Background: From the laboratory at Scripps Institution of Oceanography, one can observe the brown pelican (Pelecanus occidentalis) traveling along the crests of near-shoaling waves just outside the surf zone. In this manner, the birds travel great distances without flapping, all the while a scant ~ 30 cm off the ocean's surface. Here we derive a theoretical framework for assessing the energetic benefit of this behavior, "wave-slope soaring,'' in which an organism in flight takes advantage of updrafts caused by traveling ocean surface gravity waves.
Methods: The energy cost of steady, constant altitude flight is analyzed as a control. Potential flow theory is used to quantify the ocean wave-induced wind associated with near-shoaling, weakly nonlinear, shallow water ocean surface gravity waves. Using a regular expansion of the Stokes stream function and the Green's function for Laplace's equation in 2D with Dirichlet boundary conditions, we obtain integral expressions for the horizontal and vertical components of the wave-induced wind. The development of these relationships produces expressions for the components of the wave-induced wind in a frame of reference moving with the wave. Wave-slope soaring flight is then analyzed using an energetics-based approach for waves of typical ocean conditions (wave height of 1m, period of 10s) and the body plan of P. occidentalis .
Results: For pure ground effect flight, we calculate an upper bound mechanical advantage of ~ 20 - 25\% as compared with steady, level flight without ground effect. When wave-slope soaring is employed, we calculate an upper bound mechanical advantage of ~ 50 - 60\% as compared with steady, level flight without ground effect.
Conclusions: The theoretical development presented here suggests there are energy savings associated with wave-slope soaring. Individual brown pelicans may gain upwards of 50\% mechanical advantage utilizing this mode of flight under typical ocean conditions, as compared to steady, level flight out of ground effect. Thus wave-slope soaring appears to provide a significant benefit to these highly mobile organisms that depend on patchy prey distribution over large home ranges.