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We develop a method to estimate space-time flow statistics from a limited set of known data. While previous work has focused on modeling spatial or temporal statistics independently, space-time statistics carry fundamental information about the physics and coherent motions of the flow and provide a starting point for low-order modeling and flow control efforts. The method is derived using a statistical interpretation of resolvent analysis. The central idea of our approach is to use known data to infer the statistics of the nonlinear terms that constitute a forcing on the linearized Navier-Stokes equations, which in turn imply values for the remaining unknown flow statistics through application of the resolvent operator. Rather than making an a priori rank-1 assumption, our method allows the known input data to select the most relevant portions of the resolvent operator for describing the data, making it well-suited for highrank turbulent flows. We demonstrate the predictive capabilities of the method using two examples: the Ginzburg-Landau equation, which serves as a convenient model for a convectively unstable flow, and a turbulent channel flow at low Reynolds number. * Email address for correspondence: towne@umich.edu power spectral densities (PSDs) using knowledge of the mean flow field and power spectra at a few locations. This is accomplished using a least-squares fit at each frequency between the known power spectra and the leading singular response mode obtained from the resolvent operator (McKeon & Sharma 2010), which is derived from the linearized Navier-Stokes equations. This strategy explicitly assumes that the spectral content at frequencies of interest is dominated by the leading resolvent mode, and the method performs well when the matching points are located in regions where this hypothesis is valid. Specifically, excellent PSD estimates were obtained for the flow over a backward-facing step (Beneddine et al. 2016) and an initially laminar jet (Beneddine et al. 2017).Zare et al. (2017) developed a method that uses arbitrary known entries in the spatial covariance tensor to estimate the remaining unknown entries. Their approach is also based on linearized flow equations and entails solving a convex optimization problem that determines a matrix controlling the structure and statistics of the associated nonlinear forcing terms. The optimization problem is subject to two constraints on the estimated covariance tensor: it must reproduce the known entries and obey a Lyapunov equation that relates the forcing and flow statistics. The constrained optimization problem is computationally demanding and requires a customized algorithm (Zare et al. 2015(Zare et al. , 2017.The objective of the present paper is to build on these previous methods to estimate unknown two-point space-time flow statistics. Both the PSDs (one-point temporal statistics) and spatial covariances (two-point spatial statistics) are subsets of two-point space-time correlations, so our approach represents a generalization of these previous m...

We conduct a series of large-eddy simulations (LES) to examine the mean flow behaviour within the roughness layer of turbulent boundary layer flow over rough surfaces. We consider several configurations consisting of arrays of rectangular-prism roughness elements with various spacings, aspect ratios and height distributions. The results provide clear evidence for exponential behaviour of the mean flow with respect to the wall normal distance. Such behaviour has been proposed before (see, e.g., Cionco, 1966 Tech. Rep. DTIC document), and is represented asis the spatially/temporally averaged fluid velocity, z is the wall normal distance, h represents the height of the roughness elements and U h is the velocity at z = h. The attenuation factor a depends on the density of the roughness element distribution and details of the roughness distribution on the wall. Once established, the generic velocity profile shape is used to formulate a fully analytical model for the effective drag exerted by turbulent flow on a surface covered with arrays of rectangular-prism roughness elements. The approach is based on the von Karman-Pohlhausen integral method, in which a shape function is assumed for the mean velocity profile and its parameters are determined based on momentum conservation and other fundamental constraints. In order to determine the attenuation parameter a, wake interactions among surface roughness elements are accounted for by using the concept of flow sheltering. The model transitions smoothly between 'k' and 'd' type roughness conditions depending on the surface coverage density and the detailed geometry of roughness elements. Comparisons between model predictions and experimental/numerical data from the existing literature as well as LES data from this study are presented. It is shown that the analytical model provides good predictions of mean velocity and drag forces for the cases considered, thus raising the hope that analytical roughness modelling based on surface geometry is possible, at least for cases when the location of flow separation over surface elements can be easily predicted, as in the case of wall-attached rectangular-prism roughness elements.

A new approach for wall modeling in Large-Eddy-Simulations (LES) is proposed and tested in various applications. To properly include near-wall physics while preserving the basic economy of equilibrium-type wall models, we adopt the classical integral method of von Karman and Pohlhausen (VKP). A velocity profile with various parameters is proposed as an alternative to numerical integration of the boundary layer equations in the near-wall zone. The profile contains a viscous or roughness sublayer and a logarithmic layer with an additional linear term that can account for inertial and pressure gradient effects. Similar to the VKP method, the assumed velocity profile coefficients are determined from appropriate matching conditions and physical constraints. The proposed integral wall-modeled LES (iWMLES) method is tested in the context of a pseudo-spectral code for fully developed channel flow with a dynamic Lagrangian subgrid model as well as in a finite-difference LES code including the immersed boundary method and the dynamic Vreman eddy-viscosity model. Test cases include a fully developed half-channel at various Reynolds numbers, a fully developed channel flow with unresolved roughness, a standard developing turbulent boundary layer flows over smooth plates at various Reynolds numbers, over plates with unresolved roughness, and a case with resolved roughness elements consisting of an array of wall-mounted cubes. The comparisons with data show that the proposed iWMLES method provides accurate predictions of near-wall velocity profiles in LES while, similarly to equilibrium wall models, its cost remains independent of Reynolds number and is thus significantly lower compared to existing zonal or hybrid wall models. A sample application to flow over a surface with truncated cones (representing idealized barnacle-like roughness elements) is also presented, which illustrates effects of subgrid scale roughness when combined with resolved roughness elements. C 2015 AIP Publishing LLC. [http://dx.

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