Flow visualization data from experiments with an oscillating circular cylinder in a gravity-driven soap film

This article contains flow visualization data from experiments conducted in an inclined gravity-driven soap film intersected by a circular cylinder undergoing controlled transverse oscillations at a Reynolds number of Re≈235. The dimensionless frequency and amplitude of cylinder oscillation were varied systematically over the ranges 0.2<f*<1.8 and 0.1<A*<1.3. A high-speed camera was used to capture the interference fringe patterns reflected from the soap film. These videos show the structure of the wake behind the cylinder, including the initial formation of vortices and the extended ‘vortex street’. Several wake patterns were identified, including the classic 2S, P+S, 2P, and 2T patterns, which are discussed in detail in the accompanying research article titled “The wake of a transversely oscillating circular cylinder in a flowing soap film at low Reynolds number” [1]. The videos presented in this article can be accessed through the Virginia Tech University Libraries’ Repository at https://doi.org/10.7294/14448027.v5[2].


Value of the Data
• Researchers in the field of Vortex-Induced Vibrations (VIV) and Fluid-Structure Interac-tion (FSI), as well as fluid mechanicians interested in laminar flows and bluff body wakes, can benefit from these data. • These flow-visualization videos reveal time-dependent flow structures in the wake of a transversely-oscillating circular cylinder in a gravity-driven soap film. Insight into the classic '2S', '2P', and 'P + S' type wakes, among others, can be obtained by examining the dynamic evolution of the flow and how it is affected by the cylinder's frequency ratio and oscillation amplitude. • The 'exotic wakes' shown here are known to appear behind objects that are either free [3] or forced [4] to oscillate transverse to the direction of the background fluid flow. Controlled transverse oscillations of a circular cylinder, such as those used in this study, are a commonly-used technique to predict the nature and extent of the vortex-induced vibrations experienced by a cylindrical structure that is free to move in the transverse direction. The wake structures observed under controlled motion at a given frequency and amplitude are expected to be identical to those which arise from free vibrations at the same frequency and amplitude [5] . • Experimentalists can use these data as a benchmark when conducting similar experiments.
• These wake videos contain high resolution data of a two-dimensional, time-dependent system with significant spatio-temporal complexity that can be used as a platform for additional data analysis and technique development, including data-driven reconstruction of coherent structure dynamics, principal component analysis, neural network classification, and complex network analysis.

Data Description
This article includes video recordings of the flow past a circular cylinder that is forced to oscillate perpendicular to the mean background fluid velocity in a flowing soap film, providing a supplement to the static images in [1] . These videos show examples of different wake modes and their time-dependent evolution. Each of the 21 experiments included here correspond to a different set of oscillation frequency-amplitude pairs, which are summarized (in non-dimensional form) in Table 1 and plotted in the ( f * , A * )-plane in Fig. 1 . The dimensionless frequency is given by f * ≡ f / f St , where f is the cylinder oscillation frequency and f St is the natural frequency of vortex shedding when the cylinder is fixed. The dimensionless amplitude is given by A * ≡ A/D , where A is the amplitude of the cylinder oscillation and D is the cylinder diameter.
These experiments provide representative samples of each of the 8 wake types, or modes, identified and discussed in [1] : • 2S , for which two vortices of opposite sign are generated in each shedding cycle, synchronized with the oscillatory motion of the cylinder; • weak 2P , for which two pairs of vortices with glide-reflective symmetry are shed in each cycle, but the weaker member of each pair may not persist in the far wake, which can there resemble a 2S wake; • strong 2P , for which two pairs of vortices with glide-reflective symmetry are shed in each cycle, and these pairs persist in the far wake; • P + S , an asymmetric mode for which one pair of vortices and then a single vortex are generated from opposite sides of the cylinder during each shedding cycle; • 2T , for which two triplets of vortices with glide-reflective symmetry are shed in each oscillation cycle; • transitional , a mode that corresponds with the generation of a non-canonical pattern or with no consistent pattern being sustained for any significant length of time during any experiment;  The frequency-amplitude parameter space covered by these experiments, adapted from [1] . The region labels and data points correspond to the classification of wake types summarized in Table 1 . Each labeled point is associated with an experiment included in this article, providing examples of each wake type. For an explanation of each regime and the interpretation of the various lines, see [1] . 315. This wake most clearly resembles the 2S mode in the mid-to-far wake. During the first half of the video, the 'stray vorticity' in the braid shear layer connecting two successive vortices is relatively strong in the near-to-mid wake region, but this vorticity does not persist into the far wake. In the second half of the video, this stray vorticity has significantly weakened and the wake appears purely 2S. ( 2 _ Video _ 2mm _ 17p93.avi ) • coalescing , with a large number of vortices generated in the near wake that coalesce into a 2S-like mode in the mid-to-far wake; and • perturbed von Kármán , in which vortex shedding continues to occur at the natural frequency and does not synchronize with the cylinder's motion, producing a wake structure that be interpreted as a 2S wake superimposed along a sinusoidal 'centerline' caused by the cylinder's motion. For the duration of the experiment the wake behavior here is similar to that in the first half of Exp. II ( Fig. 3 ). Thus, this wake may be considered 'weak 2P' for the first few diameters downstream and 2S in the mid-to-far wake. This wake, and comparison with Exp. II, demonstrates the subjectivity of identifying the boundary between the 2S and 2P regions. ( 3 _ Video _ 2p5mm _ 13p61.avi ) Exp. VIII: A strong 2P wake produced by a cylinder oscillating at f * = 1 . 257, A * = 0 . 787. Near-to-mid wake behavior is similar to that in Exp. VII ( Fig. 8 ), but in the far wake region there is significant inter-vortex motion, with some pairs displaying large transverse motion leading to intermittent break-up of the wake structure, e.g., at 00:06. A detailed description of the wake dynamics exhibited by each of these modes is included in [1] . We also include one example of an experiment (XXI) from the 'uncharacterized' region in the top-left part of the wake mode map.

Experimental Design, Materials and Methods
An inclined, gravity-driven soap film channel similar to that described by [6][7][8] was used to generate the data presented in this article.

The soap film system
The experimental apparatus was built around an aluminum frame, shown schematically in Fig. 23 (a). At the top of the frame, a reservoir (not shown) held fresh soap solution, which flowed through a valve into the apex of two nylon wires attached to the frame. These nylon wires were held taut to form three distinct stages: an expanding stage, in which the wires descended steeply at an angle of 57 °with respect to the horizontal and expanded to a width of approximately 10 cm; the main test section, in which they descended at an inclination angle of 14 °while aligned in parallel approximately 10 cm apart for 1 m; and finally a contracting stage, in which they descended at an angle of 68 °and converged to the bottom of the frame where they met in an apex. The inclination angle of 14 °in the test section was selected as a compromise between keeping the mean film speed low while preventing excessive sagging of the soap film in the test section.
A constant pressure head was maintained at the top of the soap film by using two nested containers of soap solution, with the outer container serving as an 'overflow reservoir' from which solution was continually pumped into the (brimming) inner container. This soap solution source ensured that the driving pressure did not vary over the course of an experiment through depletion of the solution. In all experiments, the solution was 1% by volume of Dawn Escapes TM liquid soap (Proctor & Gamble) in water.
After the upper valve was opened, soap solution flowed onto the wires and a 'bubble' film comprising this solution was manually drawn over the entire length of the channel between the nylon guide wires using a bar of acrylic. Once the soap 'bubble' was successfully extended between the nylon wires, soap solution began to flow from the reservoir at the top of the system to a collection bucket at the bottom (not shown). In Fig. 23 (a), the developed soap film bounded on both sides by nylon guide wires is shown schematically in translucent blue.

Cylinder oscillation
A circular cylinder with diameter D = 6 . 35 mm ( = 0 . 25 in) was mounted perpendicular to the plane of the experimental section of the soap film as shown in Fig. 23 (b) and oscillated transverse to the flow direction. As shown schematically in Fig. 23 (c), the cylinder was made to oscillate with amplitude A and frequency f (or wavelength λ when viewed in a frame of reference moving with the fluid). This oscillation was accomplished by securely attaching the cylinder to a scotch-yoke mechanism that was driven steadily using a motor mounted on a vibration table. The rotational motion of the motor was transformed by the scotch-yoke mechanism into a sinusoidally-varying, linear transverse motion.
as 1 St f * U * = 1. For 10 3 ≤ Re ≤ 10 5 , the Strouhal number is approximately constant for a smooth circular cylinder, and U * and 1 / f * can be used interchangeably. However, for the data reported here, the relationship between f * and U * is Reynolds number dependent.
In this work, we used f * and A * to characterize the cylinder's oscillation, yielding the twodimensional 'parameter space' map of wake patterns shown in Fig. 1 . The range of variables f * and A * for which data were collected is shown in Fig. 24 , with each video represented by a point in the ( f * , A * ) plane. Data were collected intermittently in the frequency range 0 . 2 < f * < 1 . 8 and for thirteen amplitude values in the range 0 . 1 < A * < 1 . 3 ; our collected data points are shown in Fig. 24 . The f * and A * values corresponding to the experiments included here are provided in Table 1 .

Illumination and flow visualization
The soap film was illuminated with a three-phase monochromatic sodium lamp assembly, as shown schematically in Fig. 23 (a). A high-speed camera was placed near the light source and positioned so that it received the light from the sodium lamp as reflected from the soap film. The videos recorded by the camera capture the interference pattern from light reflected from the upper and lower surfaces of the soap film; very small variations in the thickness result in changes in the interference pattern [9] , leading to the flow visualization documented in these videos. Thus, flowing soap films provide us with a rich 'two-dimensional laboratory' for hydrodynamics experiments with minimally-invasive, particle-free flow visualization.
Videos of the wake were recorded at a frame rate of 170 Hz with a window of 2352 × 600 pixels for 1400 frames or approximately 8.2 seconds. The resulting videos were then compressed using MATLAB's Video Processing Toolbox. A total of 839 videos were recorded in order to produce the wake-mode map and conduct the analysis in [1] ; only a representative sample of each type of wake is included here, as illustrated in Fig. 24 .
Municipal electricity in the United States is supplied at 60 Hz AC. Because our frame rate was higher than this at 170 Hz, we supplied power to the sodium lamp using three independent phases of AC that were shifted 120 °relative to each other. This ensured that the soap film was illuminated approximately evenly in time and prevented a peak in the power spectrum at 60 Hz that would have corrupted the data.

Vortex identification
The illumination and visualization of soap films using interferometry, as was done in this study, is a standard technique in the field, going back at least to 1984 with the work of Couder et al. [10] . The scalar field that is captured in the video images in this study is related to the small changes in thickness that occur in a soap film due to the Marangoni effect, in which the thickness plays the role of density and the surfactant concentration plays the role of pressure in an incompressible Navier-Stokes fluid [11] . It has long been recognized by experimentalists that interferometry results are closely related to the hydrodynamic flow field, and a number of important fluid dynamics results have been replicated in soap films; see, e.g., Refs. [ 12 , 13 ]. In addition, Gillissen et. al [14] have developed a technique to reconstruct the velocity field from the scalar field obtained using interferometry of a soap film.
Recently, Eshraghi and collaborators [15] investigated the wake of a stationary circular cylinder in a flowing soap film using multiple interrogation techniques. They showed that the identification of vortex centers as circular regions in the interferometry images accurately predicts the true location of vortex centers as determined using the velocity fields obtained with digital particle image velocimetry (DPIV). In this work, we manually identified circular or nearly-circular structures, usually accompanied by rapid changes in image intensity, as vortices in the cylinder wake.

Soap film characteristics
Although the wake patterns display significant spatio-temporal complexity, these flows remained laminar. The design of the soap film channel -including the length, width and angle of inclination of the three sections -was chosen in order to achieve an approximately constant velocity throughout the test section, following Georgiev and Vorobieff [6] . Using particle-tracking velocimetry, we determined this mean background velocity to be U = 680 mm/s in our experiments.
Due to the difficulty of measuring the viscosity of a soap film, it is common to use an indirect approach to determine the Reynolds number of a flowing soap film. Gharib and Derango [16] proposed using the Strouhal number (1) for flow past an isolated cylinder to estimate the Reynolds number in a soap film, and Wen and Lin [17] showed that the Strouhal-Reynolds number relationship for a cylinder in a soap film is in good agreement with established results [18] . We used this approach to determine the Reynolds number in our experiments by measuring the vortex-shedding frequency f St and flow speed U for the flow past a stationary cylinder before each St value was then converted into a Reynolds number. The Reynolds number for these experiments was determined to be Re = 235 ± 14 .
Elastic effects in the film were determined to be negligible. By observing the change of solution level in the overflow reservoir, we measured the volumetric flowrate during steady-state operation, and using mass conservation together with an assumption of uniform flow we esti-  [11] .
The interferometry images are made possible by thickness variations in the film, but these thickness variations were judged to not interfere with the fluid dynamics. In the absence of the cylinder, the film was approximately a uniform thickness throughout the test section, consistent with the observations of Refs. [21] and [6] . For flow past a circular cylinder, Ref. [15] shows that the resulting flow structures in the wake produce thickness variations that are less than 25% of the average film thickness for 200 ≤ Re ≤ 300 . By the analogy between thickness of the film and density of a Navier-Stokes fluid, these thickness variations produce a small Boussinesq-like buoyancy effect that can be considered negligible [11] .
The wake patterns in the regimes of interest, as represented by examples I-XX, can be approximated as occurring in a planar film. In the undisturbed film, gravity caused an observed out-of-plane deformation of at most η ≤ 0 . 5 mm , or a relative displacement of η/W ≤ 0 . 5% , where W = 10 cm is the width of the test section. Oscillation of the cylinder caused additional out-of-plane displacement of the film. For the large values of oscillation amplitude and frequency achieved in the 'uncharacterized' region of Fig. 1 , the out-of-plane displacement of the film was large enough to cause dark areas to appear in the interferometry images. As seen in the video accompanying Fig. 22 , these regions of relatively large out-of-plane displacement appear intermittently throughout the film, including near the cylinder. To quantify the amplitude of these film displacements, we placed a video camera near the end of the film and oriented it to point directly upstream, creating an end-on view of the film. We monitored the out-of-plane displacement η of the soap film with the cylinder undergoing oscillations at a relatively high amplitude of A * = 0 . 94 ( A = 6 mm) for several frequencies in the range 0 . 2 < f * < 1 . 1 , where f * ≈ 1 corresponds to the edge of the 'uncharacterized' region at this oscillation amplitude. As shown in Fig. 25 , we observed a maximum peak-to-peak out-of-plane displacement amplitude of η ≈ 4 mm in the neighborhood of the cylinder. We extrapolate from this observation an estimate that the out-of-plane displacement in this system was η ≤ 5 mm for all but the 'uncharacterized' region, corresponding to a relative displacement η/W ≤ 5 %. Out-of-plane displacement of the soap film was thus assumed to have a negligible effect on the wake dynamics in examples I-XX.

Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships which have, or could be perceived to have, influenced the work reported in this article.