Calculation of primary and secondary flow and boundary shear stresses in a meandering channel

Turbulent flow in a meandering channel is computed with two Computational Fluid Dynamics (CFD) codes solving the Navier–Stokes equations by employing different turbulence closure approaches. The first CFD code solves the steady Reynolds-Averaged Navier–Stokes equations (RANS) using an isotropic turbulence closure. The second code is based on the concept of Large Eddy Simulation (LES). LES resolves the large-scale turbulence structures in the flow and is known to outperform RANS models in flows in which large-scale structures dominate the statistics. The results obtained from the two codes are compared with experimental data from a physical model study. Both, LES and RANS simulation, predict the primary helical flow pattern in the meander as well as the occurrence of an outer-bank secondary cell. Computed primary as well as secondary flow velocities are in reasonably good agreement with experimental data. Evidence is given that the outer-bank secondary cell in a meander bend is the residual of the main secondary cell of the previous bend. However, the RANS code, regardless of the turbulence model employed, overpredicts the size and strength of the outer-bank secondary cell. Furthermore, only LES is able to uphold the outer-bank second secondary cell beyond the bend apex until the exit of the bend as turbulence anisotropy contributes to its persistence. The presence of multiple secondary cells has important consequences for the distribution of shear stresses along the wetted perimeter of the channel, and thereby the sediment transport in meandering channels. Consequently, even though LES is expected to compute the bed-shear stresses along the wetted perimeter of the channel with a higher degree of accuracy than the RANS model, comparisons between LES and RANS computed wall shear stresses agree well. These findings are useful for practitioners who need to rely on RANS model predictions of the flow in meandering channels at field scale.     

Effects of shear in the convective boundary layer: analysis of the turbulent kinetic energy budget

Effects of convective and mechanical turbulence at the entrainment zone are studied through the use of systematic Large-Eddy Simulation (LES) experiments. Five LES experiments with different shear characteristics in the quasi-steady barotropic boundary layer were conducted by increasing the value of the constant geostrophic wind by 5 m s^-1 until the geostrophic wind was equal to 20 m s^-1. The main result of this sensitivity analysis is that the convective boundary layer deepens with increasing wind speed due to the enhancement of the entrainment heat flux by the presence of shear. Regarding the evolution of the turbulence kinetic energy (TKE) budget for the studied cases, the following conclusions are drawn: (i) dissipation increases with shear, (ii) the transport and pressure terms decrease with increasing shear and can become a destruction term at the entrainment zone, and (iii) the time tendency of TKE remains small in all analyzed cases. Convective and local scaling arguments are applied to parameterize the TKE budget terms. Depending on the physical properties of each TKE budget contribution, two types of scaling parameters have been identified. For the processes influenced by mixed-layer properties, boundary layer depth and convective velocity have been used as scaling variables. On the contrary, if the physical processes are restricted to the entrainment zone, the inversion layer depth, the modulus of the horizontal velocity jump and the momentum fluxes at the inversion appear to be the natural choices for scaling these processes. A good fit of the TKE budget terms is obtained with the scaling, especially for shear contribution.     

2DV modelling of sediment transport processes over full-scale ripples in regular asymmetric oscillatory flow

Wave-induced, steep vortex ripples are ubiquitous features in shallow coastal seas and it is therefore important to fully understand and model the sediment transport processes that occur over them. To this end, two two-dimensional vertical (2DV) models have been critically tested against detailed velocity and sediment concentration measurements above mobile ripples in regular asymmetric oscillatory flow. The two models are a k–ω turbulence-closure model and a discrete-vortex, particle-tracking (DVPT) model, while the data are obtained in the Aberdeen oscillatory flow tunnel (AOFT). The models and the data demonstrate that the time-dependent velocity and suspended sediment concentration above the ripple are dominated by the generation of lee-side vortices and their subsequent ejection at flow reversal. The DVPT model predicts the positions and strengths of the vortices reasonably well, but tends to overpredict the velocity close to the ripple surface. The k–ω model, on the other hand, underpredicts the height to which the vortices are lifted, but is better able to predict the velocity close to the bed. In terms of the cycle- and ripple-averaged horizontal velocity, both models are able to reproduce the observed offshore flow close to and below the ripple crest and the DVPT model is able to produce the onshore flow higher up. In the vicinity of the vortices, the DVPT model better represents the concentration (because of its better prediction of vorticity). The k–ω model, on the other hand, better represents the concentration close to the ripple surface and higher up in the flow (because of the better representation of the near-bed flow and background turbulence). The measured and predicted cycle- and ripple-averaged suspended sediment concentrations are in reasonable agreement and demonstrate the expected region of exponential decay. The models are able to reproduce the observed offshore cycle- and ripple-averaged suspended sediment flux from the ripple troughs upwards, and as a result, produce net offshore suspended sediment transport rates that are in reasonable agreement. The net measured offshore suspended transport rate, based on the integration of fluxes, was found to be consistent with the total net offshore transport measured in the tunnel as a whole once the onshore transport resulting from ripple migration was taken into account, as would be expected. This demonstrates the importance of models being able to predict ripple-migration rates. However, at present neither of the models is able to do so.     

Use of Large-Eddy Simulation for the bed shear stress estimation over a dune

Environmental flows are generally characterized by complex bed morphology and high current speeds. Such configurations favor the formation of vortex structures that strongly affect hydrody-namics and sediment transport. Large-Eddy Simulation (LES) enables investigation of the dynam-ics of the largest turbulence scales and, thanks to enhanced calculation resources, has now become applicable for simulating environmental flows. In this paper, a LES approach is developed in a CFD code (TELEMAC-3D), which was originally developed to simulate free surface flows using RANS methods. The present developments involve implementing subgrid models, boundary con-ditions and numerical schemes suitable for LES. The LES version of TELEMAC-3D was validated by comparing results on the model with experimental data for flow past a cylinder. Then, the model was applied to a test case representing flow over dunes. After validating the hydrodynamics, the model was used to assess the bottom shear stress, using both a RANS and a LES approach. Com-parison highlighted the potential contribution of LES to investigating the hydrodynamic forces acting on the bottom.     

Comparison of relative permeability–fluid saturation–capillary pressure relations in the modelling of non-aqueous phase liquid infiltration in variably saturated,layered media

The characteristic functions relating relative permeabilities and capillary pressures to fluid saturations (k_r–S–P_c models) are of great importance for the modelling of sub-surface multi-phase flow and transport. In order to test their performance and to identify their important parameters, four well-known three-phase k_r–S–P_c models have been tested against published experimental data on non-aqueous phase liquid (NAPL) migration in the unsaturated zone. Both homogenous systems and systems with embedded heterogeneities have been analysed.     

Evaluation of an interrill soil erosion model using laboratory catchment data

Physically based soil erosion simulation models require input parameters of soil detachment and sediment transport owing to the action and interactions of both raindrops and overland flow. A simple interrill soil water transport model is applied to a laboratory catchment to investigate the application of raindrop detachment and transport in interrill areas explicitly. A controlled laboratory rainfall simulation study with slope length simulation by flow addition was used to assess the raindrop detachment and transport of detached soil by overland flow in interrill areas. Artificial rainfall of moderate to high intensity was used to simulate intense rain storms. However, experiments were restricted to conditions where rilling and channelling did not occur and where overland flow covered most of the surface. A simple equation with a rainfall intensity term for raindrop detachment, and a simple sediment transport equation with unit discharge and a slope term were found to be applicable to the situation where clear water is added at the upper end of a small plot to simulate increased slope length. The proposed generic relationships can be used to predict raindrop detachment and the sediment transport capacity of interrill flow and can therefore contribute to the development of physically‐based erosion models. Copyright © 1999 John Wiley & Sons, Ltd.     

Influence of Zostera marina canopies on unidirectional flow,hydraulic roughness and sediment movement

Seagrasses develop extensive or patchy underwater meadows in coastal areas around the world, forming complex, highly productive ecosystems. Seagrass canopies exert strong effects on water flow inside and around them, thereby affecting flow structure, sediment transport and benthic ecology. The influence of Zostera marina canopies on flow velocity, turbulence, hydraulic roughness and sediment movement was evaluated through laboratory experiments in 2 flumes and using live Z. marina and a mobile sand bed. Profiles of instantaneous velocities were measured and sediment movement was identified upstream, within and downstream of patches of different sizes and shoot density and at different free-stream velocities. Flow structure was characterised by time-averaged velocity, turbulence intensity and Turbulent Kinetic Energy (TKE). When velocity data were available above the canopy, they were fitted to the Law of the Wall and shear velocities and roughness lengths were calculated. When a seagrass canopy was present, three layers were distinguishable in the water column: (1) within canopy represented by low velocities and high turbulence; (2) transition zone around the height of the canopy, where velocities increased, turbulence decreased and TKE was high; and (3) above canopy where velocities were equal or higher than free-stream velocities and turbulence and TKE were lower than below. Shoot density and patch-width influenced this partitioning of the flow when the canopy was long enough (based on flume experiments, at least more than 1 m-long). The enhanced TKE observed at the canopy/water interface suggests that large-scale turbulence is generated at the canopy surface. These oscillations, likely to be related to the canopy undulations, are then broken down within the canopy and high-frequency turbulence takes place near the bed. This turbulence ‘cascade’ through the canopy may have an important impact on biogeochemical processes. The velocity above the canopy generally followed a logarithmic profile. Roughness lengths were higher above the canopy than over bare sand and increased with increasing distance from the leading edge of the canopy; however, they were still small (<1 cm) compared to other studies in the literature. Within and downstream of the canopy, sediment movement was observed at velocities below the threshold of motion. It was likely caused by the increased turbulence at those positions. This has large implications for sediment transport in coastal zones where seagrass beds develop.     

Air–water two-phase flow modeling of turbulent surf and swash zone wave motions

Wave breaking and wave runup/rundown have a major influence on nearshore hydrodynamics, morphodynamics and beach evolution. In the case of wave breaking, there is significant mixing of air and water at the wave crest, along with relatively high kinetic energy, so prediction of the free surface is complicated. Most hydrodynamic studies of surf and swash zone are derived from single-phase flow, in which the role of air is ignored. Two-phase flow modeling, consisting of both phases of water and air, may be a good alternative numerical modeling approach for simulating nearshore hydrodynamics and, consequently, sediment transport. A two-phase flow tool can compute more realistically the shape of the free surface, while the effects of air are accounted for. This paper used models based on two-dimensional, two-phase Reynolds-averaged Navier–Stokes equations, the volume-of-fluid surface capturing technique and different turbulence closure models, i.e., k–ε, k–ω and re-normalized group (RNG). Our numerical results were compared with the available experimental data. Comparison of the employed method with a model not utilizing a two-phase flow modeling demonstrates that including the air phase leads to improvement in simulation of wave characteristics, especially in the vicinity of the breaking point. The numerical results revealed that the RNG turbulence model yielded better predictions of nearshore zone hydrodynamics, although the k–ε model also gave satisfactory predictions. The model provides new insights for the wave, turbulence and means flow structure in the surf and swash zones.     

Turbulence in the presence of internal waves in the bottom boundary layer of the California inner shelf

Turbulence measurements were collected in the bottom boundary layer of the California inner shelf near Point Sal, CA, for 2 months during summer 2015. The water column at Point Sal is stratified by temperature, and internal bores propagate through the region regularly. We collected velocity, temperature, and turbulence data on the inner shelf at a 30-m deep site. We estimated the turbulent shear production (P), turbulent dissipation rate (ε), and vertical diffusive transport (T), to investigate the near-bed local turbulent kinetic energy (TKE) budget. We observed that the local TKE budget showed an approximate balance (P?≈?ε) during the observational period, and that buoyancy generally did not affect the TKE balance. On a finer resolution timescale, we explored the balance between dissipation and models for production and observed that internal waves did not affect the balance in TKE at this depth.     

Field scale impacts of spatially correlated relative permeability in heterogeneous multiphase systems

Two-dimensional numerical simulations of two-phase (DNAPL-water) flow in spatially correlated random fields demonstrate the influence of nonwetting phase (NWP) relative permeability–saturation (k_r,N–S_W) relationships correlated to porous media intrinsic permeability (k). Both the volume of porous media invaded by the NWP and the length of time during which the NWP is migrating are under predicted if k_r,N–k correlation is not accounted for in the model formulation. Not accounting for the k_r,N–k correlation resulted in under predicting the volume of porous media invaded by up to approximately 10%, which is likely not significant for many practical applications. However, not accounting for the k_r,N–k correlation resulted in under predicting field scale migration times by up to a factor of 4, which is likely significant in that the migration times are on the order of years to several decades for the DNAPL (1,2-DCE) considered in this study. The under prediction of migration times was greater for lower permeability aquifers.     

Spherical gauges for improving the accuracy of rainfall measurements

Rain‐gauge catch efficiencies are affected by wind. Wind makes raindrops fall at an angle of inclination and the effective diameter of the rain gauge orifice smaller than if raindrops fall into the gauge vertically. Two spherical and two semi‐spherical orifices were designed to modify standard gauges and others in use today. The two spherical orifices catch rain with an effective diameter always equal to the actual diameter regardless of wind speed and direction. The semi‐spherical orifices, used side‐by‐side with a standard gauge, correct 50% of catch deficiencies made by the standard gauge. Tests based on 115 storms show that the four new gauges caught more rainfall than the standard gauge, with an average catch increase ranging from 8% to 16%. Compared with the pit gauge, average deficiency in catch ranged from ?1% (spherical rain gauge orifice with cylinders) to 4%, whereas the deficiency for the standard gauge was ?10%. Percentage deficiencies of the new gauges were positively affected by wind speed, raindrop inclination and rainfall intensity. Although the new gauges tended to underestimate the standard gauge in small storms (<0·25 cm) and overestimated the pit gauge under strong winds, their deviations are small. Underestimates for small storms could be improved by using gauge materials that reduce surface temperature, evaporation and water retention. The gauges are simple in design, easy to operate and inexpensive. In order to maintain a historically consistent set of rainfall data, a dual‐gauge (standard gauge + spherical gauge) is recommended for existing rainfall stations. The new rain gauge orifices are suitable for large‐scale applications. Copyright © 2001 John Wiley & Sons, Ltd.     

Determination of critical shear stress of non‐cohesive soils using submerged jet test and turbulent kinetic energy

Laboratory tests using Jet Erosion Testing (JET) apparatus, impinging normally on a horizontal boundary, were conducted to determine the critical shear stress (τ_c) of non‐cohesive soil samples. A three‐dimensional (3D) SonTek/YSI 16 MHz Micro‐Acoustic Doppler Velocimeter (MicroADV) was used to measure turbulent kinetic energy (TKE) at a radial limit of entrainment in the wall jet zone and the measurements were used to calculate τ_c of the samples. The results showed that TKE increases exponentially with increasing particle size. The τ_c from this study were comparable (R² = 0.8) to the theoretical τ_c from Shields diagram after bed roughness scale ratio (D/k_s), due to the non‐uniform bed conditions, was accounted for. This study demonstrated that JET and TKE can be used to determine τ_c of non‐cohesive soils. The use of JET and TKE was found to be faster and easier when compared to the conventional approach of using flumes. A relationship of TKE at the onset of incipient motion (TKE_c) and samples’ D₅₀ developed in this study can be used to predict τ_c of non‐cohesive soils under similar non‐uniform conditions. Copyright © 2015 John Wiley & Sons, Ltd.     

Flow structure over square bars at intermediate submergence: Large Eddy Simulation study of bar spacing effect

Turbulent open-channel flow over 2D roughness elements is investigated numerically by Large Eddy Simulation (LES). The flow over square bars for two roughness regimes (k-type roughness and transitional roughness between d-type and k-type) at a relative submergence of H/k = 6.5 is considered, where H is the maximum water depth and k is the roughness height. The selected roughness configurations are based on laboratory experiments, which are used for validating numerical simulations. Results from the LES, in turn, complement the experiments in order to investigate the time-averaged flow properties at much higher spatial resolution. The concept of the double-averaging (DA) of the governing equations is utilized to quantify roughness effects at a range of flow properties. Double-averaged velocity profiles are analysed and the applicability of the logarithmic law for rough-wall flows of intermediate submergence is evaluated. Momentum flux components are quantified and roughness effect on their vertical distribution is assessed using an integral form of the DA-equations. The relative contributions of pressure drag and viscous friction to the overall bed shear stress are also reported.     

Observations of submesoscale eddies using high-frequency radar-derived kinematic and dynamic quantities

The spatio-temporal variability of submesoscale eddies off southern San Diego is investigated with two-year observations of subinertial surface currents [O(1) m depth] derived from shore-based high-frequency radars. The kinematic and dynamic quantities — velocity potential, stream function, divergence, vorticity, and deformation rates — are directly estimated from radial velocity maps using optimal interpolation. For eddy detection, the winding-angle approach based on flow geometry is applied to the calculated stream function. A cluster of nearly enclosed streamlines with persistent vorticity in time is identified as an eddy. About 700 eddies were detected for each rotation (clockwise and counter-clockwise). The two rotations show similar statistics with diameters in the range of 5–25 km and Rossby number of 0.2–2. They persist for 1–7 days with weak seasonality and migrate with a translation speed of 4–15 cm s⁻¹ advected by background currents. The horizontal structure of eddies exhibits nearly symmetric tangential velocity with a maximum at the defined radius of the eddy, non-zero radial velocity due to background flows, and Gaussian vorticity with the highest value at the center. In contrast divergence has no consistent spatial shape. Two episodic events are presented with other in situ data (subsurface current and temperature profiles, and local winds) as an example of frontal-scale secondary circulation associated with drifting submesoscale eddies.     

Transient and steady-state relative permeabilities from two-phase flow experiments in planar pore networks

The water k_rw and oil k_ro relative permeability curves of a glass-etched planar pore network are estimated with history matching from transient displacement experiments performed at varying values of the capillary number, Ca  , for two fluid systems: one of intermediate and one of strong wettability. The transient _krw,_kro$k_{\text{rw}}\text{,}{k}_{\text{ro}}$ are compared to corresponding ones measured with the steady-state method on the same porous medium [Avraam DG, Payatakes AC. Flow regimes and relative permeabilities during steady-state two-phase flow in porous media. J Fluid Mech 1995;293:207–36; Avraam DG, Payatakes AC. Generalized relative permeability coefficients during steady-state two-phase flow in porous media and correlation with the flow mechanisms. Transport Porous Med 1995;20:135–68; Avraam DG, Payatakes AC. Flow mechanisms, relative permeabilities, and coupling effects in steady-state two-phase flow through porous media. The case of strong wettability. Ind Eng Chem Res 1999;38:778–86.], and potential differences from them are interpreted in the light of the differences between the transient growth pattern, and the steady-state two-phase flow regime. For intermediate wettability, the transient k_ro and k_rw exceed the corresponding steady-state functions at low Ca values and have the tendency to become smaller than the steady-state ones at high Ca values. For strong wettability, the transient k_ro and k_rw are increasing functions of Ca, the transient k_ro is higher than the steady-state one, whereas the transient k_rw decreases substantially and becomes lower than the steady-state one at low Ca values. The dynamic capillary pressure estimated from transient experiments is a decreasing function of Ca in agreement with previous theoretical and experimental studies.     

Computational fluid dynamics modeling of abutment scour under steady current using the level set method

The scour and deposition pattern around an abutment under constant discharge condition is calculated using a three dimensional (3D) Computational Fluid Dynamics (CFD) model. The Reynolds-Averaged Navier Stokes (RANS) equations are solved in three dimensions using a CFD model. The Level Set Method (LSM) is used for calculation of both free surface and bed topography. The two-equation turbulence model (k-ε and k-ω) is used to calculate the eddy viscosity in the RANS equations. The pressure term in the RANS equations on a staggered grid is modeled using the Chorin's projection method. The 5th order Weighted Essentially Non-Oscillatory (WENO) scheme discretizes the convective term of the RANS equations. The Kovacs and Parker and Dey formulations are used for the reduction in bed shear stress on the sloping bed. The model also used the sandslide algorithm which limits bed shear stress reduction during the erosion process. The numerical model solution is validated against experimental results collected at the Politecnico di Milano, Milan, Italy. Further, the numerical model is tested for performance by varying the grid sizes and key parameters like the space and time discretization schemes. The effect of varying bed porosity has been evaluated. Overall, the free surface is well represented in a realistic manner and bed topography is well predicted using the Level Set Method (LSM).     

The distribution of earthquakes with depth and stress in subducting slabs

We explain the global variation of Benioff zone seismicity with depth and the orientation of stress axes of deep and intermediate earthquakes using numerical models of subducting slabs. Models that match the seismicity and stress require a barrier to flow at the 670 km seismic discontinuity. The barrier may be a viscosity increase of at least an order of magnitude or a chemical discontinuity. Instantaneous flow is subparallel to the slabs for models with a viscosity increase but contorted for models with a chemical barrier. Log N (number of earthquakes) decreases linearly to 250–300 km depth and increases thereafter. Stress magnitude in our models shows the same pattern, in accord with experiments showing N proportional to e^kσ, with k a constant and σ stress magnitude. The models predict downdip compression in the slabs at depths below 300–400 km, as observed for earthquake stress axes.     

Rain properties controlling soil splash detachment

Laboratory experiments have been conducted to study the effects of various rain properties on sand detachment resulting from raindrop impact. Splash cups were exposed to simulated rainfall intensities ranging between 10 and 140 mm h⁻¹. The detached sand was collected and weighed whereas rain intensity, equivalent drop diameter and fall velocity of raindrops were measured with an optical spectro‐pluviometer (OSP). The properties of the simulated rain (i.e. median volume diameter and kinetic energy) were compared with those observed in natural conditions. Statistical analyses have been undertaken in order to evaluate which rain variable best predicts the mass of sand detached. Linear and non‐linear correlations between the mass of detached sediment and the product of drop size (d) by drop velocity (v), i.e. D^αV^β, with values of α varying between 1 and 6 and β between 0 and 3, have been computed. The results indicate that the coefficient of determination (R²) for α ranging between 3 and 5 and β lower or equal to 2 are satisfying. Although kinetic energy (D³V²) described splash detachment relatively well, the product of momentum by drop diameter (D⁴V) was slightly superior in describing splash detachment. Therefore, the momentum multiplied by the drop diameter is recommended as the best rain variable to describe splash detachment. Copyright © 2000 John Wiley & Sons, Ltd.     

Comparing different methods of bed shear stress estimates in simple and complex flow fields

Bed shear stress is a fundamental variable in river studies to link ?ow conditions to sediment transport. It is, however, dif?cult to estimate this variable accurately, particularly in complex ?ow ?elds. This study compares shear stress estimated from the log pro?le, drag, Reynolds and turbulent kinetic energy (TKE) approaches in a laboratory ?ume in a simple boundary layer, over plexiglas and over sand, and in a complex ?ow ?eld around de?ectors. Results show that in a simple boundary layer, the log pro?le estimate is always the highest. Over plexiglas, the TKE estimate was the second largest with a value 30 per cent less than the log estimate. However, over sand, the TKE estimate did not show the expected increase in shear stress. In a simple boundary layer, the Reynolds shear stress seems the most appropriate method, particularly the extrapolated value at the bed obtained from a turbulent pro?le. In a complex ?ow ?eld around de?ectors, the TKE method provided the best estimate of shear stress as it is not affected by local streamline variations and it takes into account the increased streamwise turbulent ?uctuations close to the de?ectors. It is suggested that when single‐point measurements are used to estimate shear stress, the instrument should be positioned close to 0·1 of the ?ow depth, which corresponds to the peak value height in pro?les of Reynolds and TKE shear stress. Copyright © 2004 John Wiley & Sons, Ltd.     

Turbulence in vegetated flows: Volume-average analysis and modelling aspects

Two approaches for the modelling of turbulence in vegetated flows have been developed in the past. The “microscopic” approach which is straightforward but limited to simple cases and the “macroscopic” approach which is based on Volume Average Theory (VAT). In this study, aspects of Volume-Average (VA) analysis and modelling are investigated for turbulent vegetated flow using computed three-dimensional results from the solution of the Reynolds-Averaged Navier-Stokes (RANS) equations around a representative vegetal element. In particular (a) the VA transport equations for k and ε, based on VAT, are properly derived, (b) the Boussinesq hypothesis for the VA quantities, employed in 〈k〉-〈ε〉 turbulence models is tested, and (c) the values of the coefficients used in such turbulence models are assessed in comparison with those used in the classical turbulence models.