Flapping dynamics of coupled flexible flags in a uniform viscous flow

Abstract

Fish schooling and aggregation are some of the most prominent social and group activities, and within the school, fish position themselves in a staggered formation to swim more efficiently using the wakes created by other fish. In order to examine vortex-to-vortex and vortex-to-flexible body interactions in a school, a group of multiple flexible flags arranged in a staggered manner is modeled by a numerical simulation using an improved version of the immersed boundary method. In addition to triangular and diamond formations of flags in which a single flag is placed at the most upstream position in a staggered alignment (Uddin et al., 2013), a collection of individuals with two flags in the first row produces inverted triangular and X-shaped formations, characterized by distinctive flapping dynamics. The flapping dynamics of the flags at the two formations are identified based on the trailing tail position, a phase plot, the energy spectrum and vorticity contours. The drag of the downstream flags is determined by either constructive or destructive interaction mode between vortices shed from the upstream and downstream flags, depending on the streamwise and spanwise gap distances between the flags. In addition, the drag of the upstream flags is positively or negatively influenced by the pressure field created by the downstream flags. Side-by-side flags undergo low drag due to the direct spanwise interactions between them with small gap distances. Although two upstream flags in an inverted triangular formation show typical flapping dynamics of side-by-side flags with a spanwise gap distance, the flapping of two side-by-side flags in the first and third rows in an X-shaped formation exhibits an in-phase mode even at a large spanwise gap distance, suggesting the presence of a two-way interaction whereby the upstream flags force the downstream flags into an in-phase flapping mode and the downstream flags in turn organize the upstream flapping into an in-phase flapping mode. An optimal configuration for the flags arranged in the X-shaped formation is provided for a highly efficient hydrodynamic effect of the flags.