  The low-frequency modal and non-modal stability characteristics of an
incompressible, pressure-gradient-induced turbulent separation bubble (TSB) are
investigated with the objective of studying the mechanism responsible for the
low-frequency contraction and expansion (breathing) commonly observed in
experimental studies. The configuration of interest is a TSB generated on a
flat test surface by a succession of adverse and favourable pressure gradients.
The base flow selected for the analysis is the average TSB from the direct
numerical simulation of Coleman et al. (J. Fluid Mech., vol. 847, 2018). Global
linear stability analysis reveals that the flow is globally stable for
wavenumbers. The mode closest to the stability threshold appears to occur at
zero frequency and low, non-zero spanwise wavenumber. Resolvent analysis is
then employed to examine the forced dynamics of the flow. At low frequency, a
region of low, non-zero spanwise wavenumber is also discernible, where the
receptivity appears to be driven by the identified weakly damped global mode.
The results from resolvent analysis are compared to the unsteady experimental
database of Le Floc'h et al. (J. Fluid Mech., vol. 902, 2020) in a similar TSB
flow. The alignment between the optimal response and the first spectral proper
orthogonal decomposition mode computed from the experiments is shown to exceed
95 %, while the spanwise wavenumber of the optimal response is consistent with
that of the low-frequency breathing motion captured experimentally. This
indicates that the fluctuations observed experimentally at low frequency
closely match the response computed from resolvent analysis. Based on these
results, we propose that the forced dynamics of the flow, driven by the weakly
damped global mode, serve as a plausible mechanism for the origin of the
low-frequency breathing motion commonly observed in experimental studies of
TSBs.
