Bifurcation of Dynamic Soaring at Horizontal Wind Gradient

Dynamic soaring is a technique that seabirds like albatrosses use uneven natural winds in the atmosphere to extend the range without flapping the wings. To reveal the dynamic soaring mechanics, the equilibrium curve composed of equilibrium points are found in the model at the horizontal wind gradient. Furthermore, the normalized dynamic equations are derived to simplify the number of parameters. On the fundamental of the normalized equations and a typical set of albatross parameters at different wind gradients, codimension 1 and 2 bifurcations of the equilibrium curve are simulated and analyzed. The results show that the ascending equilibrium curve guarantees to have a stable region, which indicates that the aircraft can automatically rise in a sufficiently large wind gradient, and the existence of the Hopf bifurcations on the descending equilibrium curve depends on the wind gradient.