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Optical flow velocimetry (OFV) is a method for determining dense and accurate velocity fields from a pair of particle images by solving the classical optical flow problem. However, this is an ill-posed inverse problem, which generally entails minimizing a weighted sum of two terms–fidelity and regularization–and the weights in the sum are parameters that require manual tuning based on the properties of both the flow and the particle images. This manual tuning has historically been a consistent challenge that has limited the general applicability of OFV for experimental data, as the calculated velocity field is sensitive to the value of the weights. This work proposes a hierarchical model for the weighting parameters in the framework of a maximum a posteriori-based Bayesian optimization approach. The method replaces the classical Lagrange multiplier weighting parameter with a new, less-sensitive parameter that can be automatically predetermined from experimental images. The resulting method is tested on three different synthetic particle image velocimetry (PIV) datasets and on experimental particle images. The method is found to be capable of self-adjusting the local weights of the optimization process in real-time while simultaneously determining the velocity field, leading to an optimally regularized estimate of the velocity field without requiring any dataset-specific manual tuning of the parameters. The presented approach is the first truly general, parameter-free optical flow method for particle image velocimetry (PIV) images. The developed method is freely available as a part of the PIVlab package. 

Abstract Optical flow methods have been developed over the past two decades for application to PIV images with the goal of acquiring higher resolution measurements of the velocity field than conventional cross-correlation-based techniques. Numerous optical flow velocimetry (OFV) algorithms have been devised to solve the ill-posed optical flow problem, with various physics-inspired strategies to tailor them to fluid flows. While OFV can be applied to continuous scalar fields, it has demonstrated the most success on images of tracer particles, i.e.\ traditional planar PIV images. Compared to state-of-the-art cross-correlation algorithms, OFV methods have demonstrated an order of magnitude increase in spatial resolution and up to a factor of two improvement in overall accuracy when evaluated on synthetic data, at the cost of increased computational time. The requirements for particle seeding density, inter-frame displacement, and image quality are also more stringent for OFV methods compared to cross-correlation. OFV has been applied sparingly in experiments to date, but appears to offer the same advantages demonstrated on synthetic data. At this stage, OFV seems best suited to planar velocity measurements, although extensions to stereoscopic measurements have been demonstrated. 

Odor-guided navigation is fundamental to the survival and reproductive success of many flying insects. Despite its biological importance, the mechanics of how insects sense and interpret odor plumes in the presence of complex flow fields remain poorly understood. This study employs numerical simulations to investigate the influence of turbulence, wingbeat-induced flow, and Schmidt number on the structure and perception of odor plumes by flying insects. Using an in-house computational fluid dynamics solver based on the immersed-boundary method, we solve the three-dimensional Navier–Stokes equations to model the flow field. The solver is coupled with the equations of motion for passive flapping wings to emulate wingbeat-induced flow. The odor landscape is then determined by solving the odor advection–diffusion equation. By employing a synthetic isotropic turbulence generator, we introduce turbulence into the flow field to examine its impact on odor plume structures. Our findings reveal that both turbulence and wingbeat-induced flow substantially affect odor plume characteristics. Turbulence introduces fluctuations and perturbations in the plume, while wingbeat-induced flow draws the odorant closer to the insect’s antennae. Moreover, we demonstrate that the Schmidt number, which affects odorant diffusivity, plays a significant role in odor detectability. Specifically, at high Schmidt numbers, larger fluctuations in odor sensitivity are observed, which may be exploited by insects to differentiate between various odorant volatiles emanating from the same source. This study provides new insights into the complex interplay between fluid dynamics and sensory biology and behavior, enhancing our understanding of how flying insects successfully navigate using olfactory cues in turbulent environments. 

Abstract High fidelity near-wall velocity measurements in wall bounded fluid flows continue to pose a challenge and the resulting limitations on available experimental data cloud our understanding of the near-wall velocity behavior in turbulent boundary layers. One of the challenges is the spatial averaging and limited spatial resolution inherent to cross-correlation-based particle image velocimetry (PIV) methods. To circumvent this difficulty, we implement an explicit no-slip boundary condition in a wavelet-based optical flow velocimetry (wOFV) method. It is found that the no-slip boundary condition on the velocity field can be implemented in wOFV by transforming the constraint to the wavelet domain through a series of algebraic linear transformations, which are formulated in terms of the known wavelet filter matrices, and then satisfying the resulting constraint on the wavelet coefficients using constrained optimization for the optical flow functional minimization. The developed method is then used to study the classical problem of a turbulent channel flow using synthetic data from a direct numerical simulation (DNS) and experimental particle image data from a zero pressure gradient, high Reynolds number turbulent boundary layer. The results obtained by successfully implementing the no-slip boundary condition are compared to velocity measurements from wOFV without the no-slip condition and to a commercial PIV code, using the velocity from the DNS as ground truth. It is found that wOFV with the no-slip condition successfully resolves the near-wall profile with enhanced accuracy compared to the other velocimetry methods, as well as other derived quantities such as wall shear and turbulent intensity, without sacrificing accuracy away from the wall, leading to state of the art measurements in the $y^{+}<1$region of the turbulent boundary layer when applied to experimental particle images.