A ridge tracking algorithm for the computation and extraction of Lagrangian coherent structures (LCS) is developed. This algorithm takes advantage of the spatial coherence of LCS by tracking the ridges which form LCS to avoid unnecessary computations away from the ridges. We also make use of the temporal coherence of LCS by approximating the time dependent motion of the LCS with passive tracer particles. To justify this approximation, we provide an estimate of the difference between the motion of the LCS and that of tracer particles which begin on the LCS. In addition to the speedup in computational time, the ridge tracking algorithm uses less memory and results in smaller output files than the standard LCS algorithm. Finally, we apply our ridge tracking algorithm to two test cases, an analytically defined double gyre as well as the more complicated example of the numerical simulation of a swimming jellyfish. In our test cases, we find up to a 35 times speedup when compared with the standard LCS algorithm.

The flow structures produced by the hydromedusae Sarsia tubulosa and Aequorea victoria are examined using direct numerical simulation and Lagrangian coherent structures (LCS). Body motion of each hydromedusa is digitized and input to a CFD program. Sarsia tubulosa uses a jetting type of propulsion, emitting a single, strong, fast-moving vortex ring during each swimming cycle while a secondary vortex of opposite rotation remains trapped within the subumbrellar region. The ejected vortex is highly energetic and moves away from the hydromedusa very rapidly. Conversely, A. victoria, a paddling type hydromedusa, is found to draw fluid from the upper bell surface and eject this fluid in pairs of counter-rotating, slow-moving vortices near the bell margins. Unlike S. tubulosa, both vortices are ejected during the swimming cycle of A. victoria and linger in the tentacle region. In fact, we find that A. victoria and S. tubulosa swim with Strouhal numbers of 1.1 and 0.1, respectively. This means that vortices produced by A. victoria remain in the tentacle region roughly 10 times as long as those produced by S. tubulosa, which presents an excellent feeding opportunity during swimming for A. victoria. Finally, we examine the pressure on the interior bell surface of both hydromedusae and the velocity profile in the wake. We find that S. tubulosa produces very uniform pressure on the interior of the bell as well as a very uniform jet velocity across the velar opening. This type of swimming can be well approximated by a slug model, but A. victoria creates more complicated pressure and velocity profiles. We are also able to estimate the power output of S. tubulosa and find good agreement with other hydromedusan power outputs. All results are based on numerical simulations of the swimming jellyfish.

Using invariant material manifolds and flow topology, the flow behavior and structure of flow around a two-dimensional Eppler 387 airfoil is examined with an emphasis on vortex shedding and the time-dependent reattachment profile. The examination focuses on low Reynolds number (Re = 60 000) flow at several angles of attack. Using specialized software, we identify invariant manifolds in the flow and use these structures to illuminate the process of vortex formation and the periodic behavior of the reattachment profile. Our analysis concludes with a topological view of the flow, including fixed points and a discussion of phase plots and the frequency spectrum of several key points in the flow. The behavior of invariant manifolds directly relates to the flow topology and illuminates some aspects seen in phase space during vortex shedding. Furthermore, it highlights the reattachment behavior in ways not seen before.

No abstract