Dynamic mode decomposition (DMD) is a powerful and increasingly popular tool for performing spectral analysis of fluid flows. However, it requires data that satisfy the Nyquist-Shannon sampling criterion. In many fluid flow experiments, such data are impossible to capture. We propose a new approach that combines ideas from DMD and compressed sensing. Given a vector-valued signal, we take measurements randomly in time (at a sub-Nyquist rate) and project the data onto a low-dimensional subspace. We then use compressed sensing to identify the dominant frequencies in the signal and their corresponding modes. We demonstrate this method using two examples, analyzing both an artificially constructed test dataset and particle image velocimetry data collected from the flow past a cylinder. In each case, our method correctly identifies the characteristic frequencies and oscillatory modes dominating the signal, proving the proposed method to be a capable tool for spectral analysis using sub-Nyquist-rate sampling.

Abstract. The development of flapping-wing micro air vehicles (MAVs) demands a systematic exploration of the available design space to identify ways in which the unsteady mechanisms governing flapping-wing flight can best be utilized for producing optimal thrust or maneuverability. Mimicking the wing kinematics of biological flight requires examining the potential effects of wing morphology on flight performance, as wings may be specially adapted for flapping flight. For example, insect wings passively deform during flight, leading to instantaneous and potentially unpredictable changes in aerodynamic behavior. Previous studies have postulated various explanations for insect wing complexity, but there lacks a systematic approach for experimentally examining the functional significance of components of wing morphology, and for determining whether or not natural design principles can or should be used for MAVs. In this work, a novel fabrication process to create centimeter-scale wings of great complexity is introduced; via this process, a wing can be fabricated with a large range of desired mechanical and geometric characteristics. We demonstrate the versatility of the process through the creation of planar, insect-like wings with biomimetic venation patterns that approximate the mechanical properties of their natural counterparts under static loads. This process will provide a platform for studies investigating the effects of wing morphology on flight dynamics, which may lead to the design of highly maneuverable and efficient MAVs and insight into the functional morphology of natural wings.

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Wake visualization experiments were conducted on a finite curved cylinder whose plane of curvature is aligned with the free stream. The stagnation face of the cylinder is oriented concave or convex to the flow at $230\leqslant Re_{D}\leqslant 916$, where $Re_{D}$ is the cylinder Reynolds number and the curvature is constant and ranges from a straight cylinder to a quarter-ring. While the magnitude of the local angle of incidence to the flow is the same for both orientations, the contrast in their wakes demonstrates a violation of a common approximation known as the ‘independence principle’ for curved cylinders. Vortex shedding always occurred for the convex-oriented cylinder for the Reynolds-number range investigated, along most of the cylinder span, at a constant vortex shedding angle. In contrast, a concave-oriented cylinder could exhibit multiple concurrent wake regimes along its span: two shedding regimes (oblique, normal) and two non-shedding regimes. The occurrence of these wake regimes depended on the curvature, aspect ratio and Reynolds number. In some cases, vortex shedding was entirely suppressed, particularly at higher curvatures. In the laminar wake regime, increasing the curvature or decreasing the aspect ratio restricts vortex shedding to smaller regions along the span of the cylinder. Furthermore, the local angle of incidence where vortex shedding occurs is self-similar across cylinders of the same aspect ratio and varying curvature. After the wake transitions to turbulence, the vortex shedding extends along most of the cylinder span. The difference in the wakes between the concave and convex orientations is attributed to the spanwise flow induced by the finite end conditions, which reduces the generation of spanwise vorticity and increases the incidence of non-shedding and obliquely shedding wakes for the concave cylinder.

In this study, coupled dynamic responses of flexible superhydrophobic surfaces during a drop impact were investigated with position sensing and high-speed imaging. A smooth polydimethylsiloxane surface was spray coated with commercially available superhydrophobic paint particles. The influence of initial and subsequent impacts of a water droplet on the surface dynamics was studied at various natural frequencies of the surface (50 < f s < 230 Hz) and Weber numbers (2 < We < 90). We discovered that the flexible superhydrophobic surface was deflected twice during contact of the droplet by an impact force of the droplet as well as its reaction force during recoil. The magnitude of the droplet reaction force was estimated to be comparable to the droplet impact force. As the Weber number increased, however, the influence of the droplet reaction force on the surface displacement was attenuated because of the instability of the droplet rim. The contact time of the droplet and surface dynamics were found to be dependent on the phase of the surface. The contact time was reduced as much as 7% when a completion of the droplet spreading matched to the upward motion of the surface. One of the two local minima of the surface position observed during the contact of the droplet was diminished by matching the instance of the droplet reaction force to the downward motion of the surface. This study provides new insight into the effect of the droplet reaction force on dynamics of flexible superhydrophobic surfaces.