Gray's paradox: a fluid mechanical perspective

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.

Numerical modeling of a self-propelled dolphin jump out of water

A computational model is developed to investigate the jump of a self-propelled dolphin out of water. This model relies on the Navier-Stokes equations, where a fictitious domain approach with the volume penalization method is used for fluid-structure coupling, and the continuous surface force approach is used to model the water-air interface, the latter being tracked in a level-set framework. The dolphin's geometry is based on freely available data from the literature. While body deformation is imposed, the leading linear and angular displacements are computed from Newton's laws. Numerical simulations show that it is necessary to generate large propulsives forces to allow the jump out of water. When the dolphin is out of water, its trajectory follows a purely ballistic one.

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.

Electrical Swath Ships with Underwater Hulls Preventing the Boundary Layer Separation

The body shapes of aquatic animals can ensure a laminar flow without boundary layer separation at rather high Reynolds numbers. The commercial efficiencies (drag-to-weight ratio) of similar hulls were estimated. The examples of neutrally buoyant vehicles of high commercial efficiency were proposed. It was shown that such hulls can be effectively used both in water and air. In particular, their application for SWATH (Small Water Area Twin Hulls) vehicles is discussed. In particular, the seakeeping characteristics of such ships can be improved due to the use of underwater hulls. In addition, the special shaping of these hulls allows the reducing of total drag, as well as the energetic needs and pollution. The presented estimations show that a weight-to-drag ratio of 165 can be achieved for a yacht with such specially shaped underwater hulls. Thus, a yacht with improved underwater hulls can use electrical engines only, and solar cells to charge the batteries.

Immersed Methods for Fluid-Structure Interaction

Fluid-structure interaction is ubiquitous in nature and occurs at all biological scales. Immersed methods provide mathematical and computational frameworks for modeling fluid-structure systems. These methods, which typically use an Eulerian description of the fluid and a Lagrangian description of the structure, can treat thin immersed boundaries and volumetric bodies, and they can model structures that are flexible or rigid or that move with prescribed deformational kinematics. Immersed formulations do not require body-fitted discretizations and thereby avoid the frequent grid regeneration that can otherwise be required for models involving large deformations and displacements. This article reviews immersed methods for both elastic structures and structures with prescribed kinematics. It considers formulations using integral operators to connect the Eulerian and Lagrangian frames and methods that directly apply jump conditions along fluid-structure interfaces. Benchmark problems demonstrate the effectiveness of these methods, and selected applications at Reynolds numbers up to approximately 20,000 highlight their impact in biological and biomedical modeling and simulation.

Quantitative flow analysis of swimming dynamics with coherent Lagrangian vortices

Undulatory swimmers flex their bodies to displace water, and in turn, the flow feeds back into the dynamics of the swimmer. At moderate Reynolds number, the resulting flow structures are characterized by unsteady separation and alternating vortices in the wake. We use the flow field from simulations of a two-dimensional, incompressible viscous flow of an undulatory, self-propelled swimmer and detect the coherent Lagrangian vortices in the wake to dissect the driving momentum transfer mechanisms. The detected material vortex boundary encloses a Lagrangian control volume that serves to track back the vortex fluid and record its circulation and momentum history. We consider two swimming modes: the C-start escape and steady anguilliform swimming. The backward advection of the coherent Lagrangian vortices elucidates the geometry of the vorticity field and allows for monitoring the gain and decay of circulation and momentum transfer in the flow field. For steady swimming, momentum oscillations of the fish can largely be attributed to the momentum exchange with the vortex fluid. For the C-start, an additionally defined jet fluid region turns out to balance the high momentum change of the fish during the rapid start.