The hydrodynamics of flexible-body manoeuvres in swimming fish

Swimming in flexible-bodied animals like fish is characterised by a travelling wave passing along the spinal chord of the body. Symmetric transverse undulations of the body generate thrust and propel the fish forward. Turns are effected by generating an asymmetric transverse movement of the fish body, frequently as a C-shaped bend. Typical fish swimming speeds allow for simplifying assumptions of incompressible and inviscid flow. The objective of the current work is to use existing theoretical models developed for forward swimming, to analyse fish turns. Lighthill’s classical elongated-body theory for fish swimming forms the fundamental basis for the 3D flow model and ‘recoil’ correction concept implemented here. In the methods developed here, transverse motion of a thin ‘waving’ plate is prescribed by a displacement signal acting along the midline, for finite time toto. Lighthill’s approach to calculate the rigid-body motion or ‘recoil’ correction is implemented to ensure zero net force and moments act on the body. Accordingly, angular and transverse motion are computed and final orientation of the plate after the manoeuvre is calculated. A 3D boundary-value algorithm has been developed using a vortex lattice method. The essential methodology, modifications for turning and comparisons with the analytical methods in the small and large aspect ratio limits are presented.