Numerical investigation of cross waves in water flume with a shoal

This study examines the symmetrical and anti-symmetrical transverse modes of cross waves in a water flume, particularly focusing on those induced by longitudinally incident waves created by a wavemaker. The primary modes with the lowest mode numbers, symmetrical (1,0) and anti-symmetrical (1,1), were the focus due to their significant energy concentration. Numerical simulations were employed to investigate their occurrence mechanism, evolution processes, and spatial patterns, along with the factors influencing their behavior. Following experimental observations and preliminary analytical solutions, the simulations delved into the detailed behavior of these transverse modes, confirming their presence and characteristics through comparison with analytical solutions. The study reveals that minor perturbations, like water surface disturbances or cross slope variations on the hyperbolic cosine shoal, are essential for exciting these modes. Notably, while symmetrical and anti-symmetrical transverse waves can be initially excited, they cannot maintain a steady form and decay rapidly, indicating their transient nature in the flume environment. The incident wave height and bathymetrical parameter significantly influence the development and characteristics of these waves, with larger incident waves promoting more frequent and varied transverse modes. The interaction between longitudinal and transverse modes on the hyperbolic cosine shoal was also preliminarily observed, aligning with previous studies and suggesting a need for further investigation into their interaction and energy transfer mechanisms.