Abstract
The authors have proposed a framework of a linear theory for finding inherent resonant states and optimal forced vibration on a given stable thermal convection field, independent of the ways of forced vibration, indicators of resonances and so on. It is based on a dynamical system theory, applicable to capture any resonance states on a stable steady system subject to a forced vibration, not limited to thermal convection fields. However, its applicability is largely dependent on the amplitude of time-varying forcing. It is clarified, in this study, that a weakly nonlinear expression of midplane Nusselt number allows us to identify the effective range of the amplitude. It implies that the weakly nonlinear analyses provide the measure on the effectiveness of the linear theory.
