Forced oscillations, optimal forcing and resonance of thermal convection under small, time-varying forcing

This study proposes a method to obtain forced oscillation induced by arbitrary small time-varying forcing on a stable thermal convection field, and a framework for finding universal and inherent resonance modes on the field, independent of the ways of forced vibration, indicators of resonance and other information. It is based on an eigenvalue analysis of a Hermitian matrix relating to the frequency response function, and the typical forced oscillation at a resonance is given by the response to the optimal forcing as the eigenvector corresponding to the largest eigenvalue of the matrix. The method also provides indicators to quantify the efficiency in realizing a given resonance mode by a specific forced vibration. We can find thereby that heat-flux vibration not on the bottom wall but on the left-hand sidewall is preferred for realizing the internal gravity wave resonance.