This work contributes to the study of flow over a circular cylinder at Reynolds number Re= 3900. Although this classical flow is widely documented in the literature, especially for this precise Reynolds number that leads to a subcritical flow regime, there is no consensus about the turbulence statistics immediately just behind the obstacle. Here, the flow is investigated both numerically with large eddy simulation and experimentally with hot-wire anemometry and particle image velocimetry. The numerical simulation is performed using high-order schemes and a specific immersed boundary method. The present study focuses on turbulence statistics and power spectra in the near wake up to ten diameters. Statistical estimation is shown to need large integration times increasing the computational cost and leading to an uncertainty of about 10% for most flow characteristics considered in this study. The present numerical and experimental results are found to be in good agreement with previous large eddy simulation data. Contrary to this, the present results show differences compared to the experimental data found in the literature, the differences being larger than the estimated uncertainty range. Therefore, previous numerical-experimental controversy for this flow seems to be reduced with the data presented in this article.

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Variational approaches to image motion segmentation has been an active field of study in image processing and computer vision for two decades. We present a short overview over basic estimation schemes and report in more detail recent modifications and applications to fluid flow estimation. Key properties of these approaches are illustrated by numerical examples. We outline promising research directions and point out the potential of variational techniques in combination with correlation-based PIV methods, for improving the consistency of fluid flow estimation and simulation.

A method for generating inflow conditions for direct numerical simulations (DNS) of spatially-developing flows is presented. The proposed method is based on variational data assimilation and adjoint-based optimization. The estimation is conducted through an iterative process involving a forward integration of a given dynamical model followed by a backward integration of an adjoint system defined by the adjoint of the discrete scheme associated to the dynamical system. The approach's robustness is evaluated on two synthetic velocity field sequences provided by numerical simulation of a mixing layer and a wake flow behind a cylinder. The performance of the technique is also illustrated in a real world application by using PIV measurements to acquire the database. This method allows to denoise experimental velocity fields and to reconstruct a continuous trajectory of motion fields from discrete and unstable measurements.

We present a variational assimilation technique (4D-Var) to reconstruct time resolved incompressible turbulent flows from measurements on two orthogonal 2D planes. The proposed technique incorporates an error term associated to the flow dynamics. It is therefore a compromise between a strong constraint assimilation procedure (for which the dynamical model is assumed to be perfectly known) and a weak constraint variational assimilation which considers a model enriched by an additive Gaussian forcing. The first solution would require either an unaffordable direct numerical simulation (DNS) of the model at the finest scale or an inaccurate and numerically unstable large scale simulation without parametrisation of the unresolved scales. The second option, the weakly constrained assimilation, relies on a blind error model that needs to be estimated from the data. This latter option is also computationally impractical for turbulent flow models as it requires to augment the state variable by an error variable of the same dimension. The proposed 4D-Var algorithm is successfully applied on a 3D turbulent wake flow in the transitional regime without specifying the obstacle geometry. The algorithm is validated on a synthetic 3D data-set with full-scale information. The performance of the algorithm is further analysed on data emulating large-scale experimental PIV observations.

Abstract-Based on physical laws describing the multi-scale structure of turbulent flows, this article proposes a regularizer for fluid motion estimation from an image sequence. Regularization is achieved by imposing some scale invariance property between histograms of motion increments computed at different scales. By reformulating this problem from a Bayesian perspective, an algorithm is proposed to jointly estimate motion, regularization hyper-parameters, and to select the most likely physical prior among a set of models. Hyper-parameter and model inference is conducted by posterior maximization, obtained by marginalizing out non-Gaussian motion variables. The Bayesian estimator is assessed on several image sequences depicting synthetic and real turbulent fluid flows. Results obtained with the proposed approach exceed the state of the art results in fluid flow estimation.

Three-dimensional direct numerical simulations of vortex shedding behind cylinders have been performed when the body diameter and the incoming flow involved spanwise linear nonuniformity. Four configurations were considered: the shear flow, the tapered cylinder and their combination which gave rise to namely the adverse and aiding cases. In contrast with the observations of other investigators, these computations highlighted distinct vortical features between the shear case and the tapered case. In addition, it was observed that the shear case and the adverse case (respectively tapered case and aiding case), yielded similarities in flow topology. This phenomenon was explained by the spanwise variations of U/D which seemed to govern these flows. Indeed, it was observed that large spanwise variations of U/D seemed to enhance three dimensionality, through the appearance of vortex adhesions and dislocations. Spanwise cellular pattern of vortex shedding was identified. Their modifications in cell size, junction position and number were correlated with the variation of U/D. In the lee side of the obstacle a wavy secondary motion was identified. Induced secondary flow due to the bending of Karman vortices in the vicinity of vortex adhesion and dislocations was suggested to explain this result.

Ensemble based optimal control schemes combine the components of ensemble Kalman filters and variational data assimilation (4DVar). They are trendy because they are easier to implement than 4DVar. In this paper, we evaluate a modified version of an ensemble based optimal control strategy for image data assimilation. This modified method is assessed with a Shallow Water model combined with synthetic data and original incomplete experimental depth sensor observations. This paper shows that the modified ensemble technique is better in quality and can reduce the computational cost.