Excitation and stability of nonlinear waves by a pair of steady waves in incompressible boundary layers

Abstract

The research explores the generation and stability of nonlinear waves in incompressible boundary layers, spotlighting the effects of dual steady waves. Using the Benjamin-Ono equation, modified for the incorporation of steady waves, we provide insights into the solitary wave generation process. A perturbed wave oscillator system is used for analyzing the stability of these nonlinear waves, uncovering that the loss of stability in low-order oscillators primarily governs wave transition and energy. Further, the study highlights the enlightening significance of complex terrain on the generation of nonlinear waves. Since the influence of terrain on the fluid passing over it usually appears as the external excitation of stationary waves, our study has important implications for terrain-fluid interactions.