Figure 3. Hydrodynamic benefits and linear phase-distance relationship in pairwise formations.

(A) Change in cost of transport compared to solitary swimmers for the inline, diagonal, side-by-side inphase, and side-by-side antiphase formations shown in Figure 1. (B) Emergent formations in pairs of swimmers in computational fluid dynamics (CFD) and vortex sheet (VS) models satisfy a linear phase-distance relationship, consistent with experimental (Ramananarivo et al., 2016; Newbolt et al., 2019; Li et al., 2020; Kurt et al., 2021; Thandiackal and Lauder, 2023) and numerical (Kim et al., 2010; Peng et al., 2018; Heydari and Kanso, 2021; Arranz et al., 2022) studies. With the exception of the antiphase side-by-side formation, swimmers in these formations have a reduced average cost of transport compared to solitary swimming.