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.

Particle image velocimetry experiments have been performed in a turbulent boundary-layer wind tunnel in order to study the coherent structures taking part in the generation and preservation of wall turbulence. The particular wind tunnel used is suitable for high-resolution experiments ($\delta \gt 0.3$ m) at high Reynolds numbers (up to $R_{\theta} = 19\,000$ in the present results). Eddy structures were identified in instantaneous velocity maps in order to determine their mean characteristics and possible relationships between these structures. In the logarithmic region, the results show that the observed eddy structures appear to organize like elongated vortices, tilted downstream, mainly at an angle of about 45° and having a cane shape. The characteristics of these vortices appear here to be universal in wall units for $R_{\theta}\,{\leq}\,19\,000$. They seem to find their origin at a wall distance of about 25 wall units as quasi-streamwise vortices and to migrate away from the wall while tilting to form a head and a leg. Away from the wall, their radius increases and their vorticity decreases very slowly so that their circulation is nearly constant. Near the wall, the picture obtained is in fair agreement with existing models. The analysis of the results indicates a universality of the buffer-layer mechanism, even at low Reynolds number, and a sensitivity of the logarithmic region to low-Reynolds-number effects.

Particle Image Velocimetry is a measurement technique which is well adapted to the study of the structure of turbulent flows as it study allows to obtain quantitative information on the spatial structure of the velocity field. This contribution presents an experimental approach to characterize the measurement noise of a PIV system and the spatial response of such a method. This approach is based on a specific spectral analysis of the velocity vector field deduced from several PIV experiments. This study was done in two steps. The first step was to measure the noise level of PIV and to determine a model for the PIV transfer function from a series of displacement fields measured in a quiet flow. The second step was to compute spectra from velocity fields obtained in a turbulent boundary layer in a plane parallel to the wall. These spectra showed that PIV behaves like a band pass filter. This series of experiments allows to build a model for the prediction of the PIV spectrum based on the real one. This model confirms that the PIV noise is white. It allows to optimize the interrogation window size in order to obtain the best compromise between the spectral response and the spatial resolution.

In this work we propose and evaluate two variational data assimilation techniques for the estimation of low order surrogate experimental dynamical models for fluid flows. Both methods are built from optimal control recipes and rely on proper orthogonal decomposition and a Galerkin projection of the Navier Stokes equation. The techniques proposed differ in the control variables they involve. The first one introduces a weak dynamical model defined only up to an additional uncertainty time-dependent function whereas the second one, handles a strong dynamical constraint in which the dynamical system's coefficients constitute the control variables. Both choices correspond to different approximations of the relation between the reduced basis on which is expressed the motion field and the basis components that have been neglected in the reduced order model construction. The techniques have been assessed on numerical data and for real experimental conditions with noisy Image Velocimetry data.

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