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This paper focuses on the concept of delaying laminar–turbulent transition in hypersonic boundary layers by stabilising fundamental resonance (FR), a key nonlinear mechanism in which finite-amplitude Mack modes support the rapid growth of oblique perturbations. As a pioneering demonstration of this control strategy, we introduce surface heating applied exclusively during the nonlinear phase. Unlike traditional control methods that target the linear phase, the suppressive effect of surface heating on secondary instability modes during FR is evident across various Reynolds numbers, wall temperatures and fundamental frequencies, as confirmed by direct numerical simulations (DNS) and secondary instability analyses (SIA). To gain deeper insights into this control concept, an asymptotic analysis is conducted, revealing an almost linear relationship between the suppression effect and the heating intensity. The asymptotic predictions align overall with the DNS and SIA calculations. The asymptotic theory reveals that the suppression effect of FR is primarily influenced by modifications to the fundamental-mode profile, while mean-flow distortion has a comparatively modest yet opposing impact on this process. This research presents a promising approach to controlling transition considering the nonlinear evolution of boundary-layer perturbations, demonstrating advantages over conventional methods that are sensitive to frequency variations.
Ji et al. (Mon,) studied this question.