The study of a turbulent air flow over capillary–gravity water surface waves: Characteristics of coherent vortical structures

Abstract

This study is concerned with the characteristics of coherent vortices within the turbulent air flow undulated by gravity and capillary–gravity water waves. The flow fields from the direct numerical simulations are analyzed. A formal scheme is developed to detect and classify the vortical structures. The scheme uses local analysis of the velocity-gradient tensor to define the vortex swirling core, and adopts the topological geometry of the swirling core to classify the vortical structures. Three types of vortical structures are identified, including quasi-streamwise vortex, reversed and forward (head pointing upstream and downstream, respectively) horseshoe vortices. Quasi-streamwise vortices are the dominant structure in the flow; their distribution initiates near the wave trough, extends downstream along the windward face, lifts up and terminates above the wave crest. More reversed horseshoe vortices are observed than the forward horseshoe vortices; both cluster around the region above wave trough. Reversed and forward horseshoe vortices, however, contribute the most to the production of Reynolds stress associated with sweep and ejection motions, respectively. The quasi-streamwise vortices contribute more to producing Reynolds stress associated with ejection event, indicating that the elongated vortices bend inward at the downstream end and can be considered as degenerate forward horseshoe vortices. The intensified distributions of horseshoe vortices near the wave trough are attributed to the combined effect of vortex turning from the spanwise turbulent component to the streamwise vortex and the vortex stretching of the streamwise vortex. The strong stretching of streamwise vortex above the windward face contributes to the continuous development of quasi-streamwise vortices. Accordingly, the presence of capillary ripples on the windward face mitigates effectively the occurrence of coherent vortices, in particular the quasi-streamwise vortices. In contrast, the presence of capillary ripples on the leeward surface presents a minor effect on the mitigation of coherent vortices.