Research on vortex breakdown: 

When a fluid moving in some direction is strongly rotated about that direction, i.e., swirled, it ends up spontaneously developing an isolated region of flow reversal (Fig. 1), referred to as vortex breakdown (VB). VB is observed in combustors, delta wings, tornadoes, etc. Based on the shape of the recirculation zone, VB can be classified as either a bubble or a conical form (BVB or CVB, see Fig. 1-3). In [1] (see Publications), we have performed the first numerical simulations of the CVB. Using hysteresis studies, we have shown that it can coexist with BVB as a bistable state (i.e., for the same boundary conditions) in both the laminar [2] (Fig. 2) and turbulent regimes [4]. Another significant feature of VB is the development of spiral structures in the flow (Fig. 1). Using linear stability analysis we have shown that these arise due to physical mechanisms unique to swirling jets [1]. We have also demonstrated how multiple such spiral structures can coexist as bistable states [2] and proposed an alternate hypothesis on the origins of the spiral form of VB [4]. 

The physical mechanisms governing VB remain unclear, although several mathematical models have been proposed previously. By finding analytical and numerical solutions we have shown in [3] that a popular model proposed by Benjamin (J. Fluid Mech., 1962), which explains VB as analogous to shock waves, is erroneous. We also show that the inviscid model proposed by Wang and Rusak (J. Fluid Mech., 1997) predicts unbounded recirculation zones.

Research on transonic buffet: 

The occurrence of self-sustained periodic flow oscillations on wing sections in the transonic regime is referred to as transonic buffet, which is detrimental to aircraft performance and manoeuvrability.  Using Large-Eddy Simulations, a spectral proper orthogonal decomposition and a low-rank flow reconstruction based only on the mode at buffet frequency, we show that the essential characteristics are the same for what were previously proposed as different transonic buffet types [5-7]. Further, we show that there are conditions for which buffet-like oscillations are present where the entire flow field is subsonic and demonstrate that it is directly linked to low-frequency oscillations observed in the incompressible regime [8]. This suggests that shock waves play only a secondary role in driving this instability.