This paper introduces several methods, generally used in fluid dynamics, to provide low-rank approximations. The algorithm describing these methods are mainly based on singular value decomposition (SVD) and dynamic mode decomposition (DMD) techniques, and are suitable to analyze turbulent flows. The application of these methods will be illustrated in the analysis of the turbulent wake of a wall-mounted cylinder, a geometry modeling a skyscraper. A brief discussion about the large and small size structures of the flow will provide the key ideas to represent the general dynamics of the flow using low-rank approximations. If the flow physics is understood, then it is possible to adapt these techniques, or some other strategies, to solve general complex problems with reduced computational cost. The main goal is to introduce these methods as machine learning strategies that could be potentially used in the field of fluid dynamics, and that can be extended to any other research field.

The development in supercomputing power allows running full-complexity Earth System Models (ESM) at increasingly higher spatial resolutions on a global scale. We show here a recent example where increased model resolution leads to a fundamentally different large-scale fluid dynamical adjustment of the mean wind pattern to the presence of an ice sheet over Europe compared to a coarse resolution simulation. While the higher resolution allows for a more realistic representation of atmospheric flow interaction with complex topographic features, the interpretation and prediction of the model results with a stronger bottom-up mechanical and thermal forcing on the atmosphere becomes increasingly difficult to be studied within a fully coupled model. We emphasize that interdisciplinary approaches should be pursued where the experience from engineering approaches of studying flow around objects and the influence of boundary-layer processes can help to disentangle the complexity within ESM. Ultimately, such engineering approaches will add a more fundamental theoretical understanding and prediction of expected flow interactions and will help to design full-complexity atmospheric model experiments accordingly.

The effect of a streamwise pressure gradient on the wake developed by wall-attached square ribs in a turbulent boundary layer is investigated experimentally. Favourable-, adverse- and zero-pressure-gradient conditions (FPG, APG and ZPG, respectively) are reproduced at matched friction Reynolds number and non-dimensional rib height. Flow-field measurements are carried out by means of Particle Image Velocimetry (PIV). Turbulence statistics are extracted at high resolution using an Ensemble Particle Tracking Velocimetry approach. Modal analysis is performed with Proper Orthogonal Decomposition (POD). We demonstrate that a non-dimensional expression of the pressure gradient and shear stress is needed to quantify the pressure-gradient effects in the wake developing past wall-attached ribs. We suggest the Clauser pressure-gradient parameter beta, commonly used in the literature for the characterization of turbulent boundary layers under the effect of a pressure gradient, as a suitable parameter. The results show that, in presence of an adverse pressure gradient, the recirculation region downstream of the rib is increased in size, thus delaying the reattachment, and that the peak of turbulence intensity and the shed eddies are shifted towards larger wall-normal distances than in the ZPG case. The observed changes with respect to the ZPG configuration appear more intense for larger magnitude of beta, which are more likely to be obtained in APG than in FPG due to the reduced skin friction and increased displacement thickness.

In the present work, we assess the capabilities of neural networks to predict temporally evolving turbulent flows. In particular, we use the nine-equation shear flow model by Moehlis et al. [New J. Phys. 6, 56 (2004)] to generate training data for two types of neural networks: the multilayer perceptron (MLP) and the long short-term memory (LSTM) networks. We tested a number of neural network architectures by varying the number of layers, number of units per layer, dimension of the input, and weight initialization and activation functions in order to obtain the best configurations for flow prediction. Because of its ability to exploit the sequential nature of the data, the LSTM network outperformed the MLP. The LSTM led to excellent predictions of turbulence statistics (with relative errors of 0.45% and 2.49% in mean and fluctuating quantities, respectively) and of the dynamical behavior of the system (characterized by Poincare maps and Lyapunov exponents). This is an exploratory study where we consider a low-order representation of near-wall turbulence. Based on the present results, the proposed machine-learning framework may underpin future applications aimed at developing accurate and efficient data-driven subgrid-scale models for large-eddy simulations of more complex wall-bounded turbulent flows, including channels and developing boundary layers.

Many recent investigations on the scale interactions in wall-bounded turbulent flows focus on describing so-called amplitude modulation, the phenomenon that deals with the influence of large scales in the outer region on the amplitude of the small-scale fluctuations in the near-wall region. The present study revisits this phenomenon regarding two aspects, namely the method for decomposing the scales and the quantification of the modulation. First, the paper presents a summary of the literature that has dealt with either or both aspects. Second, for decomposing the scales, different spectral filters (temporal, spatial or both) and empirical mode decomposition (EMD) are evaluated and compared. The common data set is a well-resolved large-eddy simulation that offers a wide range of Reynolds numbers spanning Re-theta = 880-8200. The quantification of the amplitude modulation is discussed for the resulting scale components. Particular focus is given to evaluate the efficacy of the various filters to separate scales for the range of Reynolds numbers of interest. Different to previous studies, the different methods have been evaluated using the same data set, thereby allowing a fair comparison between the various approaches. It is observed that using a spectral filter in the spanwise direction is an effective approach to separate the small and large scales in the flow, even at comparably low Reynolds numbers, whereas filtering in time should be approached with caution in the low-to-moderate Re range. Additionally, using filters in both spanwise and time directions, which would separate both wide and long-living structures from the small and fast scales, gives a cleaner image for the small-scales although the contribution to the scales interaction from that filter implementation has been found negligible. Applying EMD to decompose the scales gives similar results to Fourier filters for the energy content of the scales and thereby for the quantification of the amplitude modulation using the decomposed scales. No direct advantage of EMD over classical Fourier filters could be seen. Potential issues regarding different decomposition methods and different definitions of the amplitude modulation are also discussed.

Different types of thermal boundary conditions are conceivable in numerical simulations of convective heat transfer problems. Isoflux, isothermal and a mixed-type boundary condition are compared by means of direct numerical simulations (for the lowest Reynolds number) and well-resolved large-eddy simulations of a turbulent forced convection pipe flow over a range of bulk Reynolds numbers from Re-b = 5300 to Re-b = 37700, at two Prandtl numbers, i.e. Pr = 0.71 and Pr = 0.025. It is found that, while for Pr = 0.71 the Nusselt number is hardly affected by the type of thermal boundary condition, for Pr = 0.025 the isothermal boundary condition yields approximate to 20% lower Nusselt numbers compared to isoflux and mixedtype over the whole range of Reynolds numbers. A decomposition of the Nusselt number is derived. In particular, we decompose it into four contributions: laminar, radial and streamwise turbulent heat flux as well as a contribution due to the turbulent velocity field. For Pr = 0.71 the contribution due to the radial turbulent heat flux is dominant, whereas for Pr = 0.025 the contribution due to the turbulent velocity field is dominant. Only at a moderately high Reynolds number, such as Re-b = 37700, both turbulent contributions are of similar magnitude. A comparison of first- and second-order thermal statistics between the different types of thermal boundary conditions shows that the statistics are not only influenced in the near-wall region but also in the core region of the flow. Power spectral densities illustrate large thermal structures in low-Prandtl-number fluids as well as thermal structures located right at the wall, only present for the isoflux boundary condition. A database including the first- and second-order statistics together with individual contributions to the budget equations of the temperature variance and turbulent heat fluxes is hosted in the open access repository KITopen (DOI : https: //doi.org/10.5445/IR/1000096346).

Three methods are evaluated to estimate the streamwise velocity fluctuations of a zero-pressure-gradient turbulent boundary layer of momentum-thickness-based Reynolds number up to using as input velocity fluctuations at different wall-normal positions. A system identification approach is considered where large-eddy simulation data are used to build single and multiple-input linear and nonlinear transfer functions. Such transfer functions are then treated as convolution kernels and may be used as models for the prediction of the fluctuations. Good agreement between predicted and reference data is observed when the streamwise velocity in the near-wall region is estimated from fluctuations in the outer region. Both the unsteady behaviour of the fluctuations and the spectral content of the data are properly predicted. It is shown that approximately 45 % of the energy in the near-wall peak is linearly correlated with the outer-layer structures, for the reference case. These identified transfer functions allow insight into the causality between the different wall-normal locations in a turbulent boundary layer along with an estimation of the tilting angle of the large-scale structures. Differences in accuracy of the methods (single- and multiple-input linear and nonlinear) are assessed by evaluating the coherence of the structures between wall-normally separated positions. It is shown that the large-scale fluctuations are coherent between the outer and inner layers, by means of an interactions which strengthens with increasing Reynolds number, whereas the finer-scale fluctuations are only coherent within the near-wall region. This enables the possibility of considering the wall-shear stress as an input measurement, which would more easily allow the implementation of these methods in experimental applications. A parametric study was also performed by evaluating the effect of the Reynolds number, wall-normal positions and input quantities considered in the model. Since the methods vary in terms of their complexity for implementation, computational expense and accuracy, the technique of choice will depend on the application under consideration. We also assessed the possibility of designing and testing the models at different Reynolds numbers, where it is shown that the prediction of the near-wall peak from wall-shear-stress measurements is practically unaffected even for a one order of magnitude change in the corresponding Reynolds number of the design and test, indicating that the interaction between the near-wall peak fluctuations and the wall is approximately Reynolds-number independent. Furthermore, given the performance of such methods in the prediction of flow features in turbulent boundary layers, they have a good potential for implementation in experiments and realistic flow control applications, where the prediction of the near-wall peak led to correlations above 0.80 when wall-shear stress was used in a multiple-input or nonlinear scheme. Errors of the order of 20 % were also observed in the determination of the near-wall spectral peak, depending on the employed method.

The implementation of adaptive mesh refinement (AMR) in Nek5000 is used for the first time on the simulation of the flow over wings. This is done by simulating the flow over a NACA4412 profile with 5 degrees angle of attack at chord-based Reynolds number 200,000. The mesh is progressively refined by means of AMR which allows for high resolution near the wall whereas significantly larger elements are used in the far-field. The resultant mesh shows higher resolution than previous conformal meshes, and it allows for larger computational domains,which avoid the use of RANS to determine the boundary condition, all of this with, approximately, 3 times lower total number of grid points. The results ofthe turbulence statistics show a good agreement with the ones obtained with the conformal mesh. Finally, using AMR on wings leads to simulations at higher Reynolds numbers (i.e. Rec = 850, 000) in order to analyse the effect of adverse pressure gradients at high Reynolds numbers.

In this work we extend the vorticity-flux approach, proposed by Brown and Roshko (2012) for the analysis of turbulent shear layers and wakes, to the study of secondary flows of Prandtl's second kind. To this end, we assess direct numerical simulations (DNSs) of turbulent flow through sinusoidal channels (Vidal et al., 2018a) at bulk Reynolds numbers Re h = 2500 and 5000, and with various wall wave parameters, leading to a range of secondary flow intensities. We find that the fluctuating vorticity-flux difference (w'omega(y)') over bar (+) - (v'omega(z)') over bar (+) is closely connected to the in-plane cross-flow, in particular the large negative values present around the wall peak, which enhance the transport of near-wall momentum towards the channel core. The tilting of sweep events at the wall valley is also connected to the secondary flow magnitude, and is associated with positive values of the fluctuating vorticity-flux difference. Furthermore, conditionally averaged fields show that, unlike what is observed in channels with flat walls, the behavior in the vorticity-flux field at the peak is mostly due to Q1 and Q4 events, which essentially tilt momentum towards the peak.

In this study, the sources of uncertainty of hot-wire anemometry (HWA) and oil-film interferometry (OFI) measurements are assessed. Both statistical and classical methods are used for the forward and inverse problems, so that the contributions to the overall uncertainty of the measured quantities can be evaluated. The correlations between the parameters are taken into account through the Bayesian inference with error-in-variable (EiV) model. In the forward problem, very small differences were found when using Monte Carlo (MC), Polynomial Chaos Expansion (PCE) and linear perturbation methods. In flow velocity measurements with HWA, the results indicate that the estimated uncertainty is lower when the correlations among parameters are considered, than when they are not taken into account. Moreover, global sensitivity analyses with Sobol indices showed that the HWA measurements are most sensitive to the wire voltage, and in the case of OFI the most sensitive factor is the calculation of fringe velocity. The relative errors in wall-shear stress, friction velocity and viscous length are 0.44%, 0.23% and0.22%, respectively. Note that these values are lower than the ones reported in other wall-bounded turbulence studies. Note that in most studies of wall-bounded turbulence the correlations among parameters are not considered, and the uncertainties from the various parameters are directly added when determining the overall uncertainty of the measured quantity. In the present analysis we account for these correlations, which may lead to a lower overall uncertainty estimate due to error cancellation Furthermore, our results also indicate that the crucial aspect when obtaining accurate inner-scaled velocity measurements is the wind-tunnel flow quality, which is more critical than the accuracy in wall-shear stress measurements.