Complex flow structures beneath rotational depression solitary waves in gravity-capillary flows

Particle trajectories beneath depression solitary gravity-capillary waves in the weakly nonlinear weakly dispersive regime in a sheared channel with finite depth and constant vorticity are investigated. A fifth-order Korteweg-de Vries equation that incorporates the surface tension and the vorticity effects is derived asymptotically from the full Euler equations when the Bond number is nearly a critical value that depends on the vorticity. The velocity field in the bulk fluid is approximated which allow us to study the submarine structures beneath depression solitary waves. The dynamical system of particle trajectories is reformulated in the moving wave frame and its features are seen through the streamlines. We show that for large values of the vorticity parameter there are always stagnation points in the bulk fluid, which produce rich cat's-eyes structures. In this case, particle trajectories can undergo vertical excursions, describing closed orbits or undergo pure horizontal transport. Furthermore, bifurcation diagrams according to the number of stagnation points and complex flow structures beneath depression solitary waves with multiple local extrema are shown.(c) 2022 Elsevier B.V. All rights reserved.