Dynamical systems analysis of fluid transport in time-periodic vortex ring flows

It is known that the stable and unstable manifolds of dynamical systems theory provide a powerful tool for understanding Lagrangian aspects of time-periodic flows. In this work we consider two time-periodic vortex ring flows. The first is a vortex ring with an elliptical core. The manifolds provide information about entrainment and detrainment of irrotational fluid into and out of the volume transported with the ring. The likeness of the manifolds with features observed in flow visualization experiments of turbulent vortex rings suggests that a similar process might be at play. However, what precise modes of unsteadiness are responsible for stirring in a turbulent vortex ring is left as an open question. The second situation is that of two leapfrogging rings. The unstable manifold shows striking agreement with even the fine features of smoke visualization photographs, suggesting that fluid elements in the vicinity of the manifold are drawn out along it and begin to reveal its structure. We suggest that interpretations of these photographs that argue for complex vorticity dynamics ought to be reconsidered. Recently, theoretical and computational tools have been developed to locate structures analogous to stable and unstable manifolds in aperiodic, or finite-time systems. The usefulness of these analogs is demonstrated, using vortex ring flows as an example, in the paper by Shadden, Dabiri, and Marsden [Phys. Fluids 18, 047105 (2006)]

Layout of Multiple Views for Volume Visualization: A User Study

Abstract. Volume visualizations can have drastically different appearances when viewed using a variety of transfer functions. A problem then occurs in trying to organize many different views on one screen. We conducted a user study of four layout techniques for these multiple views. We timed participants as they separated different aspects of volume data for both time-invariant and time-variant data using one of four different layout schemes. The layout technique had no impact on performance when used with time-invariant data. With time-variant data, however, the multiple view layouts all resulted in better times than did a single view interface. Surprisingly, different layout techniques for multiple views resulted in no noticeable difference in user performance. In this paper, we describe our study and present the results, which could be used in the design of future volume visualization software to improve the productivity of the scientists who use it

The influence of wing–wake interactions on the production of aerodynamic forces in flapping flight

We used two-dimensional digital particle image velocimetry (DPIV) to visualize flow patterns around the flapping wing of a dynamically scaled robot for a series of reciprocating strokes starting from rest. The base of the wing was equipped with strain gauges so that the pattern of fluid motion could be directly compared with the time history of force production. The results show that the development and shedding of vortices throughout each stroke are highly stereotyped and influence force generation in subsequent strokes. When a wing starts from rest, it generates a transient force as the leading edge vortex (LEV) grows. This early peak, previously attributed to added-mass acceleration, is not amenable to quasi-steady models but corresponds well to calculations based on the time derivative of the first moment of vorticity within a sectional slice of fluid. Forces decay to a stable level as the LEV reaches a constant size and remains attached throughout most of the stroke. The LEV grows as the wing supinates prior to stroke reversal, accompanied by an increase in total force. At stroke reversal, both the LEV and a rotational starting vortex (RSV) are shed into the wake, forming a counter-rotating pair that directs a jet of fluid towards the underside of the wing at the start of the next stroke. We isolated the aerodynamic influence of the wake by subtracting forces and flow fields generated in the first stroke, when the wake is just developing, from those produced during the fourth stroke, when the pattern of both the forces and wake dynamics has reached a limit cycle. This technique identified two effects of the wake on force production by the wing: an early augmentation followed by a small attenuation. The later decrease in force is consistent with the influence of a decreased aerodynamic angle of attack on translational forces caused by downwash within the wake and is well explained by a quasi-steady model. The early effect of the wake is not well approximated by a quasi-steady model, even when the magnitude and orientation of the instantaneous velocity field are taken into account. Thus, the wake capture force represents a truly unsteady phenomenon dependent on temporal changes in the distribution and magnitude of vorticity during stroke reversal

Development of the wake behind a circular cylinder impulsively started into rotatory and rectilinear motion: Intermediate rotation rates

The temporal development of two-dimensional viscous incompressible flow generated by a circular cylinder started impulsively into steady rotatory and rectilinear motion is studied by integration of a velocity/vorticity formulation of the governing equations, using an explicit finite-difference/pseudo-spectral technique and an implementation of the Biot-Savart law. Results are presented for a Reynolds number of 200 (based on the cylinder diameter 2a and the magnitude U of the rectilinear velocity) for several values of the angular/rectilinear speed ratio alpha = (omega x a)/U (where omega is the angular speed) up to 3.25. Several aspects of the kinematics and dynamics of the flow not considered earlier are discussed. For higher values of alpha, the results indicate that for Re = 200, vortex shedding does indeed occur for alpha = 3.25. The shedding process is; however, very different from that which gives rise to the usual Karman vortex street for alpha = 0. In particular, consecutive vortices shed by the body can be shed from the same side and be of the same sense, in contrast to the nonrotating case, in which mirror-image vortices of opposite sense are shed alternately on opposite sides of the body. The implications of the results are discussed in relation to the possibility of suppressing vortex shedding by open or closed-loop control of the rotation rate