wing section, appearing in the following order of increasing frequency: (a) a low-frequency transonic buffet mode, (b) an intermediate-frequency separation bubble mode, and (c) high-frequency wake modes associated with vortex shedding. Simulations are run over a range of Reynolds and Mach numbers to connect the lower frequency modes from moderate to high Reynolds numbers and from pre-buffet to established buffet conditions. The intermediate frequency mode is found to be more sensitive to Reynolds-number effects compared to those of Mach number, which is the opposite trend to that observed for transonic buffet. Spectral proper orthogonal decomposition is used to extract the spatial structure of the modes. The buffet mode involves coherent oscillations of the suction-side shock structure, consistent with previous studies including global mode analysis. The laminar separation-bubble mode at intermediate frequency is fundamentally different, with a phase relationship between separation and reattachment that does not correspond to a simple ‘breathing’ mode and is not at the same Strouhal number observed for shock-induced separation bubbles. Instead, a Strouhal number based on separation bubble length and reverse flow magnitude is found to be independent of Reynolds number within the range of cases studied.