Stokes Ian A, Lucas Andrew J
Dept. of Mechanical and Aerospace Engineering, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92037, USA.
Scripps Institution of Oceanography, University of California, San Diego, 8622 Kennel Way, La Jolla, CA 92037, USA.
Mov Ecol. 2021 Mar 22;9(1):13. doi: 10.1186/s40462-021-00247-9.
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. 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.
The 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.
For 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.
The 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.
在斯克里普斯海洋研究所的实验室附近，经常能看到褐鹈鹕（Pelecanus occidentalis）沿着海浪区近海的波峰飞行。以这种方式飞行时，鸟儿可以在不拍打翅膀的情况下，在海面上方几厘米处飞行很长距离。在此，我们推导了一个理论框架，用于评估与这种“波坡翱翔”行为相关的能量节省情况，即飞行中的生物体利用行进的海洋表面重力波引起的局部上升气流。
将进出地面效应时稳定、恒定高度飞行的能量成本作为对照进行分析。利用势流理论来量化与近浅滩、弱非线性、浅水海洋表面重力波相关的海浪诱导风，这些海浪在最初静止的大气中移动。使用微扰理论和二维拉普拉斯方程在狄利克雷边界条件下的格林函数，我们在随波移动的参考系中获得了海浪诱导风的水平和垂直分量的积分。然后，使用基于能量学的方法，针对一系列海洋条件和褐鹈鹕的身体结构，对波坡翱翔飞行进行分析。
对于地面效应飞行，与在地面效应之外的稳定水平飞行相比，我们计算得出运输成本降低了约15% - 25%。在典型海洋条件（波高2米，周期15秒）下，当在约2米的飞行高度采用波坡翱翔时，与在地面效应中飞行相比，我们计算得出运输成本降低了60% - 70%。涌浪振幅相对较小的增加或飞行高度的降低，可使高达100%的运输成本被波坡翱翔行为抵消。
此处提出的理论发展表明，波坡翱翔存在能量节省。在典型海洋条件下，个体褐鹈鹕利用这种飞行模式可能会显著降低其运输成本。因此，波坡翱翔可能为这些高度移动的生物提供适应性优势，这些生物依赖于大片栖息地中零散的猎物分布。
