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An optimal sensor placement procedure is proposed within the framework of variational data assimilation (DA) for unsteady flows, with the aim of maximizing the efficiency of the DA procedure. It is dedicated to the a priori design of a sensor network, and relies on a first-order adjoint approach. The proposed methodology first consists in identifying, via optimal control, the locations in the flow that have the greatest sensitivity with respect to a change in the initial condition, boundary conditions or model parameters. In a second step, sensors are placed at these locations for DA purposes. The use of this optimal sensor placement procedure does not require extra development in the case where a variational DA suite is available. The proposed methodology is applied to the reconstruction of unsteady bidimensional flows past a rotationally oscillating cylinder. More precisely, the possibilities of reconstructing the rotational speed of the cylinder and the initial flow, which here encompasses upstream conditions, from various types of observations are investigated via variational DA. Then, the observation optimization procedure is employed to identify optimal locations for placing velocity sensors downstream of the cylinder. Both reduction in the computational cost and improvement in the quality of the reconstructed flow are achieved through optimal sensor placement, encouraging the application of the proposed methodology to more complex and realistic flows.

The present paper provides an up-to-date survey of the use of large eddy simulation (LES) and sequels for engineering applications related to aerodynamics. Most recent landmark achievements are presented. Two categories of problem may be distinguished whether the location of separation is triggered by the geometry or not. In the first case, LES can be considered as a mature technique and recent hybrid Reynolds-averaged Navier-Stokes (RANS)-LES methods do not allow for a significant increase in terms of geometrical complexity and/or Reynolds number with respect to classical LES. When attached boundary layers have a significant impact on the global flow dynamics, the use of hybrid RANS-LES remains the principal strategy to reduce computational cost compared to LES. Another striking observation is that the level of validation is most of the time restricted to time-averaged global quantities, a detailed analysis of the flow unsteadiness being missing. Therefore, a clear need for detailed validation in the near future is identified. To this end, new issues, such as uncertainty and error quantification and modelling, will be of major importance. First results dealing with uncertainty modelling in unsteady turbulent flow simulation are presented.

Both theoretical analysis and eddy-damped quasi-normal Markovian (EDQNM) simulations are carried out to investigate the different decay regimes of an initially non-self-similar isotropic turbulence. Breakdown of self-similarity is due to the consideration of a composite three-range energy spectrum, with two different slopes at scales larger than the integral length scale. It is shown that, depending on the initial conditions, the solution can bifurcate towards a true self-similar decay regime, or sustain a non-self-similar state over an arbitrarily long time. It is observed that these non-self-similar regimes cannot be detected, restricting the observation to time exponents of global quantities such as kinetic energy or dissipation. The actual reason is that the decay is controlled by large scales close to the energy spectrum peak. This theoretical prediction is assessed by a detailed analysis of triadic energy transfers, which show that the largest scales have a negligible impact on the total transfers. Therefore, it is concluded that details of the energy spectrum near the peak, which may be related to the turbulence production mechanisms, are important. Since these mechanisms are certainly not universal, this may at least partially explain the significant discrepancies that exist between experimental data and theoretical predictions. Another conclusion is that classical self-similarity theories, which connect the asymptotic behaviour of either the energy spectrum $E(k\\ensuremath{\\rightarrow} 0)$ or the velocity correlation function $f(r\\ensuremath{\\rightarrow} + \\infty )$ and the turbulence decay exponent, are not particularly relevant when the large-scale spectrum shape exhibits more than one range.

A nonlinear spectral model in terms of spherically averaged descriptors is derived for the prediction of homogeneous turbulence dynamics in the presence of arbitrary mean-velocity gradients. The governing equations for the tensor $\\hat{\\unicode[STIX]{x1D619}}_{ij}(\\boldsymbol{k},t)$ , the Fourier transform of the two-point second-order correlation tensor, are first closed by an anisotropic eddy-damped quasinormal Markovian procedure. This closure is restricted to turbulent flows where linear effects induced by mean-flow gradients have no essential qualitative effects on the dynamics of triple correlations compared with the induced production effects in the equations for second-order correlations. Truncation at the first relevant order of spectral angular dependence allows us to derive from these equations in vector $\\boldsymbol{k}$ our final model equations in terms of the wavenumber modulus $k$ only. Analytical spherical integration results in a significant decrease in computational cost. Besides, the model remains consistent with the decomposition in terms of directional anisotropy and polarization anisotropy, with a spherically averaged anisotropic spectral tensor for each contribution. Restriction of anisotropy to spherically averaged descriptors, however, entails a loss of information, and realizability conditions are considered to quantify the upper boundary of anisotropy that can be investigated with the proposed model. Several flow configurations are considered to assess the validity of the present model. Satisfactory agreement with experiments on grid-generated turbulence subjected to successive plane strains is observed, which confirms the capability of the model to account for production of anisotropy by mean-flow gradients. The nonlinear transfer terms of the model are further tested by considering the return to isotropy (RTI) of different turbulent flows. Different RTI rates for directional anisotropy and polarization anisotropy allow us to correctly predict the apparent delayed RTI shown after axisymmetric expansion. The last test case deals with homogeneous turbulence subjected to a constant pure plane shear. The interplay between linear and nonlinear effects is reproduced, yielding the eventual exponential growth of the turbulent kinetic energy.

Direct numerical simulation (DNS) and large-eddy simulation (LES) are carried out to investigate the frequency effect of zero-net-mass-flux forcing (synthetic jet) on a generic separated flow. The selected test case is a rounded ramp at a Reynolds number based on the step height of 28 275. The incoming boundary layer is fully turbulent with Rθ=1410. The whole flow in the synthetic jet cavity is computed to ensure an accurate description of the actuator effect on the flow field. In a first step, DNS is used to validate LES of this particular flow. In a second step, the effect of a synthetic jet at two reduced frequencies of 0.5 and 4 (based on the separation length of the uncontrolled case and the free-stream velocity) is investigated using LES. It is demonstrated that, with a proper choice of the oscillating frequency, separation can be drastically reduced for a velocity ratio between the jet and the flow lower than one. The low frequency is close to the natural vortex shedding frequency. Two different modes of the synthetic jet have been identified. A vorticity-dominated mode is observed in the low-frequency forcing case for which the separation length is reduced by 54%, while an acoustic-dominated mode is identified in the high-frequency forcing case for which the separation length is increased by 43%. The decrease of the separation length in the low-frequency forcing case is correlated with an increase of the turbulent kinetic energy level and consequently with an increase of the entrainment in the separated zone. A linear inviscid stability analysis shows that the increase of the separation length in the high-frequency forcing case is due to a modification of the mean velocity profile suggested by Stanek and coworkers. The result is a lower amplification of the perturbations and consequently, a lower entrainment into the mixing layer. To our knowledge, it is the first time that Stanek's hypothesis has been assessed, thanks to numerical simulations of fully turbulent flow.

A theoretical analysis is presented on the behaviour of the model coefficients for the well-known Smagorinsky model and two variational multi-scale (VMS) variants of the Smagorinsky model. The dependency on two important parameters is addressed, i.e. the ratio of the LES-filter width $\\varDelta$ and the Kolmogorov scale $\\eta$ on the one hand, and the ratio of the integral length scale $L$ and the LES-filter width $\\varDelta$ on the other hand. First of all, it is demonstrated that the model coefficients vary strongly with $\\varDelta/\\eta$. By evaluating the model coefficients as functions of the subgrid activity $s$ (which expresses the relative contribution of the subgrid-scale model in the total dissipation, and corresponds to a nonlinear transformation of $\\varDelta/\\eta$), we show that a classical Lilly–Smagorinsky model overestimates the dissipation, even in cases where the dissipation of the subgrid-scale model is dominant. Therefore, generic and easy-to-use modifications to the different models are proposed, which provide close approximations to the models employing ‘exact’ coefficients. For the standard Smagorinsky model, this modified model corresponds to approximating the eddy viscosity $\\nu_t$ as $\\nu_t\\,{=}\\,(\\nu_{\\mbox{\\textit{\\scriptsize Lilly}}}^2\\,{+}\\,\\nu^2)^{1/2} -\\nu$, with $\\nu_{\\mbox{\\textit{\\scriptsize Lilly}}}$ the turbulent viscosity obtained by employing Lilly's classical Smagorinsky constant and $\\nu$ the laminar viscosity. Similar easy-to-use relations are presented for the variational multi-scale Smagorinsky models. Next to the $\\varDelta/\\eta$ dependence of the model coefficients, the $L/\\varDelta$ behaviour is also elaborated. Although a strong dependence on $L/\\varDelta$ is observed for low values of the ratio, we do not advocate the use of $L/\\varDelta$-dependent model coefficients. Rather, the asymptotic $L/\\varDelta$ independence and the speed of asymptotic convergence are used as a tool to compare the quality of subgrid-scale models (e.g. $L/\\varDelta \\,{>}\\, 10$ is a minimum order of magnitude for the small–small VMS model), and differences are observed between the standard Smagorinsky model and its two VMS variants. Finally, for the VMS models, the influence of the shape of the high-pass filter, used in the variational multi-scale formulation, is investigated. We observed that smooth high-pass filters result in more robust VMS Smagorinsky models.

The time evolution of pressure statistics in freely decaying homogeneous isotropic turbulence (HIT) is investigated via eddy-damped quasi-normal Markovian (EDQNM) computations. The present results show that the time decay rate of pressure-based statistical quantities, such as pressure variance and pressure gradient variance, are sensitive to the breakdown of permanence of large eddies. New formulae for the associated time-decay exponents are proposed, which extend previous relations proposed in Lesieur, Ossia & Metais (Phys. Fluids, vol. 11, 1999, p. 1535). Particular attention is paid to finite-Reynolds-number (FRN) effects on the pressure spectrum and pressure statistics. The results also suggest that $R{e}_{\\lambda } = O(1{0}^{4} )$ must be considered to observe a one-decade inertial range in the pressure spectrum with Kolmogorov $- 7/ 3$ scaling. This threshold value is larger than almost all existing direct numerical simulation (DNS) and experimental data, justifying the discussion about other possible scaling laws. The $- 5/ 3$ slope reported in some DNS data is also recovered by the EDQNM model, but it is observed to be a low-Reynolds-number effect. Another important result is that FRN effects yield a departure from asymptotic theoretical behaviours which appear similar to some effects attributed to intermittency by most authors. This is exemplified by the ratio between pressure-based and velocity-based Taylor microscales. Therefore, high-Reynolds-number DNS or experiments such that $R{e}_{\\lambda } = O(1{0}^{4} )$ would be required in order to remove FRN effects and to analyse pure intermittency effects.

A large‐eddy simulation tool is developed for simulating the dynamics of atmospheric boundary layers (ABLs) using lattice Boltzmann method (LBM), which is an alternative approach for computational fluid dynamics and proved to be very well suited for the simulation of low‐Mach flows. The equations of motion are coupled with the global complex physical models considering the coupling among several mechanisms, namely basic hydro‐thermodynamics and body forces related to stratification, Coriolis force, canopy effects, humidity transport, and condensation. Mass and momentum equations are recovered by an efficient streaming, collision, and forcing process within the framework of LBM while the governing equations of temperature, liquid, and vapor water fraction are solved using a finite volume method. The implementation of wall models for ABL, subgrid models, and interaction terms related to multiphysic phenomena (e.g., stratification, condensation) is described, implemented, and assessed in this study. An immersed boundary approach is used to handle flows in complex configurations, with application to flows in realistic urban areas. Applications to both wind engineering and atmospheric pollutant dispersion are illustrated. Plain Language Summary We have described a new tool for large‐eddy simulation (LES) of atmospheric flows in this paper. LES with the lattice Boltzmann method (LBM) was used to simulate dry and cloudy atmospheric boundary layers (ABLs), along with flows in complex urban areas. To validate our LBM‐LES solver, we first simulated the four basic ABL cases coming from the previous intercomparison of LES codes. These were the neutral, convective, stable, and cloudy convective boundary layers. Then three extra cases for ABL with canopy effects were performed by our solver. The altitude‐dependent drag force and heat release source term were introduced and assessed in the present solver compared reference data. At last, the ProLB tool was successfully assessed considering two urban flow configurations: wind prediction in Shinjuku district in Tokyo, and gaseous pollutant dispersion in the Champs Elysées district in Paris. In both cases, very satisfactory comparisons with experimental data were recovered. Key Points An efficient large‐eddy simulation tool within framework of lattice Boltzmann method is developed for simulating the dynamics of atmospheric boundary layers and urban flows Immersed boundary approach coupled with wall models is introduced to handle flows in complex configurations, with application to turbulent flows in realistic urban areas The basic core, wall models, subgrid models, and interaction terms are described, implemented, and assessed in various micro‐meteorological flows and urban flows

This unique book gives a general unified presentation of the use of the multiscale/multiresolution approaches in the field of turbulence. The coverage ranges from statistical models developed for engineering purposes to multiresolution algorithms for the direct computation of turbulence. It provides the only available up-to-date reviews dealing with the latest and most advanced turbulence models (including LES, VLES, hybrid RANS/LES, DES) and numerical strategies.