Modelling lateral manoeuvres in fish

We propose a method to model manoeuvres in self-propelled flexible-bodied fish by modelling the hydrodynamics coupled to the body inertia. Flexible body motion is prescribed and the equations of motion are solved for the position of the centre of mass and rotation of the body. The governing equations are formulated by applying the conservation of linear and angular momentum. Two independent methods to model the fluid dynamics are pursued: Model 1 is an extension of elongated-body theory, modified for self-propulsion and flexible motion. Model 2 applies a numerical boundary-element formulation with the fish modelled as an infinitely thin rectangular body. The manoeuvring response to an impulsive input is first examined to understand the rigid-body characteristics of the fish. A flexible bend action is included to model C-bends of the type observed during escapes in fish. Models 1 and 2 are used to cross-verify the respective implementations as well as to develop physical insights into manoeuvring. A parameter study shows that fish of intermediate body depths are best adapted to rapid turns whereas the initial dynamic state of the fish is instrumental in affecting the sign as well as the magnitude of the turn angle, for a prescribed bend deflection. Computations for combined swimming and turning show that the initial rigid-body dynamics of the fish is much more effective than the induced effect of the prior shed wake in enhancing the turning response.