Stochastic dynamics of vortex-acoustic lock-in: effects of coloured, multiplicative noise

The paper discusses the stochastic dynamics of the vortex shedding process in the presence of external harmonic excitation and coloured multiplicative noise. The situation is encountered in a turbulent practical combustor experiencing combustion instability. Acoustic feedback and turbulent flow are imitated by the harmonic and stochastic excitations, respectively. The Ornstein–Uhlenbeck process is used to generate the noise. A low-order model for vortex shedding is used. The Fokker–Planck framework is used to obtain the evolution of the probability density function of the shedding time period. Stochastic lock-in and resonance characteristics are studied for various parameters associated with the harmonic (amplitude, frequency) and noise (amplitude, correlation time, multiplicative noise factor) excitations. We observed that: (i) the stochastic lock-in (s-lock-in) boundary strongly depends on the noise correlation time; (ii) the parameter sites for s-lock-in can be approximately identified from the noise-induced shedding statistics; and (iii) stochastic resonance is significant for some intermediate correlation times. The effects of the above-mentioned observations are discussed in the context of combustion instability.