Dynamic mode decomposition (DMD) represents an effective means for capturing the essential features of numerically or experimentally generated flow fields. In order to achieve a desirable tradeoff between the quality of approximation and the number of modes that are used to approximate the given fields, we develop a sparsity-promoting variant of the standard DMD algorithm. Sparsity is induced by regularizing the least-squares deviation between the matrix of snapshots and the linear combination of DMD modes with an additional term that penalizes the l(1)-norm of the vector of DMD amplitudes. The globally optimal solution of the resulting regularized convex optimization problem is computed using the alternating direction method of multipliers, an algorithm well-suited for large problems. Several examples of flow fields resulting from numerical simulations and physical experiments are used to illustrate the effectiveness of the developed method. (C) 2014 AIP Publishing LLC.

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.

An eddy-viscosity based, subgrid-scale model for large eddy simulations is derived from the analysis of the singular values of the resolved velocity gradient tensor. The proposed σ-model has, by construction, the property to automatically vanish as soon as the resolved field is either two-dimensional or two-component, including the pure shear and solid rotation cases. In addition, the model generates no subgrid-scale viscosity when the resolved scales are in pure axisymmetric or isotropic contraction/expansion. At last, it is shown analytically that it has the appropriate cubic behavior in the vicinity of solid boundaries without requiring any ad-hoc treatment. Results for two classical test cases (decaying isotropic turbulence and periodic channel flow) obtained from three different solvers with a variety of numerics (finite elements, finite differences, or spectral methods) are presented to illustrate the potential of this model. The results obtained with the proposed model are systematically equivalent or slightly better than the results from the Dynamic Smagorinsky model. Still, the σ-model has a low computational cost, is easy to implement, and does not require any homogeneous direction in space or time. It is thus anticipated that it has a high potential for the computation of non-homogeneous, wall-bounded flows.

The effect of domain size on direct numerical simulations of turbulent channels with periodic boundary conditions is studied. New simulations are presented up to Re-tau = 4179 in boxes with streamwise and spanwise sizes of 2 pi h x pi h, where h is the channel half-height. It is found that this domain is large enough to reproduce the one-point statistics of larger boxes. A simulation in a box of size 60 pi h x 6 pi h is used to show that a contour of the two-dimensional premultiplied spectrum of the streamwise velocity containing 80% of the kinetic energy closes lambda(x) approximate to 100h. (C) 2014 AIP Publishing LLC.

It is well known that when wind turbines are deployed in large arrays, their efficiency decreases due to complex interactions among themselves and with the atmospheric boundary layer (ABL). For wind farms whose length exceeds the height of the ABL by over an order of magnitude, a "fully developed" flow regime can be established. In this asymptotic regime, changes in the streamwise direction can be neglected and the relevant exchanges occur in the vertical direction. Such a fully developed wind-turbine array boundary layer (WTABL) has not been studied systematically before. A suite of large eddy simulations (LES), in which wind turbines are modeled using the classical "drag disk" concept, is performed for various wind-turbine arrangements, turbine loading factors, and surface roughness values. The results are used to quantify the vertical transport of momentum and kinetic energy across the boundary layer. It is shown that the vertical fluxes of kinetic energy are of the same order of magnitude as the power extracted by the forces modeling the wind turbines. In the fully developed WTABL, the kinetic energy extracted by the wind turbines is transported into the wind-turbine region by vertical fluxes associated with turbulence. The results are also used to develop improved models for effective roughness length scales experienced by the ABL. The effective roughness scale is often used to model wind-turbine arrays in simulations of atmospheric dynamics at larger (regional and global) scales. The results from the LES are compared to several existing models for effective roughness lengths. Based on the observed trends, a modified model is proposed, showing improvement in the predicted effective roughness length.

One-point statistics are presented for new direct simulations of the zero-pressure-gradient turbulent boundary layer in the range Re-theta = 2780-6680, matching channels and pipes at delta(+) approximate to 1000-2000. For tripped boundary layers, it is found that the eddy-turnover length is a better criterion than the Reynolds number for the recovery of the largest flow scales after an artificial inflow. Beyond that limit, the integral parameters, mean velocities, Reynolds stresses, and pressure fluctuations of the new simulations agree very well with the available numerical and experimental data, but show clear differences with internal flows when expressed in wall units at the same wall distance and Reynolds number. Those differences are largest in the outer layer, independent of the Reynolds number, and apply to the three velocity components. The logarithmic increase with the Reynolds number of the maximum of the streamwise velocity and pressure fluctuations is confirmed to apply to experimental and numerical internal and external flows. The new simulations also extend to a wider range of Reynolds numbers, and to more than a decade in wall distance, the evidence for logarithmic intensity profiles of the spanwise velocity and of the pressure intensities. Streamwise velocity fluctuations appear to require higher Reynolds numbers to develop a clear logarithmic profile, but it is argued that the comparison of the available near-wall data with fluctuation profiles experimentally obtained by other groups at higher Reynolds numbers can only be explained by assuming the existence of a mesolayer for the fluctuations. The statistics of the new simulation are available in our website. (C) 2013 AIP Publishing LLC.

In the present article, the improvement of nanofluid heat transfer inside a porous cavity by means of a non-equilibrium model in the existence of Lorentz forces has been investigated by employing control volume based finite element method. Nanofluid properties are estimated by means of Koo-Kleinstreuer-Li. The Darcy-Boussinesq approximation is utilized for the nanofluid flow. Roles of the solid-nanofluid interface heat transfer parameter Nhs, Hartmann number Ha, porosity ε, and Rayleigh number Ra were presented. Outputs demonstrate that the convective flow decreases with the rise of Nhs, but it enhances with the rise of Ra. Porosity has opposite relationship with the temperature gradient.

Coherent structures in wall turbulence transport momentum and provide a means of producing turbulent kinetic energy. Above the viscous wall layer, the hairpin vortex paradigm of Theodorsen coupled with the quasistreamwise vortex paradigm have gained considerable support from multidimensional visualization using particle image velocimetry and direct numerical simulation experiments. Hairpins can autogenerate to form packets that populate a significant fraction of the boundary layer, even at very high Reynolds numbers. The dynamics of packet formation and the ramifications of organization of coherent structures (hairpins or packets) into larger-scale structures are discussed. Evidence for a large-scale mechanism in the outer layer suggests that further organization of packets may occur on scales equal to and larger than the boundary layer thickness.

Simultaneous effects of viscous dissipation and Joule heating in flow by rotating disk of variable thickness are examined. Radiative flow saturating porous space is considered. Much attention is given to entropy generation outcome. Developed nonlinear ordinary differential systems are computed for the convergent series solutions. Specifically, the results of velocity, temperature, entropy generation, Bejan number, coefficient of skin friction, and local Nusselt number are discussed. Clearly the entropy generation rate depends on velocity and temperature distributions. Moreover the entropy generation rate is a decreasing function of Hartmann number, Eckert number, and Reynolds number, while they gave opposite behavior for Bejan numbers.

Resolution requirements for large eddy simulation (LES), estimated by Chapman [AIAA J. 17 , 1293 (1979)], are modified using accurate formulae for high Reynolds number boundary layer flow. The new estimates indicate that the number of grid points ( N ) required for wall-modeled LES is proportional to Re L x , but a wall-resolving LES requires N ̃ Re L x 13 / 7 , where L x is the flat-plate length in the streamwise direction. On the other hand, direct numerical simulation, resolving the Kolmogorov length scale, requires N ̃ Re L x 37 / 14 .

In this paper, we demonstrate that periodic, micropatterned superhydrophobic surfaces, previously noted for their ability to provide laminar flow drag reduction, are capable of reducing drag in the turbulent flow regime. Superhydrophobic surfaces contain micro- or nanoscale hydrophobic features which can support a shear-free air-water interface between peaks in the surface topology. Particle image velocimetry and pressure drop measurements were used to observe significant slip velocities, shear stress, and pressure drop reductions corresponding to drag reductions approaching 50%. At a given Reynolds number, drag reduction is found to increase with increasing feature size and spacing, as in laminar flows. No observable drag reduction was noted in the laminar regime, consistent with previous experimental results for the channel geometry considered. The onset of drag reduction occurs at a critical Reynolds number where the viscous sublayer thickness approaches the scale of the superhydrophobic microfeatures and performance is seen to increase with further reduction in viscous sublayer height. These results indicate superhydrophobic surfaces may provide a significant drag reducing mechanism for marine vessels.

Coherent structures in wall turbulence transport momentum and provide a means of producing turbulent kinetic energy. Above the viscous wall layer, the hairpin vortex paradigm of Theodorsen coupled with the quasistreamwise vortex paradigm have gained considerable support from multidimensional visualization using particle image velocimetry and direct numerical simulation experiments. Hairpins can autogenerate to form packets that populate a significant fraction of the boundary layer, even at very high Reynolds numbers. The dynamics of packet formation and the ramifications of organization of coherent structures (hairpins or packets) into larger-scale structures are discussed. Evidence for a large-scale mechanism in the outer layer suggests that further organization of packets may occur on scales equal to and larger than the boundary layer thickness.

When deployed as large arrays, wind turbines significantly interact among themselves and with the atmospheric boundary layer. In this study, we integrate a three-dimensional large-eddy simulation with an actuator line technique to examine the characteristics of wind-turbine wakes in an idealized wind farm inside a stable boundary layer (SBL). The wind turbines, with a rotor diameter of 112 m and a tower height of 119 m , were "immersed" in a well-known SBL case that bears a boundary layer height of approximately 175 m . Two typical spacing setups were adopted in this investigation. The super-geostrophic low-level jet near the top of the boundary layer was eliminated owing to the energy extraction and the enhanced mixing of momentum. Non-axisymmetric wind-turbine wakes were observed in response to the non-uniform incoming turbulence, the Coriolis effect, and the rotational effects induced by blade motion. The Coriolis force caused a skewed spatial structure and drove a part of the turbulence energy away from the center of the wake. The SBL height was increased, while the magnitude of the surface momentum flux was reduced by more than 30%, and the magnitude of the surface buoyancy flux was reduced by more than 15%. The wind farm was also found to have a strong effect on vertical turbulent fluxes of momentum and heat, an outcome that highlights the potential impact of wind farms on local meteorology.

Using the salient properties of the flow observed in the equatorial Pacific as a guide, an asymptotic procedure is applied to the Euler equation written in a suitable rotating frame. Starting from the single overarching assumption of slow variations in the azimuthal direction in a two-layer, steady flow that is symmetric about the equator, a tractable, fully nonlinear, and three-dimensional system of model equations is derived, with the Coriolis terms consistent with the β-plane approximation retained. It is shown that this asymptotic system of equations can be solved exactly. The ability of this dynamical model to capture simultaneously fundamental oceanic phenomena, which are closely inter-related (such as upwelling/downwelling, zonal depth-dependent currents with flow reversal, and poleward divergence along the equator), is a novel and compelling feature that has hitherto been elusive. While details are presented for the equatorial flow in the Pacific, the analysis demonstrates that other flow configurations can be accommodated within the framework of this approach, depending on the choice of the underlying velocity profile and of the various parameters; the method is therefore applicable to a range of ocean flows with a similar three-dimensional structure.

The current state of knowledge about the structure of wall-bounded turbulent flows is reviewed, with emphasis on the layers near the wall in which shear is dominant, and particularly on the logarithmic layer. It is shown that the shear interacts with scales whose size is larger than about one third of their distance to the wall, but that smaller ones, and in particular the vorticity, decouple from the shear and become roughly isotropic away from the wall. In the buffer and viscous layers, the dominant structures carrying turbulent energy are the streamwise velocity streaks, and the vortices organize both the dissipation and the momentum transfer. Farther from the wall, the velocity remains organized in streaks, although much larger ones than in the buffer layer, but the vortices lose their role regarding the Reynolds stresses. That function is taken over by wall-attached turbulent eddies with sizes and lifetimes proportional to their heights. Two kinds of eddies have been studied in some detail: vortex clusters, and ejections and sweeps. Both can be classified into a detached background, and a geometrically self-similar wall-attached family. The latter is responsible for most of the momentum transfer, and is organized into composite structures that can be used as models for the attached-eddy hierarchy hypothesized by Townsend ["Equilibrium layers and wall turbulence," J. Fluid Mech. 11, 97-120 (1961)]. The detached component seems to be common to many turbulent flows, and is roughly isotropic. Using a variety of techniques, including direct tracking of the structures, it is shown that an important characteristic of wall-bounded turbulence is temporally intermittent bursting, which is present at all distances from the wall, and in other shear flows. Its properties and time scales are reviewed, and it is shown that bursting is an important part of the production of turbulent energy from the mean shear. It is also shown that a linearized model captures many of its characteristics. C (C) 2013 AIP Publishing LLC.

In this work, the effect of the presence of a heat source and its location on natural convection in a C-shaped enclosure saturated by a nanofluid is investigated numerically using the lattice Boltzmann method. Fifteen cases consisting of different heat source locations attached to an isolated wall of the enclosure have been considered to achieve the best configuration at different Rayleigh numbers (103-106) and various solid volume fractions of the nanofluid (0-0.05). Results are shown in terms of the streamlines, isothermal lines, velocity profiles, and the local and average Nusselt numbers. The numerical solution is benchmarked against published results from previous studies for validation, and a good agreement is demonstrated. According to the results, at Ra = 103, the maximum Nusselt number is achieved when the heat source is located within the upper horizontal cavity. Moreover, at higher Rayleigh numbers (Ra = 106) and locations of the heat source within the vertical cavity yield the best Nusselt numbers. Compared to the base fluid and at low Rayleigh numbers, the increase in the Nusselt number of the nanofluid is not found to be dependent on the location of the heat source. However, for high Rayleigh numbers, the maximum increase is obtained when the heat source is located in the upper part of the vertical.

We investigate the hydrodynamic friction properties of superhydrophobic surfaces and quantify their superlubricating potential. On such surfaces, the contact of the liquid with the solid roughness is minimal, while most of the interface is a liquid-gas one, resulting in strongly reduced friction. We obtain scaling laws for the effective slip length at the surface in terms of the generic surface characteristics (roughness length scale, depth, solid fraction of the interface, etc.). These predictions are successfully compared to numerical results in various geometries (grooves, posts or holes). This approach provides a versatile framework for the description of slip on these composite surfaces. Slip lengths up to 100 μ m are predicted for an optimized patterned surface.