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

Inertial particles in homogeneous shear turbulence: Experiments and direct numerical simulation

The properties of the transport of heavy inertial particles in a uniformly sheared turbulent flow have been investigated by combining experimental and numerical data at particle Stokes number St ≈ 0.3 ÷ 0.5 respectively. As in isotropic turbulence, particles are observed to avoid zones of intense enstrophy and to cluster in strain-dominated regions, resulting in highly intermittent spatial distributions. Moreover, the anisotropy of the mean flow is found to imprint a clear preferential orientation of the particle clusters in the direction of the maximum mean strain. These features are observed both in the numerics and in the experiments, and have been consistently quantified by a number of complementary statistical tools, such as the Voronoï tessellations and the pair correlation function. The latter quantity has been generalized in the form of the Angular Distribution Function and has allowed to evaluate the anisotropy content of the particle field at each scale. The behavior of this observable exhibits the same trend in the two datasets and suggests that, owing to increased inertia, the particle distribution starts to recover isotropy at scales smaller than the carrier velocity field. A proper rescaling of the two datasets in terms of their respective values of the shear scale allows to account for differences in the Reynolds number of experiments and numerics in the range of scales dominated by the mean shear. © 2013 Springer Science+Business Media Dordrecht

Aquatic Locomotion for Self-propelled Fishlike Bodies and Different Styles of Swimming

Fish swimming is an intriguing subject of interest in fluid mechanics at the border with other disciplines in the field of environmental sciences. The main complexity is given by the interaction between the fish body and the unbounded fluid domain, otherwise at rest. The theoretical approach has to consider the full body-fluid system to obtain from the exchanged internal forces the whole motion, i.e. locomotion plus recoil displacements, which define, together with the prescribed body deformation, the free swimming behavior. The impulse formulation allows for an easy calculation of the potential contribution, related to the added mass, and of the vortical contribution related to bound and released vorticity. A simple two- dimensional and non-diffusive model is adopted for the numerical simulations to generate neat results able to clarify several physical phenomena. The aim is a unified procedure for both undulatory and oscillatory swimming to obtain valid answers for cruising speed and expended energy, hence for the performance in terms of the cost of transport. The paper describes the theoretical aspects of the model within the context of the relevant literature and summarizes the more significant results obtained recently by the research group of the authors

Motion of an elliptical vortex under rotating strain: conditions for asymmetric merging

The analysis of the motion of a uniform vortex (patch) of elliptical shape under a relating strain field is employed to investigate the conditions leading to merging for two co-rotating elliptical patches of equal vorticity but different circulation. The motion of the patch having smaller circulation under the rotating strain field induced by the other vortex is analyzed, by considering both the intensity and the rotation rate of the strain constant. Under this assumption, we may adopt a first integral of motion which has been already used to discuss the different kinds of motion experienced by the elliptical patch. In the present paper, the dependence of the motion on the initial conditions and on the strain parameters is analyzed in further detail, to provide an overall picture of the elliptical patch dynamics. These results are employed in the analysis of the merging conditions. To this aim, the strain parameters, written in terms of the circulation of the larger vortex and of the distance between the two vortices, are kept frozen at their initial values. For a given circulation of the larger vortex and for a given vorticity and initial configuration of the smaller one, it is possible to find a particular distance between the vortices - transitional distance, d(t) - to which a significant change in the dynamics of the smaller elliptical patch is associated. It is always slightly lower than the critical distance and the difference between the two values decreases for vanishing size of the smaller vortex. The analysis of the first integral shows that, for an initial distance larger than d(t), the motion of the vortex leads to small periodic variations of its second-order moment. On the contrary, when the distance is smaller than d(t), the motion implies a large growth of its second-order moment, that is able to force the merging for frozen strain parameters. (C) 1998 The Japan Society of Fluid Mechanics Incorporated and Elsevier Science B.V. All rights reserved

Weakly nonlinear analysis of a localized disturbance in Poiseuille flow

In this article, we investigate, via a perturbation analysis, some important nonlinear features related to the process of transition to turbulence in a wall-bounded flow subject to a spatially localized disturbance that is harmonic in time. We show that the perturbation expansion, truncated at second order, is able to capture the generation of streamwise vorticity as a weakly nonlinear effect. The results of the perturbation approach are discussed in comparison with direct numerical simulation data for a sample case by extracting the contribution of the different orders. The main aim is to provide a tool to select the most effective nonlinear interactions to enlighten the essential features of the transitional process