Abstract
BackgroundFrom the laboratory at Scripps Institution of Oceanography, it is common to see the brown pelican (Pelecanus occidentalis) traveling along the crests of ocean waves just offshore of the surf-zone. When flying in this manner, the birds can travel long distances without flapping, centimeters above the ocean’s surface. Here we derive a theoretical framework for assessing the energetic savings related to this behavior, ‘wave-slope soaring,’ in which an organism in flight takes advantage of localized updrafts caused by traveling ocean surface gravity waves.MethodsThe energy cost of steady, constant altitude flight in and out of ground effect are analyzed as controls. Potential flow theory is used to quantify the ocean wave-induced wind associated with near-shoaling, weakly nonlinear, shallow water ocean surface gravity waves moving through an atmosphere initially at rest. Using perturbation theory and the Green’s function for Laplace’s equation in 2D with Dirichlet boundary conditions, we obtain integrals for the horizontal and vertical 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 under a range of ocean conditions and the body plan of P. occidentalis.ResultsFor ground effect flight, we calculate a ∼15 - 25% reduction in cost of transport as compared with steady, level flight out of ground effect. When wave-slope soaring is employed at flight heights ∼2m in typical ocean conditions (2m wave height, 15s period), we calculate 60-70% reduction in cost of transport as compared with flight in ground effect. A relatively small increase in swell amplitude or decrease in flight height allows up to 100% of the cost of transport to be offset by wave-slope soaring behavior.ConclusionsThe theoretical development presented here suggests there are energy savings associated with wave-slope soaring. Individual brown pelicans may significantly decrease their cost of transport utilizing this mode of flight under typical ocean conditions. Thus wave-slope soaring may provide fitness benefit to these highly mobile organisms that depend on patchy prey distribution over large home ranges.
Highlights
From the laboratory at Scripps Institution of Oceanography, it is common to see the brown pelican (Pelecanus occidentalis) traveling along the crests of ocean waves just offshore of the surf-zone
Our description of the energetics uses energy consumption per distance travelled, or ‘cost of transport’ (COT) as the minimizing function [5]. These two results provide a baseline with which to compare the energy savings associated with wave-slope soaring flight, since flight in ground effect has demonstrated flight efficiency benefits [14,15,16,17,18]
From our control, we find the minimum COT in steady, constant altitude pelican flight out of ground effect ∼1.5 J/m with a corresponding minimum-cost velocity of ∼13.4 m/s (Fig. 2)
Summary
From the laboratory at Scripps Institution of Oceanography, it is common to see the brown pelican (Pelecanus occidentalis) traveling along the crests of ocean waves just offshore of the surf-zone. When flying in this manner, the birds can travel long distances without flapping, centimeters above the ocean’s surface. Some birds are able to fly with little flapping by exploiting energy present in the ambient wind-field [1,2,3,4,5] When these energy gains are great enough to offset the cost of flight, the phenomenon is known as ‘soaring’ [1, 6]. ‘Slope soaring’ takes advantage of updrafts that are created by the vertical redirection of airflow over cliffs and steep hills [2, 4]
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