Self-propelled fish locomotion in an otherwise quiescent fluid

Since the deep observations by Leonardo da Vinci, understanding fish locomotion in water has always attracted the attention of scientists in many fields, from fluid mechanics to other disciplines concerning environmental sciences. The complexity of this problem is mainly given by the non-linear interaction between the fish body and the surrounding fluid otherwise at rest, leading to the desired forward locomotion and to the unavoidable angular and lateral recoil reactions, which are essential for a correct evaluation of the swimming performance. Despite many advances have been obtained for the study of fish self-propulsion in recent years, from simple mathematical models up to complex numerical solutions, the main mechanisms underlying fish locomotion are not fully clarified and still require further investigations. In this thesis free swimming conditions is deeply analyzed for both steady swimming and fast maneuvers by a theoretical approach which considers the full body-fluid system to obtain the ex- changed internal forces. The focus is on the added mass and the vortex shedding contributions to the locomotion performance and on the role of recoil motions which, together with the prescribed body deformation, define the free swimming behavior. To this purpose, the impulse formulation allows for an easy isolation of the potential contri- bution, related to the added mass, and of the vortical contribution related to bound and released vorticity and a simple two-dimensional numerical model with concentrated vorticity is adopted for the numerical simulations to generate meaningful results able to clarify these physical phenomena. The aim is a unified procedure for both undulatory and oscillatory swimming to obtain valid an- swers for cruising speed, expended energy and kinematics, hence for the swimming performance in terms of the cost of transport and propulsive efficiency. The same model is also able to give new insights on the impressive performance characterizing fish fast maneuvers. The extreme turning capability and the large acceleration, so essential to fish survival along pray-predator encounters, are studied by highlighting the potential and the vortical impulses and their interplay induced by recoil motions, to show their relevance for the realization of the maneuver

The relevance of recoil and free swimming in aquatic locomotion

The study of the free swimming of undulating bodies in an otherwise quiescent fluid has always encountered serious difficulties for several reasons. When considering the full system, given by the body and the unbounded surrounding fluid, the absence of external forces leads to a subtle interaction problem dominated, at least at steady state conditions, by the equilibrium of strictly related internal forces, e.g. thrust and drag, under the forcing of a prescribed deformation. A major complication has been dictated by the recoil motion induced by the non linear interactions, which may find a quite natural solution when considering as unknowns the velocity components of the body center of mass. A simplified two-dimensional model in terms of impulse equations has been used and a fruitful separation of the main contributions due to added mass and to vorticity release is easily obtained. As main results we obtain either the mean locomotion speed and the oscillating recoil velocity components which have a large effect on the overall performance of free swimming. Several constrained gaits are considered to highlight the relevance of recoil for realizing graceful and efficient trajectories and to analyze its potential means for active control

AN INVISCID MODEL FOR SELF PROPELLED SWIMMING OF UNDULATING BODIES

Atwo-dimensionalinviscidpotentialmodelwithvorticityreleasehasbeendevelopedinordertoinvestigatetheselfpropelled swimming of undulating bodies. The body is free to move not only in the forward and lateral directions, but it can also rotate around its center of mass, according to the forces and moments induced by the flowfield generated by its own prescribed undulation. The numerical model is based on an unsteady potential panel code for deformable airfoil. The vortex shedding process is modeled by an unsteady Kutta condition. The model is able to predict the full kinematics of the undulating airfoil by expressing forces and moments in terms of hydrodynamic impulse

The fish ability to accelerate and suddenly turn in fast maneuvers

Velocity burst and quick turning are performed by fish during fast maneuvers which might be essential to their survival along pray-predator encounters. The parameters to evaluate these truly unsteady motions are totally different from the ones for cruising gaits since a very large acceleration, up to several times the gravity, and an extreme turning capability, in less than one body length, are now the primary requests. Such impressive performances, still poorly understood, are not common to other living beings and are clearly related to the interaction with the aquatic environment. Hence, we focus our attention on the water set in motion by the body, giving rise to the relevant added mass and the associated phenomena in transient conditions, which may unveil the secret of the great maneuverability observed in nature. Many previous studies were almost exclusively concentrated on the vortical wake, whose account, certainly dominant at steady state, is not sufficient to explain the entangled transient phenomena. A simple two-dimensional impulse model with concentrated vorticity is used for the self-propulsion of a deformable body in an unbounded fluid domain, to single out the potential and the vortical impulses and to highlight their interplay induced by recoil motions

The relevance of recoil and free swimming in aquatic locomotion

The study of the free swimming of undulating bodies in an otherwise quiescent fluid has always encountered serious difficulties for several reasons. When considering the full system, given by the body and the unbounded surrounding fluid, the absence of external forces leads to a subtle interaction problem dominated, at least at steady state conditions, by the equilibrium of strictly related internal forces, e.g. thrust and drag, under the forcing of a prescribed deformation. A major complication has been dictated by the recoil motion induced by the non linear interactions, which may find a quite natural solution when considering as unknowns the velocity components of the body center of mass. A simplified two-dimensional model in terms of impulse equations has been used and a fruitful separation of the main contributions due to added mass and to vorticity release is easily obtained. As main results we obtain either the mean locomotion speed and the oscillating recoil velocity components which have a large effect on the overall performance of free swimming. Several constrained gaits are considered to highlight the relevance of recoil for realizing graceful and efficient trajectories and to analyze its potential means for active control

The performance of a flapping foil for a self-propelled fishlike body

Several fish species propel by oscillating the tail, while the remaining part of the body essentially contributes to the overall drag. Since in this case thrust and drag are in a way separable, most attention was focused on the study of propulsive efficiency for flapping foils under a prescribed stream. We claim here that the swimming performance should be evaluated, as for undulating fish whose drag and thrust are severely entangled, by turning to self‐propelled locomotion to find the proper speed and the cost of transport for a given fishlike body. As a major finding, the minimum value of this quantity corresponds to a locomotion speed in a range markedly different from the one associated with the optimal efficiency of the propulsor. A large value of the feathering parameter characterizes the minimum cost of transport while the optimal efficiency is related to a large effective angle of attack. We adopt here a simple two‐dimensional model for both inviscid and viscous flows to proof the above statements in the case of self‐propelled axial swimming. We believe that such an easy approach gives a way for a direct extension to fully free swimming and to real‐life configurations

How Free Swimming Fosters the Locomotion of a Purely Oscillating Fish-like Body

The recoil motions in free swimming, given by lateral and angular rigid motions due to the interaction with the surrounding water, are of great importance for a correct evaluation of both the forward locomotion speed and efficiency of a fish-like body. Their contribution is essential for calculating the actual movements of the body rear end whose prominent influence on the generation of the proper body deformation was established a long time ago. In particular, the recoil motions are found here to promote a dramatic improvement of the performance when damaged fishes, namely for a partial functionality of the tail or even for its complete loss, are considered. In fact, the body deformation, which turns out to become oscillating and symmetric in the extreme case, is shown to recover in the water frame a kind of undulation leading to a certain locomotion speed though at the expense of a large energy consumption. There has been a deep interest in the subject since the infancy of swimming studies, and a revival has recently arisen for biomimetic applications to robotic fish-like bodies. We intend here to apply a theoretical impulse model to the oscillating fish in free swimming as a suitable test case to strengthen our belief in the beneficial effects of the recoil motions. At the same time, we intend to exploit the linearity of the model to detect from the numerical simulations the intrinsic physical reasons related to added mass and vorticity release behind the experimental observations