Multiscale Analysis and Computation for the Three-Dimensional Incompressible Navier–Stokes Equations

In this paper, we perform a systematic multiscale analysis for the three-dimensional incompressible Navier–Stokes equations with multiscale initial data. There are two main ingredients in our multiscale method. The first one is that we reparameterize the initial data in the Fourier space into a formal two-scale structure. The second one is the use of a nested multiscale expansion together with a multiscale phase function to characterize the propagation of the small-scale solution dynamically. By using these two techniques and performing a systematic multiscale analysis, we derive a multiscale model which couples the dynamics of the small-scale subgrid problem to the large-scale solution without a closure assumption or unknown parameters. Furthermore, we propose an adaptive multiscale computational method which has a complexity comparable to a dynamic Smagorinsky model. We demonstrate the accuracy of the multiscale model by comparing with direct numerical simulations for both two- and three-dimensional problems. In the two-dimensional case we consider decaying turbulence, while in the three-dimensional case we consider forced turbulence. Our numerical results show that our multiscale model not only captures the energy spectrum very accurately, it can also reproduce some of the important statistical properties that have been observed in experimental studies for fully developed turbulent flows

A new LES subgrid-scale approach for turbulence modulation by droplets

We present a new modelling approach for turbulence modulation by droplets on the subgrid-scale (SGS) level of Large-Eddy-Simulations (LES). Many SGS models exist for the effect of gas phase SGS on the droplet phase, but very few for the mechanisms vice versa on the turbulent intensity of the gas phase. The reasons are a lack of physical understanding and limited computational resources for extensive DNS studies. To address both problems a dimension-reduced and consequently less costly model, namely One-Dimensional- Turbulence (ODT), is used to gather information about this specific flow phenomena. ODT is a stochastic tool simulating turbulent flows along a notional 1D line of sights. For modeling the turbulent advection instantaneous maps are applied to the line which represent the effect of individual eddies on property fields and the dispersed phase. After validating the general test case of a droplet-laden shear flow against DNS data, a concept is presented on how to gather turbulence modulation for several parameter ranges in a data base and how to make them accessible on the flight for LES. The three most significant parameters, the unladen flow Reynolds number, the droplet loading and the particle momentum number, are chosen to construct an efficient data base

Assessing different imaging velocimetry techniques to measure shallow runoff velocities during rain events using an urban drainage physical model

Although surface velocities are key in the calibration of physically based urban drainage models, the shallow water depths developed during non-extreme precipitation and the potential risks during flood events limit the availability of this type of data in urban catchments. In this context, imaging velocimetry techniques are being investigated as suitable non-intrusive methods to estimate runoff velocities, when the possible influence of rain has yet to be analyzed. This study carried out a comparative assessment of different seeded and unseeded imaging velocimetry techniques based on large-scale particle image velocimetry (LSPIV) and bubble image velocimetry (BIV) through six realistic but laboratory-controlled experiments, in which the runoff generated by three different rain intensities was recorded. First, the use of naturally generated bubbles and water shadows and glares as tracers allows unseeded techniques to measure extremely shallow flows. However, these techniques are more affected by raindrop impacts, which even lead to erroneous velocities in the case of high rain intensities. At the same time, better results were obtained for high intensities and in complex flows with techniques that use artificial particles. Finally, the study highlights the potential of these imaging techniques for measuring surface velocities in real field applications as well as the importance of considering rain properties to interpret and assess the results obtained. The robustness of the techniques for real-life applications yet remains to be proven by means of further studies in non-controlled environments.The project receives funding from the Spanish Ministry of Science and Innovation under POREDRAIN project RTI2018-094217-B-C33 (MINECO/FEDER-EU)

A Streamwise Constant Model of Turbulence in Plane Couette Flow

Streamwise and quasi-streamwise elongated structures have been shown to play a significant role in turbulent shear flows. We model the mean behavior of fully turbulent plane Couette flow using a streamwise constant projection of the Navier Stokes equations. This results in a two-dimensional, three velocity component ($2D/3C$) model. We first use a steady state version of the model to demonstrate that its nonlinear coupling provides the mathematical mechanism that shapes the turbulent velocity profile. Simulations of the $2D/3C$ model under small amplitude Gaussian forcing of the cross-stream components are compared to DNS data. The results indicate that a streamwise constant projection of the Navier Stokes equations captures salient features of fully turbulent plane Couette flow at low Reynolds numbers. A system theoretic approach is used to demonstrate the presence of large input-output amplification through the forced $2D/3C$ model. It is this amplification coupled with the appropriate nonlinearity that enables the $2D/3C$ model to generate turbulent behaviour under the small amplitude forcing employed in this study.Comment: Journal of Fluid Mechanics 2010, in pres

Wall-bounded turbulent flows at high Reynolds numbers: Recent advances and key issues

Wall-bounded turbulent flows at high Reynolds numbers have become an increasingly active area of research in recent years. Many challenges remain in theory, scaling, physical understanding, experimental techniques, and numerical simulations. In this paper we distill the salient advances of recent origin, particularly those that challenge textbook orthodoxy. Some of the outstanding questions, such as the extent of the logarithmic overlap layer, the universality or otherwise of the principal model parameters such as the von Kármán “constant,” the parametrization of roughness effects, and the scaling of mean flow and Reynolds stresses, are highlighted. Research avenues that may provide answers to these questions, notably the improvement of measuring techniques and the construction of new facilities, are identified. We also highlight aspects where differences of opinion persist, with the expectation that this discussion might mark the beginning of their resolution

The spatio-temporal spectrum of turbulent flows

Identification and extraction of vortical structures and of waves in a disorganised flow is a mayor challenge in the study of turbulence. We present a study of the spatio-temporal behavior of turbulent flows in the presence of different restitutive forces. We show how to compute and analyse the spatio-temporal spectrum from data stemming from numerical simulations and from laboratory experiments. Four cases are considered: homogeneous and isotropic turbulence, rotating turbulence, stratified turbulence, and water wave turbulence. For homogeneous and isotropic turbulence, the spectrum allows identification of sweeping by the large scale flow. For rotating and for stratified turbulence, the spectrum allows identification of the waves, precise quantification of the energy in the waves and in the turbulent eddies, and identification of physical mechanisms such as Doppler shift and wave absorption in critical layers. Finally, in water wave turbulence the spectrum shows a transition from gravity-capillary waves to bound waves as the amplitude of the forcing is increased.Comment: Added new references and analysi

The Sun's Supergranulation

Supergranulation is a fluid-dynamical phenomenon taking place in the solar photosphere, primarily detected in the form of a vigorous cellular flow pattern with a typical horizontal scale of approximately 30--35~megameters, a dynamical evolution time of 24--48~h, a strong 300--400~m/s (rms) horizontal flow component and a much weaker 20--30~m/s vertical component. Supergranulation was discovered more than sixty years ago, however, explaining its physical origin and most important observational characteristics has proven extremely challenging ever since, as a result of the intrinsic multiscale, nonlinear dynamical complexity of the problem concurring with strong observational and computational limitations. Key progress on this problem is now taking place with the advent of 21st-century supercomputing resources and the availability of global observations of the dynamics of the solar surface with high spatial and temporal resolutions. This article provides an exhaustive review of observational, numerical and theoretical research on supergranulation, and discusses the current status of our understanding of its origin and dynamics, most importantly in terms of large-scale nonlinear thermal convection, in the light of a selection of recent findings.Comment: Major update of 2010 Liv. Rev. Sol. Phys. review. Addresses many new theoretical, numerical and observational developments. All sections, including discussion, revised extensively. Also includes previously unpublished results on nonlinear dynamics of convection in large domains, and lagrangian transport at the solar surfac