Linear modeling of a family of turbulent separation bubbles

The low-frequency linear dynamics of a family of incompressible, pressure-gradient (PG)-induced turbulent separation bubbles (TSBs) are studied by means of modal and nonmodal linear analysis. The investigated data consist of Reynolds-averaged Navier-Stokes simulations and experimental measurements that are used for validation purposes. The TSBs are generated on a flat plate by means of adverse (APG) and favorable (FPG) PGs, such that the family of TSBs consists of three distinct cases—small, medium, and large—where the size of the separation bubble is controlled by the strength and location of the maximum APG and FPG. The investigation of the linear dynamics of the family of TSBs reveals two significant results: First, the low-frequency receptivity of the TSB flow, characterized by the low-pass filter behavior of the optimal gain, remains unaffected by the absence of a closed TSB in the time average for the small-sized TSB (small-bubble case). Second, although the large TSB flow is predicted to be globally unstable for a set of spanwise wavenumbers, the amplifier dynamics of the flow appear to dominate over the oscillator dynamics, as evidenced by the persistence of low-frequency unsteadiness in the experimental large-bubble flow. These results suggest that a common physical mechanism, characterized by the stationary, weakly damped global mode, governs the low-frequency unsteadiness across the entire family of TSBs, irrespective of their separation extent or stability characteristics.