On the estimation of swimming and flying forces from wake measurements

The transfer of momentum from an animal to fluid in its wake is fundamental to many swimming and flying modes of locomotion. Hence, properties of the wake are commonly studied in experiments to infer the magnitude and direction of locomotive forces. The determination of which wake properties are necessary and sufficient to empirically deduce swimming and flying forces is currently made ad hoc. This paper systematically addresses the question of the minimum number of wake properties whose combination is sufficient to determine swimming and flying forces from wake measurements. In particular, it is confirmed that the spatial velocity distribution (i.e. the velocity field) in the wake is by itself insufficient to determine swimming and flying forces, and must be combined with the fluid pressure distribution. Importantly, it is also shown that the spatial distribution of rotation and shear (i.e. the vorticity field) in the wake is by itself insufficient to determine swimming and flying forces, and must be combined with a parameter that is analogous to the fluid pressure. The measurement of this parameter in the wake is shown to be identical to a calculation of the added-mass contribution from fluid surrounding vortices in the wake, and proceeds identically to a measurement of the added-mass traditionally associated with fluid surrounding solid bodies. It is demonstrated that the velocity/pressure perspective is equivalent to the vorticity/vortex-added-mass approach in the equations of motion. A model is developed to approximate the contribution of wake vortex added-mass to locomotive forces, given a combination of velocity and vorticity field measurements in the wake. A dimensionless parameter, the wake vortex ratio (denoted Wa), is introduced to predict the types of wake flows for which the contribution of forces due to wake vortex added-mass will become non-negligible. Previous wake analyses are reexamined in light of this parameter to infer the existence and importance of wake vortex added-mass in those cases. In the process, it is demonstrated that the commonly used time-averaged force estimates based on wake measurements are not sufficient to prove that an animal is generating the locomotive forces necessary to sustain flight or maintain neutral buoyancy

Role of vertical migration in biogenic ocean mixing

Recent efforts to empirically measure and numerically simulate biogenic ocean mixing have consistently observed low mixing efficiency. This suggests that the buoyancy flux achieved by swimming animals in the ocean may be negligible in spite of the observed large kinetic energy dissipation rates. The present letter suggests that vertical migration across isopycnals may be necessary in order to generate overturning and subsequent mixing at length scales significantly larger than the individual animals. The animal-fluid interactions are simulated here using a simplified potential flow model of solid spheres migrating vertically in a stably stratified fluid. The interaction of successive solid bodies with each parcel of fluid is shown to lead, under certain conditions, to vertical displacement of the fluid parcels over distances much larger than the individual body size. These regions of displaced fluid are unstably stratified and, hence, amenable to large-scale overturning and efficient mixing

Optimal vortex formation as a unifying principle in biological propulsion

I review the concept of optimal vortex formation and examine its relevance to propulsion in biological and bio-inspired systems, ranging from the human heart to underwater vehicles. By using examples from the existing literature and new analyses, I show that optimal vortex formation can potentially serve as a unifying principle to understand the diversity of solutions used to achieve propulsion in nature. Additionally, optimal vortex formation can provide a framework in which to design engineered propulsions systems that are constrained by pressures unrelated to biology. Finally, I analyze the relationship between optimal vortex formation and previously observed constraints on Strouhal frequency during animal locomotion in air and water. It is proposed that the Strouhal frequency constraint is but one consequence of the process of optimal vortex formation and that others remain to be discovered

Note on the induced Lagrangian drift and added-mass of a vortex

Darwin (1953) introduced a simple heuristic that relates the Lagrangian fluid drift induced by a solid body propagating in irrotational flow to its virtual- or added-mass. The force required to accelerate the solid body must also overcome this added-mass. An extension of Darwin's (1953) method to the case of vortices propagating in a real fluid is described here. Experiments are conducted to demonstrate the existence of an added-mass effect during uni-directional vortex motion, which is analogous to the effect of solid bodies in potential flow. The definition of the vortex added-mass coefficient is modified from the solid body case to account for entrainment of ambient fluid by the vortex. This modified coefficient for propagating vortices is shown to be equal in magnitude to the classical coefficient for a solid body of equivalent boundary geometry. An implication of these results is that the vortex added-mass concept can be used as a surrogate for the velocity potential, in order to facilitate calculations of the pressure contribution to forces required to set fluid into unsteady vortical motion. Application of these results to unsteady wake analyses and fluid–structure interactions such as vortex-induced vibrations is suggested

Theoretical framework to surpass the Betz limit using unsteady fluid mechanics

The Betz limit expresses the maximum proportion of the kinetic energy flux incident on an energy conversion device that can be extracted from an unbounded flow. The derivation of the Betz limit requires an assumption of steady flow through a notional actuator disk that is stationary in the streamwise direction. The present derivation relaxes the assumptions of steady flow and streamwise actuator disk stationarity, which expands the physically realizable parameter space of flow conditions upstream and downstream of the actuator disk. A key consequence of this generalization is the existence of unsteady motions that can, in principle, lead to energy conversion efficiencies that exceed the Betz limit not only transiently but also in time-averaged performance. Potential physical implementations of those unsteady motions are speculated

Introduction to Focus Issue: Lagrangian Coherent Structures

The topic of Lagrangian coherent structures (LCS) has been a rapidly growing area of research in nonlinear dynamics for almost a decade. It provides a means to rigorously define and detect transport barriers in dynamical systems with arbitrary time dependence and has a wealth of applications, particularly to fluid flow problems. Here, we give a short introduction to the topic of LCS and review the new work presented in this Focus Issue

An overview of a Lagrangian method for analysis of animal wake dynamics

The fluid dynamic analysis of animal wakes is becoming increasingly popular in studies of animal swimming and flying, due in part to the development of quantitative flow visualization techniques such as digital particle imaging velocimetry (DPIV). In most studies, quasi-steady flow is assumed and the flow analysis is based on velocity and/or vorticity fields measured at a single time instant during the stroke cycle. The assumption of quasi-steady flow leads to neglect of unsteady (time-dependent) wake vortex added-mass effects, which can contribute significantly to the instantaneous locomotive forces. In this paper we review a Lagrangian approach recently introduced to determine unsteady wake vortex structure by tracking the trajectories of individual fluid particles in the flow, rather than by analyzing the velocity/vorticity fields at fixed locations and single instants in time as in the Eulerian perspective. Once the momentum of the wake vortex and its added mass are determined, the corresponding unsteady locomotive forces can be quantified. Unlike previous studies that estimated the time-averaged forces over the stroke cycle, this approach enables study of how instantaneous locomotive forces evolve over time. The utility of this method for analyses of DPIV velocity measurements is explored, with the goal of demonstrating its applicability to data that are typically available to investigators studying animal swimming and flying. The methods are equally applicable to computational fluid dynamics studies where velocity field calculations are available

Delay of vortex ring pinchoff by an imposed bulk counterflow

The Kelvin–Benjamin variational principle has been previously used to predict that vortex ring pinchoff can be delayed if the energy of the leading vortex ring is decreased during formation and/or the energy delivered by the vortex generator is increased. We present experimental results in which the former and latter energy effects were simultaneously accomplished by imposing a bulk axisymmetric counterflow during vortex ring formation. Measurements indicate that the formation number is retarded sufficiently to allow increased ingestion of fluid circulation by the leading vortex ring. This serves as a first demonstration of artificial manipulation of vortex ring formation for potential propulsive benefits in starting jets

Starting flow through nozzles with temporally variable exit diameter

Starting flow through a nozzle or orifice typically results in the transient formation of a leading vortex ring and trailing jet. Experiments are conducted to investigate the dynamics of this process in the case of a temporally variable nozzle exit diameter, with the aim of understanding these flows as they occur in Nature and emerging technologies. By kinematically decoupling the source flow from the nozzle motion, comparison across several classes of exit diameter temporal variation is facilitated. Kinematic models of the starting flows are used to accurately predict the fluid circulation produced by the vortex generators, and to emphasize the special role of the nozzle boundary layer in dictating the nature of the global flow patterns. A dimensionless temporal parameter is derived in order to track the vortex formation process for the various classes of nozzle motion. Dynamics of vortex ring disconnection from the source flow are studied in this new dimensionless framework. We show that temporally increasing the nozzle exit diameter as the starting flow develops results in higher-energy vortex ring structures with peak vorticity located further from the axis of symmetry relative to a static nozzle case. In addition, the normalized energy supplied by the vortex generator is increased in this process. We do not observe a delay in the onset of vortex ring disconnection from the trailing jet, as predicted by previous numerical simulations. In contrast, growth of the leading vortex ring is substantially augmented by temporally decreasing the nozzle exit diameter during fluid ejection, as noted in a previous experiment. Normalized vortex ring circulation is increased 35% in these cases, and the normalized energy of the generated vortex rings is equivalent to that of Hill's spherical vortex. These observed effects are explained by considering the measured vorticity distribution and energy of the starting flows. Strategies are suggested to exploit the discovered dynamics for various pulsed-jet applications