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Multiflow is a research program, funded by the European Research Council, whose goal is to improve our understanding of the multiscale dynamics of turbulence in fluids. Its first Summer School on Turbulence took place at the School of Aeronautics of the Universidad Politécnica de Madrid over the months of June and July of 2013, with the goal of providing a meeting place for theoreticians, experimentalists and simulators, in which to develop and test new ideas on turbulence physics and structure. Around forty, mostly young, participants from twenty international groups met for five weeks of collaborative work, primarily using the computational data archived in the receiving institution but, in many cases, also contributing their own. Although the format included a few invited formal seminars and periodic plenary meetings, most of the work took place in small groups that, in many cases, changed their composition during the workshop. The papers in these proceedings reflect the results of the work of those groups which, in many cases, later continued in the form of new collaborations.

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All papers published in this volume of Journal of Physics: Conference Series have been peer reviewed through processes administered by the proceedings Editors. Reviews were conducted by expert referees to the professional and scientific standards expected of a proceedings journal published by IOP Publishing.

This paper presents the large eddy simulation (LES) of turbulent channel flow using a self-energy (SE) subgrid model with coefficients determined from reference direct numerical simulations (DNSs). In contrast to standard approaches that develop subgrid models based upon physical hypotheses, in the present SE approach the model coefficients are determined from the subgrid statistics of a DNS, with physical interpretations made apostiori. This technique is applied here for the first time to wall-bounded flows, specifically channel flow. The stochastic SE subgrid model consists of a meanfield shift, deterministic drain dissipation acting on the resolved field and a stochastic backscatter force. The deterministic SE subgrid model comprises of a net dissipation representing the net effect of the drain and backscatter. We present LESs that reproduce the time-averaged kinetic energy spectra of the DNS within the resolved scales. The direction and magnitude of the energy transfers in scale space can then be determined from the coefficients of the SE subgrid model. Results are presented for friction velocity based Reynolds numbers up to Re_τ = 950.

A model for off-wall boundary conditions for turbulent flow is investigated. The objective of such a model is to circumvent the need to resolve the buffer layer near the wall, by providing conditions in the logarithmic layer for the overlying flow. The model is based on the self-similarity of the flow at different heights in the logarithmic layer. It was first proposed by Mizuno and Jiménez (2013), imposing at the boundary plane a velocity field obtained on-the-fly from an overlying region. The key feature of the model was that the lengthscales of the field were rescaled to account for the self-similarity law. The model was successful at sustaining a turbulent logarithmic layer, but resulted in some disagreements in the flow statistics, compared to fully-resolved flows. These disagreements needed to be addressed for the model to be of practical application. In the present paper, a more refined, wavelength-dependent rescaling law is proposed, based on the wavelength-dependent dynamics in fully-resolved flows. Results for channel flow show that the new model eliminates the large artificial pressure fluctuations found in the previous one, and a better agreement is obtained in the bulk properties, the flow fluctuations, and their spectral distribution across the whole domain.

The determination of the local Lagrangian evolution of the flow topology in wall-bounded turbulence, and of the Lagrangian evolution associated with entrainment across the turbulent / non-turbulent interface into a turbulent boundary layer, require accurate tracking of a fluid particle and its local velocity gradients. This paper addresses the implementation of fluid-particle tracking in both a turbulent boundary layer direct numerical simulation and in a fully developed channel flow simulation. Determination of the sub-grid particle velocity is performed using both cubic B-spline, four-point Hermite spline and higher-order Hermite spline interpolation. Both wall-bounded flows show similar oscillations in the Lagrangian tracers of both velocity and velocity gradients, corresponding to the movement of particles across the boundaries of computational cells. While these oscillation in the particle velocity are relatively small and have negligible effect on the particle trajectories for time-steps of the order of CFL = 0.1, they appear to be the cause of significant oscillations in the evolution of the invariants of the velocity gradient tensor.

S3T (Stochastic Structural Stability Theory) employs a closure at second order to obtain the dynamics of the statistical mean turbulent state. When S3T is implemented as a coupled set of equations for the streamwise mean and perturbation states, nonlinearity in the dynamics is restricted to interaction between the mean and perturbations. The S3T statistical mean state dynamics can be approximately implemented by similarly restricting the dynamics used in a direct numerical simulation (DNS) of the full Navier-Stokes equations (referred to as the NS system). Although this restricted nonlinear system (referred to as the RNL system) is greatly simplified in its dynamics in comparison to the associated NS, it nevertheless self-sustains a turbulent state in wall-bounded shear flow with structures and dynamics comparable to those observed in turbulence. Moreover, RNL turbulence can be analysed effectively using theoretical methods developed to study the closely related S3T system. In order to better understand RNL turbulence and its relation to NS turbulence, an extensive comparison is made of diagnostics of structure and dynamics in these systems. Although quantitative differences are found, the results show that turbulence in the RNL system closely parallels that in NS and suggest that the S3T/RNL system provides a promising reduced complexity model for studying turbulence in wall-bounded shear flows.

The present work describes the multidimensional behaviour of wall-bounded turbulence in the space of cross-scales (spanwise and wall-normal) and distances from the wall. This approach allows us to understand the cascade mechanisms by which scale-energy is transmitted scale-by-scale away from the wall, through the overlap layer, and into the bulk flow. Two distinct cascades are identified involving the attached and detached scales of motion, respectively. From the near-wall region, scale-energy is transferred towards the bulk, flowing through the attached scales of motion, while among the detached scales it converges towards small scales, ascending again to the channel centre. It is then argued that the attached scales of wall-bounded turbulence are involved in a reverse cascade process that starts from the wall and ends in the bulk flow. On the other hand, the detached scales belong to a direct forward cascade process towards dissipation. Hence, at a given distance from the wall the attached motion is fed by smaller attached scales located closer to the wall. In turn this attached motion is responsible for creating the scale-energy that sustains larger attached scales farther from the wall and smaller detached scales that are responsible for connecting the scale-energy at large scales to the dissipation at small scales through a forward cascade.

Granger causality is based on the idea that if a variable helps to predict another one, then they are probably involved in a causality relationship. This technique is based on the identification of a predictive model for causality detection. The aim of this paper is to use Granger causality to study the dynamics and the energy redistribution between scales and components in wall-bounded turbulent flows. In order to apply it on flows, Granger causality is generalized for snapshot-based observations of large size using linear-model identification methods coming from model reduction. Optimized DMD, a variant of the Dynamic Mode Decomposition, is considered for building a linear model based on snapshots. This method is used to link physical events and extract physical mechanisms associated to the bursting process in the logarithmic layer of a turbulent channel flow.

A strongly decelerated turbulent boundary layer is investigated by direct numerical simulation. Transition to turbulence is triggered by a trip wire which is modelled using the immersed boundary method. The Reynolds number close to the exit of the numerical domain is Re_θ = 2175 and the shape-factor is H = 2.5. The analysis focuses on the latter portion of the flow with large velocity defect, at higher Reynolds numbers and further from the transition region. Mean velocity profiles do not reveal a logarithmic law. Departure from the law of the wall occurs throughout the inner region. The production and Reynolds stress peaks move to roughly the middle of the boundary layer. The profiles of the uv correlation factor reveal that u and v become less correlated throughout the boundary layer as the mean velocity defect increases, especially near the wall. The structure parameter is low in the present flow, similar to equilibrium APG flows and mixing layers, and decreases as the mean velocity defect increases. The statistics of the upper half of the boundary layer resemble those of a mixing layer. Furthermore, various two-dimensional two-point correlation maps are obtained. The C_vv and C_ww correlations obtained far from the transition region at Re_θ = 2175 and at y/δ = 0.4 coincide with results obtained for a ZPG boundary layer, implying that the structure of the v,w fluctuations is the same as in ZPG. However, C_uu indicates that the structure of the u fluctuation in this APG boundary layer is almost twice as short as the ZPG one. The APG structures are also less correlated with the flow at the wall. The near-wall structures are different from ZPG flow ones in that streaks are much shorter or absent.

The present work addresses the question whether hairpin vortices are a dominant feature of near-wall turbulence and which role they play during transition. First, the parent-offspring mechanism is investigated in temporal simulations of a single hairpin vortex introduced in a mean shear flow corresponding to turbulent channels and boundary layers up to Re_τ = 590. Using an eddy viscosity computed from resolved simulations, the effect of a turbulent background is also considered. Tracking the vortical structure downstream, it is found that secondary hairpins are created shortly after initialization. Thereafter, all rotational structures decay, whereas this effect is enforced in the presence of an eddy viscosity.

In a second approach, a laminar boundary layer is tripped to transition by insertion of a regular pattern of hairpins by means of defined volumetric forces representing an ejection event. The idea is to create a synthetic turbulent boundary layer dominated by hairpin-like vortices. The flow for Re_τ < 250 is analysed with respect to the lifetime of individual hairpin-like vortices. Both the temporal and spatial simulations demonstrate that the regeneration process is rather short-lived and may not sustain once a turbulent background has formed. From the transitional flow simulations, it is conjectured that the forest of hairpins reported in former DNS studies is an outer layer phenomenon not being connected to the onset of near-wall turbulence.

Critical points in the skin friction field of wall-bounded ows were investigated using data from direct numerical simulations of channels at Re_τ = 934 and Re_τ = 1834. A method for their detection and characterisation is outlined, and a statistical description of their properties is reported. Their lifetime, average distance, velocity and area density were computed. Conditionally averaged fields were calculated in order to examine the average ow in the vicinity of a critical point. It was found that the critical points are connected to surprisingly large features in the channel. A mechanism for the generation of the critical points is postulated, based on the conditional averages and analysis of time sequences in the ow above them.

Direct numerical simulation data of fully developed turbulent pipe flow are extensively compared with those of turbulent channel flow and zero-pressure-gradient boundary layer flow for Re_τ up to 1000. In the near-wall region, a high degree of similarity is observed in the three flow cases in terms of one-point statistics, probability density functions of the wall-shear stress and pressure, spectra, Reynolds stress budgets and advection velocity of the turbulent structures. This supports the notion that the near-wall region is universal for pipe and channel flow. Probability density functions of the wall shear stress, streamwise turbulence intensities, one-dimensional spanwise/azimuthal spectra of the streamwise velocity and Reynolds-stress budgets are very similar near the wall in the three flow cases, suggesting that the three canonical wall-bounded flows share many features. In the wake region, the mean streamwise velocity and Reynolds stress budgets show some expected differences.

Scaling of pressure spectrum in zero-pressure-gradient turbulent boundary layers is discussed. Spatial DNS data of boundary layer at one time instant (Re_θ = 4500) are used for the analysis. It is observed that in the outer regions the pressure spectra tends towards the -7/3 law predicted by Kolmogorov's theory of small-scale turbulence. The slope in the pressure spectra varies from -1 close to the wall to a value close to -7/3 in the outer region. The streamwise velocity spectra also show a -5/3 trend in the outer region of the flow. The exercise carried out to study the amplitude modulation effect of the large scales on the smaller ones in the near-wall region reveals a strong modulation effect for the streamwise velocity, but not for the pressure fluctuations. The skewness of the pressure follows the same trend as the amplitude modulation coefficient, as is the case for the velocity. In the inner region, pressure spectra were seen to collapse better when normalized with the local Reynolds stress than when scaled with the local turbulent kinetic energy

We explore the mechanisms behind vortical structural interactions modifying large-scale structures in wall turbulence. The evidence for this in terms of vortex interactions, such as merging and intense vortex strengthening, is found in [4] in ideal flow conditions. Here, these interactions are studied experimentally and numerically in turbulent boundary layer and channel flows respectively. This is done by extracting statistical information from conditional averaging of different events based on the spanwise swirling strength. Experimental results showed vortex merger leading to vortex intensification. This was in good agreement with the results of [4]. However, numerical results did not show complete agreement with experimental results. This may be due to the difference in spatial resolution of experimental and numerical data. Furthermore, the peak Reynolds shear stress did reveal a relative increase in magnitude when two vortices merged in the numerical data.

A detailed characterization of the shear layer in a direct numerical simulation of a Mach 3, separated shock/turbulent boundary layer interaction over a 24° compression ramp is presented. Similarity solutions are identified in the time-averaged shear layer and the growth of the shear layer is found to be approximately linear. In addition to the time averaged spatial organization of the shear layer, the characteristic frequencies and time scales of the large Kelvin- Helmholtz vortices are determined and are found to be consistent with the energized frequency content in the pre-multiplied power spectra of the wall pressure. The three-dimensional nature of the mixing layer vortices are identified using two-dimensional correlation contour plots and a technique for the identification of individual vortices. The large vortices shed from the separated region are found to lie in a plane parallel to the ramp surface, but angled at ±45° to the freestream direction.

The effect of the boundary conditions on the organization of vortex clusters is analyzed in two separate cases: rough channel flow and grid-generated turbulence. The aim is to understand how far the fluid structures are affected by the presence of roughness and the geometry of the grid. The grid-turbulence cases show that the single- and multi-scale geometries generate a flow strongly dominated by the shear at the beginning. The shear is initially caused by the presence of the body and, for the multi-scale grids, subsequently by the large differences between the scales. Further downstream from the grid these shear-dominated structures break up and form more isotropic clusters, whose dimensions seem to depend little on the particular geometry of the grid. For fractal grids, clusters are formed right downstream of the grid, resulting in a flow with less inhomogeneities than for single- and multi-scale grids. Eight different rough surfaces have been analyzed. In the smooth channel, both attached and detached clusters have been found and, depending on the geometry, the roughness affects the attached structures. Roughnesses made of aligned obstacles with a large separation seem to reduce the number of these structures in the flow. When the roughness elements are closely packed, both for transverse and aligned obstacles, the attached clusters are not able to reach within the roughness elements, and they seem to be anchored to the plane of the crests.

The characteristics of turbulent/nonturbulent interfaces (TNTI) from boundary layers, jets and shear-free turbulence are compared using direct numerical simulations. The TNTI location is detected by assessing the volume of turbulent flow as function of the vorticity magnitude and is shown to be equivalent to other procedures using a scalar field. Vorticity maps show that the boundary layer contains a larger range of scales at the interface than in jets and shear-free turbulence where the change in vorticity characteristics across the TNTI is much more dramatic. The intermittency parameter shows that the extent of the intermittency region for jets and boundary layers is similar and is much bigger than in shear-free turbulence, and can be used to compute the vorticity threshold defining the TNTI location. The statistics of the vorticity jump across the TNTI exhibit the imprint of a large range of scales, from the Kolmogorov micro-scale to scales much bigger than the Taylor scale. Finally, it is shown that contrary to the classical view, the low-vorticity spots inside the jet are statistically similar to isotropic turbulence, suggesting that engulfing pockets simply do not exist in jets.