The present study focuses on the evaluation of the impact of marine stable stratification on turbine performance and wake characteristics. Stratification is usually present in regions where marine turbines are installed; this is the case of estuarine basins and shelf seas. Stratification influences the turbine efficiency and rotor wake development; on the other hand, the turbine wake may increase vertical mixing and reduce stratification in the water basin. To evaluate mutual interaction between a marine turbine and vertical stratification, two types of stable stratified conditions are simulated, a weak and a strong stratified condition, respectively. The numerical analysis is carried out using Large Eddy Simulation (LES) coupled with a Blade Element Momentum (BEM) turbine module. The capability of the model in reproducing power and thrust characteristics of a turbine is proved by comparison with experimental data. Results show that stratification has a remarkable impact on wake development: concerning power performance, as the stratification intensifies, it increases due to the growth of streamwise velocity; meanwhile, the power coefficient slightly increases. Also, the recovery of wake velocity deficit is faster in case of strong stratification, thus reducing the extension of the downward region affected by the presence of the turbine. Results also show that the turbine modifies stratification, specifically the mixing effect is higher in case of strong stratification; this phenomenon is ascribed to the strong vertical meandering of the wake and the development of an eddy that overturns high-density fluid over lower-density fluid.

In nature and in many industrial applications, the boundary of a channel flow is made of solid particles which form a porous wall, so that there is a mutual influence between the free flow and the subsurface flow developing inside the pores. While the influence of the porous wall on the free flow has been well studied, less well characterized is the subsurface flow, due to the practical difficulties in gathering information in the small spaces given by the pores. It is also not clear whether the subsurface flow can host turbulent events able to contribute significantly to the build-up of forces on the particles, potentially leading to their dislodgement. Through large eddy simulations, we investigate the interface between a free flow and a bed composed of spherical particles in a cubic arrangement. The communication between surface and subsurface flow is in this case enhanced, with relatively strong turbulent events happening also inside the pores. After comparing the simulation results with a previous experimental work from a similar setting, the forces experienced by the boundary particles are analysed. While it remains true that the lift forces are largely dependent on the structure of the free flow, turbulence inside the pores can also give a significant contribution. Pressure inside the pores is weakly correlated to the pressure in the free flow, and strong peaks above and below a particle can happen independently. Ignoring the porous layer below the particle from the computations leads then in this case to an underestimation of the lift forces.

Large Eddy simulations of lock-exchange gravity currents propagating over a mobile reach are presented. The numerical setting allows to investigate the sediment pick up induced by the currents and to study the underlying mechanisms leading to sediment entrainment for different Grashof numbers and grain sizes. First, the velocity field and the bed shear-stress distribution are investigated, along with turbulent structures formed in the flow, before the current reaches the mobile bed. Then, during the propagation of the current above the erodible section of the bed the contour plots of the entrained material are presented as well as the time evolution of the areas covered by the current and by the sediment at this section. The numerical outcomes are compared with experimental data showing a very good agreement. Overall, the study confirms that sediment pick up is prevalent at the head of the current where the strongest turbulence occurs. Further, above the mobile reach of the bed, settling process seems to be of minor importance, with the entrained material being advected downstream by the current. Additionally, the study shows that, although shear stress is the main mechanism that sets particles in motion, turbulent bursts as well as vertical velocity fluctuations are also necessary to counteract the falling velocity of the particles and maintain them into suspension. Finally, the analysis of the stability conditions of the current shows that, from one side, sediment concentration gives a negligible contribution to the stability of the front of the current and from the other side, the stability conditions provided by the current do not allow sediments to move into the ambient fluid.

Gravity currents are flows driven by buoyancy differences between two contacting fluids caused by differences in temperature, salinity, or by the presence of suspended particles. Such flows can reach high velocities near the bed, especially on the area behind the front of the current. As a result, rapid morphological changes may take place in river and estuarine beds due to the passage of these flows. Essential to determine the erosion induced by the current, are the spatial and temporal distributions of the bed shear stress. However, these are troublesome to measure in laboratory or in the field. To bridge this difficulty, the eddy-solving numerical simulations may be used. This study presents here the three-dimensional numerical simulations of lock-exchange salinity currents flowing over a mobile bed. It is aimed at the characterization of the sediment entrainment capacity of the current. The large eddy simulation technique is employed for analyzing the evolution and the structure of the current. For the sediment simulation, an Euler-Euler methodology based on a single phase approach is used. The main features of the current are compared with experimental data obtained in the laboratory. Velocity fields and bed shear stress distributions for different initial current densities are analyzed and linked to entrainment scenarios. The influence of small variations in particle size of the mobile bed is also discussed.

Lock-exchange gravity currents propagating up a slope are investigated by large eddy simulations, focusing on the entrainment and mixing processes occurring between the dense current and the ambient fluid. Relevant parameters, such as the aspect ratio of the initial volume of dense fluid in the lock R, the angle between the bottom boundary and the horizontal direction θ and the depth aspect ratio ϕ, are varied. The numerical results are compared with laboratory experiments and a good agreement is found. Entrainment and mixing in a lock-release gravity current are studied using different entrainment parameters and an energy budget method. The entrainment is found to depend on both Froude, Fr, and Reynolds, Re, numbers. In addition, the dependence of both entrainment and mixing on the parameters varied is discussed. The entrainment decreases with increasing steepness of the bottom and R. Irreversible mixing is not affected by the varied parameters during the slumping phase, while during the successive phases of motion, it is found to decrease with the increase of θ and R. Low entrainment and mixing occur for ϕ < 1.

The dynamics of lock-release density currents propagating up a sloping bottom are investigated by Large Eddy Simulations (LES). The flow dynamics are deduced by the analysis of the density and velocity fields obtained by LES. The density current, during its propagation, is observed to develop different flow regimes: a slumping phase followed by a self-similar phase. A decrease in the velocities of the current is observed with the increase of the angle between the bottom boundary and the horizontal direction, theta. A smoother behaviour of the current profile is also visible for high values of theta. The presence of a backward flow close to the bottom of the domain is detected and it is found to depend on the inclination of the bottom theta. An accumulation of dense fluid in the lock region of the tank caused by the reverse flow is also observed. Entrainment processes occurring between the ambient fluid and the dense current are observed and investigated. In particular, during the propagation of the current, light ambient fluid is entrained by the dense current, which increases in volume. It is found that the entrainment is affected by the inclination of the bottom and, in particular, a decrease of the entrainment with the increase of the steepness of the bottom is observed.

Large Eddy Simulations are used to investigate the dynamics of gravity currents produced by the lock-release technique. Three simulations are carried out varying the initial reduced gravity of the lock fluid. The gravity currents develop two different flow regimes, a slumping phase followed by a self-similar phase, in agreement with the shallow water theory. When the dense fluid is released, a gravity current forms and Kelvin-Helmholtz instabilities develop at the interface between the two fluids, causing entrainment of ambient fluid. Two entrainment parameters, a bulk and a local one, are evaluated from an analysis of the instantaneous increase in volume of the gravity current. Entrainment of ambient fluid is found to occur in both the slumping and the self-similar phases. The analysis of the local entrainment parameter shows the determinant role of Kelvin-Helmholtz instabilities in the entrainment dynamics and mixing.

The problem of pollutant dispersion is a crucial issue for life quality in urban areas.

Three-dimensional Large Eddy Simulations and laboratory experiments of lock exchange gravity currents propagating on up-sloping boundaries are presented. Different sloping angles were tested, while all the other parameters were fixed. The LES reproduce the same domain as the laboratory experiments by a very high resolution computational grid. A very good agreement is found between the numerical simulations and laboratory experiments. The gravity current, moving on a horizontal boundary, mixes with the ambient fluid and shows its classical features: a head region followed by a tail region. When a gravity current propagates on an up-sloping boundary, a reverse flow, close to the bed in the gate region, occurs. The reverse flow produces an accumulation region in the left part of the tank. The intensity of the reverse flow and the thickness of the head of the gravity current are found to be dependent on the sloping angle.

In the present paper a state-of-the-art large eddy simulation model (LES-COAST), suited for the analysis of water circulation and mixing in closed or semi-closed areas, is presented and applied to the study of the hydrodynamic characteristics of the Muggia bay, the industrial harbor of the city of Trieste, Italy. The model solves the non-hydrostatic, unsteady Navier–Stokes equations, under the Boussinesq approximation for temperature and salinity buoyancy effects, using a novel, two-eddy viscosity Smagorinsky model for the closure of the subgrid-scale momentum fluxes. The model employs: a simple and effective technique to take into account wind-stress inhomogeneity related to the blocking effect of emerged structures, which, in turn, can drive local-scale, short-term pollutant dispersion; a new nesting procedure to reconstruct instantaneous, turbulent velocity components, temperature and salinity at the open boundaries of the domain using data coming from large-scale circulation models (LCM). Validation tests have shown that the model reproduces field measurement satisfactorily. The analysis of water circulation and mixing in the Muggia bay has been carried out under three typical breeze conditions. Water circulation has been shown to behave as in typical semi-closed basins, with an upper layer moving along the wind direction (apart from the anti-cyclonic veering associated with the Coriolis force) and a bottom layer, thicker and slower than the upper one, moving along the opposite direction. The study has shown that water vertical mixing in the bay is inhibited by a large level of stable stratification, mainly associated with vertical variation in salinity and, to a minor extent, with temperature variation along the water column. More intense mixing, quantified by sub-critical values of the gradient Richardson number, is present in near-coastal regions where upwelling/downwelling phenomena occur. The analysis of instantaneous fields has detected the presence of large cross-sectional eddies spanning the whole water column and contributing to vertical mixing, associated with the presence of sub-surface horizontal turbulent structures. Analysis of water renewal within the bay shows that, under the typical breeze regimes considered in the study, the residence time of water in the bay is of the order of a few days. Finally, vertical eddy viscosity has been calculated and shown to vary by a couple of orders of magnitude along the water column, with larger values near the bottom surface where density stratification is smaller.

The scope of this paper is to analyze the performance of wall-layer model Large Eddy Simulation (WLES) in the prediction of flow separation under stable stratification. This is a fundamental problem of practical importance both in industrial and in environmental applications. We consider turbulent flow in a plane asymmetric diffuser because this simple configuration is particularly challenging for testing the performance of numerical models to reproduce flow separation. Further, this flow has been previously investigated both experimentally and numerically. A sketch of the geometry is in Fig. 1. Depending on the slope of the diffuser and on the Reynolds number (Re=ul/ν with u and l characteristic velocity and length scale of the problem, while ν is the kinematic viscosity) separation occurs.

A Large Eddy Simulation (LES) of mixing in the estuarine area of the Tiber river is performed. Sea coastal domains are characterized by a strong grid anisotropy due to the different length scales on the horizontal and vertical direction. We propose to model the sub-grid stress by means of a directional eddy viscosity model. The density anomaly, due to salinity difference between the river fresh water and the sea basin, is treated as an active scalar in the momentum equation. Besides the complex geometry due to bathymetry, coast line and human structures is treated with a combination of curvilinear grid and an Immersed Boundary Method (IBM). The results show that the flow feels the Coriolis force tending to the north direction and that the fresh light water tends to rise and to spread over the sea water that is heavier. In general the model seems to be able to catch the sea coastal dynamics.

The study of mixing in coastal area is a key issue in environmental fluid mechanics. In most applications it requires a three-dimensional approach in order to take into account phenomena related to buoyancy effects and to complex geometry. In a coastal shallow-water environment the wind-driven upper boundary layer may encroach upon the bottom boundary layer creating a complex turbulent field, making difficult proper modelization with simple RANS-like methodologies. A LES methodology is presented aimed at studying turbulent mixing in coastal areas under general forcing and geometric configuration. The strong grid anisotropy, between the horizontal length scale of kilometers and the vertical one of about 10–100m, is handled expressing the subgrid stress by means of directional eddy viscosities. Geometry is modeled using a combination of curvilinear grid and the Immersed Boundary Method. Proper validation of the model has been carried out and the superiority with respect to the standard one-coefficient version clearly shown. The model has been applied to the investigation of mixing within the Muggia bay under wind forcing. Overall the model has shown to be able to reproduce the peculiarities of coastal dynamics. The model proved to be successful for the study of shallow-water in-shore fundamental processes.

In the present paper we propose an extension of the direct-forcing immersed boundary technique, recently developed and employed by Verzicco and co-authors [Fadlun EA, Verzicco R, Orlandi P, Mohd-Yusof J. Combined immersed-boundary finite-difference methods for three-dimensional complex flow simulations. J Comput Phys 2000;161:35–60; Verzicco R, Fatica M, Iaccarino G, Moin P, Khalighi B. Large eddy simulation of a road vehicle with drag-reduction devices. AIAA J 2002;40(12):2447–55; Cristallo A, Verzicco R. Combined immersed boundary/large-eddy-simulations of incompressible three-dimensional complex flows. Flow Turbul Combust 2006;77(1–4):3–26.] and successively improved by Balaras and co-authors [Gilmanov A, Sotiropoulos F, Balaras E. A general reconstruction algorithm for simulating flows with complex 3D immersed boundaries on Cartesian grids. J Comput Phys 2003;191:660–9; Balaras E. Modeling complex boundaries using an external force field on fixed Cartesian grids in large-eddy simulations. Comput Fluids 2004;33:375–404]. We extend the aforementioned technique to curvilinear-coordinate, structured grid, Navier–Stokes solvers. This improved technique allows for more flexibility and efficiency when compared to standard methods in which the technique is coupled with orthogonal-grid solvers. Additional modifications are also proposed with respect to the state-of-art, which allow to deal with general shaped, multiple-body immersed surfaces and to make the interpolation of the velocity field off the body suitable for curvilinear grids. Several tests have been carried out to check the reliability of the proposed technique: first we have considered the three-dimensional Stokes flow around a sphere, and compared the numerical results with the analytical ones. Second we have considered the two-dimensional unsteady flow around a circular cylinder placed between two parallel solid walls and compared the results with those of the database of the Priority Research Program ‘Flow Simulation on High Performance Computers’ of the German Research Association (DFG). Third, we have considered the two-dimensional flow within a S-shaped duct containing an elliptical valve. Finally, we have applied the technique to the study of a practical high-Reynolds number industrial problem.

Examples of application of the model are also discussed. Specifically we show some results of the simulation of the Tevere river runoff in the Tyrrhenian sea and of the three-dimensional transport and mixing in the Muggia Bay (Gulf of Trieste) under breeze forcing. The numerical model is presently used for research as well for consultant activity for the prediction of dispersion phenomena in shallow-water near-shore areas.

The use of wall-layer models is a well established procedure in LES or RANS of high Reynolds number flows. The use of wall layer models in conjunction with Immersed Boundary Method (IBM) however is still an open issue. In this paper we introduce an approach to work with IBM at high Reynolds with LES. A new interpolation scheme for velocity and a modified Smagorinsky model at the immersed boundary interface are used. Results for a turbulent channel flow are shown. METHOD In Large Eddy Simulation only the energy-carrying scales of motion are directly resolved while the small ones are modelled through a subgrid-scale (SGS) model reducing substantially the computational requirements compared to Direct Numerical Simulation (DNS). However near a solid boundary the computational requirements of LES, although smaller than DNS, scale in almost the same way with the Reynolds number as DNS [1]. Hence, for real-life problems characterized by high Reynolds numbers some sort of wall modelling has to be introduced. Wall-layer models to skip the solution of the viscous layer are one of the possible strategies to overcome this limitation (for a detailed review see [1]). They allow to put the first computational node format a sizable distance off the wall, typically in the logarithmic region. Usually the wall shear stress computed from the tangential velocity at the first computational node is used as a boundary condition for the flow. Its implementation is easy for body-fitted grids but can be problematic working with IBM. Indeed the immersed body surface usually does not coincide with the cell boundary and so the direct imposition of the wall shear stress not trivial. Another key point of the IBM is the reconstruction of the velocity field at the interface region between the solid phase and the resolved fluid phase. For DNS or wall-resolving LES (LES that resolves the viscous sublayer) a linear scheme can be used with good accuracy, but a different interpolation procedure is needed if the computational node is far from the wall, for example in the logarithmic region. Tessicini et al. [2] and Cristallo et al. [3] use a boundary layer equation to work at high Reynolds number with IBM, whereas Choi et al. [4] use an interpolation scheme with a power law. Our method is to use an interpolation scheme derived from the logarithmic law. To find the velocity at an interface node IB we consider its normal to the immersed boundary, then we interpolate the resolved velocity field onto a fictitious node V lying on this normal line. If the logarithmic law is assumed to hold on both these nodes IB and V, one obtains the following relation to determine the velocity at IB: IB V w V IB d d u u log 1

A wall-layer model is proposed for large eddy simulation of high Reynolds number turbulent flows in conjunction with immersed boundaries. The model is based on two main steps: the reconstruction of the velocity field at the first grid point off the immersed body and the modelization of the actual wall shear stress at the immersed boundary through imposition of a Reynolds averaged Navier–Stokes-like eddy viscosity obtained by means of analytical considerations. The model is tested in a turbulent plane channel flow with walls reproduced by immersed boundaries considering both Cartesian and curvilinear grids. Even with coarse and distorted grids the proposed methodology is able to reproduce accurately both first- and second-order turbulent statistics.

Dispersion of a buoyant jet of particles (i.e. fresh water) in a salt water thermally stratified environment is investigated. The carrying flow field is a wind-driven mid-latitude Ekman layer. The investigation is carried out using Large Eddy Simulation. The dispersed phase is simulated in a Lagrangian way, solving a modified form of the Maxey and Riley equation for each particle of the jet. In order to simulate a large Reynolds number flow, the thin wall layer is not directly resolved and the wall stress and the wall heat flux are directly imposed at the free surface. Results of the simulations show that the presence of incoming heat flux produces a thin region of large density gradients below the free surface and inhibits turbulent transport. In particular, the turbulent penetration depth is strongly reduced by stratification as well as the level of the turbulent fluctuations. In order to consider the effect of the actual density field on the particle dynamics, an improved version of the particle-motion equation is here proposed. The results of our simulations show that the dispersion of the buoyant plume of particles is dramatically modified by stratification. In the neutral case, the plume is spread over the horizontal direction in the free surface region and is driven by the mean Ekman current. In the stratified case, the particles remain entrapped in wavy motion present in the region of large mean density gradients. The horizontal transport is strongly reduced for two reasons: first in the region where large density gradients develop the mean velocity is small compared with the value reached at the free surface; second, the turbulent transport is very small due to the suppression of velocity fluctuations. Finally, our results show that very inaccurate predictions are obtained if the variation of density due to the vertical stratification is not taken into account in the particle motion equation.