A unified theory of slender wings in asymmetric motion, with an application to a swimming sea snake

Abstract

Abstract The slender body theory is extended to accommodate cases where a wing, in generally non-uniform motion, sideslips at sufficiently large angle to make the flow separate from one of its long edges but not from any part of the other. In those cases, an approximately triangular wake forms to the side of the wing, rendering the pressure loads on the wing not only asymmetrical, but also dependent on the history of the wing's motion. The theory can have a wide range of possible applications, from estimating lift and drag of a slender wing in pronouncedly asymmetric flight, through analysing an aero-elastic stability of that wing, to estimating thrust, lift and power of a sea snake that swims at an angle to its body axis. Coherence of the theory is demonstrated through numerous numerical simulations.