Emad Masroor

We introduce a new definition of vortex formation length for uniform steady flow past a circular cylinder using Proper Orthogonal Decomposition (POD) of the pressure field. Previous definitions each identify a single characteristic length for a given value of Reynolds number. We use the leading modes of the pressure POD to define upper and lower bounds on the vortex formation length. Identifying a range for the vortex formation length is consistent with the hysteresis observed in the critical spacing of two tandem cylinders.

The fluid motion produced by a periodic array of identical, axisymmetric, thin-cored vortex rings is investigated. It is well known that such an array moves uniformly without change of shape or form in the direction of the central axis of symmetry, and is therefore an equilibrium solution of Euler’s equations. In a frame of reference moving together with the system of vortex rings, the motion of passive fluid particles is investigated as a function of the two non-dimensional parameters that define this system: }\backslashvarepsilon = a/R}, the ratio of minor radius to major radius of the torus-shaped vortex rings, and }\backslashlambda = L/R}, the separation of the vortex rings normalized by their radii. Two bifurcations in the streamline topology are found that depend significantly on }\backslashvarepsilon} and }\backslashlambda}; these bifurcations delineate three distinct shapes of the ’atmosphere’ of fluid particles that move together with the vortex ring for all time. Analogous to the case of an isolated vortex ring, the atmospheres can be ’thin-bodied’ or ’thick-bodied’. Additionally, we find the occurrence of a ’connected’ system, in which the atmospheres of neighboring rings touch at an invariant ring of fluid particles that is stationary in a frame of reference moving with the rings.

An inclined gravity-driven soap film channel was used to study the wake patterns formed behind a transversely oscillating cylinder at Re=235±14. The natural frequency of vortex shedding from a stationary cylinder, fSt, was used to identify the oscillation frequencies of interest. The (dimensionless) frequency, f∗=f∕fSt, and amplitude, A∗=A∕D, of the cylinder’s motion was varied over a large portion of the fundamental synchronization region (i.e., for f∗≈1), and a ‘map’ of wake patterns was constructed in (f∗,A∗) space. Lock-on between the frequency of the cylinder’s motion and the dominant frequency of the resulting vortex wake was observed for a large range of this parameter space, predominantly manifested as synchronized ‘2S’ and ‘2P’ wake modes. Synchronized ‘P+S’, ‘2T’, and ‘transitional’ wakes were also found in smaller regions of parameter space. Unsynchronized ‘coalescing’ and ‘perturbed von Kármán’ wakes were observed as the oscillation frequency became sufficiently different from fSt. The wake patterns and vortex formation processes found in this study, particularly the 2P mode wakes, bear a strong resemblance to previous three-dimensional experimental results, despite the physical constraint from the soap film that limits three-dimensional effects in the wake.