Turbulence Closure Scheme Research Articles

The perturbation method - A novel large-eddy simulation technique to model realistic turbulence: Application to tidal flow

Turbulence in the ocean dominates the vertical movement of heat and salt, as well as chemical and biological particulates. The modelling of turbulence is therefore essential to forecast the strength of the biological pump, for example, in which CO2 is drawn out of the atmosphere and trapped in the deep ocean. Obtaining observations of turbulence is an expensive process and the modelling of turbulence still remains an open problem. Using state-of-the-art 3D hydrodynamic models, such as Large-Eddy Simulation and Direct Numerical Simulation, to understand turbulence driven by mean flow is a popular method. However in this approach, the turbulence creates its own mean flow contribution which, in some applications, results in an undesirable divergence from the prescribed mean flow. Here, the perturbation method is introduced. This technique ensures zero divergence to the prescribed mean flow. Results reveal the high level of accuracy this approach has in replicating the observed turbulent field when using ADCP mean current data to prescribe the model mean flow. It is envisaged that the user-friendly nature of this method will enable non-specialists to derive turbulence data when turbulence profilers are not a tractable resource. This modelling approach also sets a rigid framework for the testing of turbulence closure schemes.

Generation of Water Waves Using Momentum Source Wave‐Maker Applied to a RANS Solver

Nowadays, as the development of Computational Fluid Dynamics (CFD) and the numerical wave tank (NWT) has advanced, numerical analysis has become increasingly useful and powerful for the ship designing and ship hydrodynamics. In this study, a momentum source wave‐maker and an analytical relaxation wave absorber were embedded into 2D RANS equation model with RSM turbulence closure scheme to establish the NWT for ship designing and hydrodynamics. The VOF (volume‐of‐fluid) method was applied to accurately capture the water free surface. The body force‐weighted scheme is chosen for pressure interpolation and the second order upwind scheme for discretization of the momentum equation. In order to calculate convection and diffusion fluxes through the control volume faces, PISO algorithm is adopted for pressure‐velocity coupling. The momentum source function for wave generation and the analytical relaxation function for wave absorption were deduced for constructing the NWT (numerical wave tank). The proposed NWT was then validated by the laboratory measurements of Umeyama and the analytical solution, indicating that the constructed NWT is effective and accurate.

Large eddy simulation of turbulent flow over and through a rough permeable bed

This work elucidates the impacts of model construction choices on turbulence characteristics and solution fidelity in the simulation of coupled freestream and porous turbulent flows. A freestream-porewater interface is modeled numerically as a matrix of regularly spaced spheres submerged in a surrounding flow. Simulations are conducted to solve the continuity and momentum equations via Large Eddy Simulation (LES) using the Control Volume Finite Element Method (CVFEM) on an unstructured, surface-conforming mesh, and simulated flow fields are compared with experimental results. Key parameters are identified, allowing for model creation recommendations. A mesh refinement study is performed, and characteristic required mesh sizes in both the bed and the freestream are identified that achieve a good trade-off between accuracy and efficiency. Additionally, it is shown that similar to wall-bounded flows, the computational domain for a coupled freestream and porous flow must be sufficiently large to capture the relevant largest-sized eddies and to avoid the spanwise locking of flow structures; such structures may affect the flow field in the pores as well as in the freestream. Dimensions of 7.5H × 3.5H × H, where H is the freestream height, are found to give satisfactory comparison with experimental results for the cases studied. Finally, it is found that the wall-adapting local eddy-viscosity (WALE) turbulence closure scheme is better able to model the fluid velocity in the problem domain compared with the Smagorinsky model. Failure to select the proper turbulence closure model or domain size leads to a misrepresentation of the turbulent structures. Because of the strong coupling between the porewater flow and the freestream, these modeling errors propagate in both flow regions.

Model Development and Hindcast Simulations of NOAA’s Integrated Northern Gulf of Mexico Operational Forecast System

NOAA’s National Ocean Service is upgrading three existing northern Gulf of Mexico (GOM) operational nowcast/forecast systems (OFS) by integrating them into one single system (INGOFS) and developing additional domain coverage to encompass the lower Mississippi River, Lake Pontchartrain, Texas coastal embayments, and Mexican coastal waters. The system will produce real-time nowcast and short-range forecast guidance for water levels, 3-dimensional currents, water temperature, and salinity. INGOFS will be implemented using the Finite Volume Community Ocean Model (FVCOM). This paper describes the model configuration and results from a one-year (2 August 2016–1 August 2017) hindcast simulation. The model grid is composed of about 300,000 nodes and 600,000 elements, and has a spatial resolution ranging from 45 m near the coast to around 10 km on the open ocean boundary. It uses the FVCOM wetting and drying feature, the quadratic bottom friction scheme, and the two-equation model of the Mellor-Yamada Level 2.5 turbulence closure scheme. The hindcast results of water levels, surface temperatures, and salinity were verified by comparing the model time series with in situ observations. The root-mean-squared errors are about 0.08 m for water levels, about 1.1 °C for temperatures, and about 3.7 psu for salinity. The hindcast configuration will be further tested in a nowcast/forecast environment for a one-year period. The upgraded system is anticipated to be in operational production in mid-2020.

On the numerical performance of turbulent closure schemes in a 1D lake model

The turbulence closure is a crucial part of a lake model. The closures commonly used are different in underlying physics and mathematical properties, leading to contrasting numerical stability and computational efficiency. We tested the performance of the one-dimensional model LAKE using the k − ε closure and Henderson–Sellers turbulence parameterizations, with a convective mixing scheme, in idealized Kato-Phillips experiment and Lake Kuivajärvi (Finland) simulations. Our results demonstrate that k−ε closure allows for a physically realistic solution at timesteps Δt < 450 s, and the convergence of numerical scheme is attained at Δt < 100 s. In contrast, convergence of the lake model scheme using Henderson–Sellers diffusivity is achieved if Δt < 3600 s, resulting in drastic reduction of the lake model runtime as compared to using k − ε parameterization. At the same time, the performance of the model involving both schemes in respect to measurements is similar.

The Influence of Intra-Array Wake Dynamics on Depth-Averaged Kinetic Tidal Turbine Energy Extraction Simulations

Assessing the tidal stream energy resource, its intermittency and likely environmental feedbacks due to energy extraction, relies on the ability to accurately represent kinetic losses in ocean models. Energy conversion has often been implemented in ocean models with enhanced turbine stress terms formulated using an array-averaging approach, rather than implementing extraction at device-scale. In depth-averaged models, an additional drag term in the momentum equations is usually applied. However, such array-averaging simulations neglect intra-array device wake interactions, providing unrealistic energy extraction dynamics. Any induced simulation error will increase with array size. For this study, an idealized channel is discretized at sub 10 m resolution, resolving individual device wake profiles of tidal turbines in the domain. Sensitivity analysis is conducted on the applied turbulence closure scheme, validating results against published data from empirical scaled turbine studies. We test the fine scale model performance of several mesh densities, which produce a centerline velocity wake deficit accuracy (R2) of 0.58–0.69 (RMSE = 7.16–8.28%) using a k-Ɛ turbulence closure scheme. Various array configurations at device scale are simulated and compared with an equivalent array-averaging approach by analyzing channel flux differential. Parametrization of array-averaging energy extraction techniques can misrepresent simulated energy transfer and removal. The potential peak error in channel flux exceeds 0.5% when the number of turbines nTECs ≈ 25 devices. This error exceeds 2% when simulating commercial-scale turbine array farms (i.e., &gt;100 devices).

Free-flow discharge estimation method for Piano Key weir geometries

Currently, many existing spillways located throughout the globe require rehabilitation due to dam safety issues. Consequently, there is an increasing need for design tools that facilitate better, more economical spillway designs. Piano Key weirs (PK weirs), the focus of this study, represent one option to address spillway deficiencies. Two design approaches used by practitioners for estimating PK weir discharge were examined: (1) empirical prediction methods ranging from simple to sophisticated and (2) computational fluid dynamics. This evaluation included five published empirical design methods and CFD simulations featuring two different turbulence models (i.e., LES and RNG k-ε). The results indicate that, depending on geometry, differences exceeding 30% can exist between predictive method and experimental results. Also, CFD discharge results were relatively independent of turbulence closure schemes and showed very good agreement with experimental data (mean relative errors of 3–4%). Finally, recommendations are presented to designers that include a new empirical equation for Type-A PK weir geometries and rectangular labyrinth weirs.

Comparison of in situ microstructure measurements to different turbulence closure schemes in a 3-D numerical ocean circulation model

In situ measurements of kinetic energy dissipation rate ε and estimates of eddy viscosity KZ from the Gulf of Lion (NW Mediterranean Sea) are used to assess the ability of k−ɛ and k−ℓ closure schemes to predict microscale turbulence in a 3-D numerical ocean circulation model. Two different surface boundary conditions are considered in order to investigate their influence on each closure schemes’ performance. The effect of two types of stability functions and optical schemes on the k−ɛ scheme is also explored. Overall, the 3-D model predictions are much closer to the in situ data in the surface mixed layer as opposed to below it. Above the mixed layer depth, we identify one model’s configuration that outperforms all the other ones. Such a configuration employs a k−ɛ scheme with Canuto A stability functions, surface boundary conditions parameterizing wave breaking and an appropriate photosynthetically available radiation attenuation length. Below the mixed layer depth, reliability is limited by the model’s resolution and the specification of a hard threshold on the minimum turbulent kinetic energy.

Influence of Superparameterization and a Higher‐Order Turbulence Closure on Rainfall Bias Over Amazonia in Community Atmosphere Model Version 5

AbstractWe evaluate the Community Atmosphere Model Version 5 (CAM5) with a higher‐order turbulence closure scheme, named Cloud Layers Unified By Binomials (CLUBB), and a Multiscale Modeling Framework, referred to as the “superparameterization” (SP) with two different microphysics configurations to investigate their influences on rainfall simulations over southern Amazonia. The two different microphysics configurations in SP are the one‐moment cloud microphysics without aerosol treatment (SP1) and two‐moment cloud microphysics coupled with aerosol treatment (SP2). Results show that both SP2 and CLUBB effectively reduce the low biases of rainfall, mainly during the wet season, and reduce low biases of humidity in the lower troposphere with further reduced shallow clouds and increased surface solar flux. These changes increase moist static energy in the lower atmosphere and contribute to stronger convection and more rainfall. SP2 appears to realistically capture the observed increase of relative humidity prior to deep convection, and it significantly increases rainfall in the afternoon; CLUBB significantly delays the afternoon peak rainfall and produces more precipitation in the early morning, due to more gradual transition between shallow and deep convection. In CAM5 and CAM5 with CLUBB, occurrence of more deep convection appears to be a result of stronger heating rather than higher relative humidity.

Sensitivity Analysis of Hurricane Arthur (2014) Storm Surge Forecasts to WRF Physics Parameterizations and Model Configurations

Abstract Through a case study of Hurricane Arthur (2014), the Weather Research and Forecasting (WRF) Model and the Finite Volume Coastal Ocean Model (FVCOM) are used to investigate the sensitivity of storm surge forecasts to physics parameterizations and configurations of the initial and boundary conditions in WRF. The turbulence closure scheme in the planetary boundary layer affects the prediction of the storm intensity: the local closure scheme produces lower equivalent potential temperature than the nonlocal closure schemes, leading to significant reductions in the maximum surface wind speed and surge heights. On the other hand, higher-class cloud microphysics schemes overpredict the wind speed, resulting in large overpredictions of storm surge at some coastal locations. Without cumulus parameterization in the outermost domain, both the wind speed and storm surge are grossly underpredicted as a result of large precipitation decreases in the storm center. None of the choices for the WRF physics parameterization schemes significantly affect the prediction of Arthur’s track. Sea surface temperature affects the latent heat release from the ocean surface and thus storm intensity and storm surge predictions. The large-scale atmospheric circulation models provide the initial and boundary conditions for WRF, and influence both the track and intensity predictions, thereby changing the spatial distribution of storm surge along the coastline. These sensitivity analyses underline the need to use an ensemble modeling approach to improve the storm surge forecasts.

Atmospheric Boundary Layer Turbulence Closure Scheme for Wind-Following Swell Conditions

Abstract Over the ocean, atmospheric boundary layer turbulence can be altered by underlying waves. Under swell conditions, the impact of waves on the atmosphere is more complicated compared to that under wind-wave conditions. Based on large-eddy simulation (LES), the wind-following swell impact on the atmospheric boundary layer is investigated through three terms: swell-induced surface momentum flux, the vertical profile of swell-induced momentum flux, and the swell impact on atmospheric mixing. The swell-induced surface momentum flux displays a decreasing trend with increasing atmospheric convection. The swell-induced momentum flux decays approximately exponentially with height. Compared with atmospheric convection, the decay coefficient is more sensitive to wave age. Atmospheric mixing is enhanced under swell conditions relative to a flat stationary surface. The swell impact on the atmospheric boundary layer is incorporated into a turbulence closure parameterization through the three terms. The modified turbulence closure parameterization is introduced into a single-column atmospheric model to simulate LES cases. Adding only the swell impact on the atmospheric mixing has a limited influence on wind profiles. Adding both the impact of swell on the atmospheric mixing and the profile of swell-induced momentum flux significantly improves the agreement between the 1D atmospheric simulation results and the LES results, to some extent simulating the wave-induced low-level wind jet. It is concluded that the swell impact should be included in atmospheric numerical models.

Numerical simulation on Bay of Bengal's response to cyclones using the Princeton ocean model

ABSTRACT This study used the Princeton ocean model (POM) which includes second-order turbulent closure scheme to investigate the fluid dynamics of the Bay of Bengal (BoB) in the upper ocean's response to a cyclone. The model uses an orthogonal curvilinear grid and 26 sigma levels in conformity with realistic bottom topography. The model is forced with wind and heat plus salinity fluxes as surface forcing to simulate the BoB's response during a cyclone. In order to provide the realistic cyclonic vortex the model as input, the synthetic cyclonic vortex is generated and superimposed on the QSCAT/NCEP blended ocean wind fields. Analyses of results show significant sea surface temperature (SST) cooling on both sides of the storm track. This cooling could be attributed to the strong cyclonic winds, surface divergence and upwelling. However, less commonly observed features such as a leftward bias in SST cooling due to the relatively slower motion of TC and southward moving coastal boundary currents are also reported in this study. Model SST is compared with the observed Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI) filled up SST for the evaluation of the model's performance. Moreover, not only sea surface cooling but subsurface warming due to intense downwelling and coastal jet parallel to the coast were also observed in the model's simulation. The mixed layer depth (MLD) variation is revealed by the model. MLD deepening due to the convergence of near surface flow at the periphery of the cyclone is observed; however, beneath the cyclone centre, in the direction of the track the upsloping of isotherms due to the surface divergence and upwelling causes the shoaling of the MLD. Modeled surface currents are compared with 5-day interval OSCAR (Ocean Surface Current Analyses - Real time) surface currents, which are not very coherent, though some of the important features like higher values of boundary layer currents are captured. However, strong near surface, asymmetrical responses such as divergent currents in the open oceanic region are reflected by the model but when the cyclone approaches the coast the current patterns do not show the right bias due to interaction with the coast.

Numerical modeling of open channel flow with suspended canopy

Suspended canopies are common in aquatic environments. The mean flow velocity and Reynolds stress in the open channels with the suspended canopies were studied through laboratory experiments and numerical simulations. Numerical modeling was conducted with a modified version of the Delft3D-Flow model using a k–ε turbulence closure scheme. The resistance effects of the suspended canopy were modeled by adding a resistance term in the momentum equations of fluid flow, along with an addition production and dissipation term in the k and ε equations respectively. The numerical results for mean flow velocity and Reynolds stress agreed well with the experimental data of this study and the previously published data by Plew (2010). The spatial evolution of the mixing layer near the bottom of the suspended canopy can be broadly separated into the diverging flow, developing, and fully developed zones. The thickness and density of the suspended canopy significantly influenced the flow characteristics.

The effect of stratification on the vertical structure of the tidal ellipse in the Changjiang River estuary, China

A field study was undertaken to understand the possible effect of stratification on the vertical structure of the M2 semidiurnal tidal ellipses in the Changjiang River estuary. A pycnocline occurs at each station along the North Passage on a neap tide only. Calculated potential energy anomalies within the North Passage are 100–200J·m−3 larger on a neap tide than on a spring tide. The tidal ellipses degenerate to rectilinear motion at each layer of the water column at each station along the North Passage, while they rotate clockwise at each station over the Hengsha Shoal. The surface-to-bottom inclination angle difference of the tidal ellipse at a seaward station is 40° on a neap tide but a few degrees on a spring tide. The vertical phase shifts of the tidal ellipses range from 20° to 50° at most stations along the North Passage on a neap tide, while they are less than 10° on a spring tide. Rapid changes in the inclination angles and phase shifts of the tidal ellipses occur at the pycnocline. An abrupt reduction in the vertical eddy viscosity at the pycnocline seems to be the major cause for the vertical variability of ellipticity, inclination angle and phase of the tidal ellipses on a strongly stratified neap tide. The surface-to-bottom ellipticity difference appears to have a positive linear relation with the overall Richardson number mainly along the North Passage on a neap tide. A one-dimensional coastal model with vertical turbulence closure scheme seems to be able to reproduce the major features of the vertical structure of the tidal ellipses at a seaward station on a spring tide.

Measurement and Numerical Study of Vertical Mixing Microstructure in the Bohai Strait

ABSTRACT Zhang, Y.; Liang, S., and Sun, Z., 2017. Measurement and numerical study of vertical mixing microstructure in the Bohai Strait. Vertical mixing plays an important role in three-dimensional hydrodynamic and water quality models. The purpose of this study is to analyze the characteristics of vertical mixing in strong tidal waters and the simulation capability of turbulence closure models under the influence of flow velocity variations and temperature distribution. The distribution characteristics of thermocline and vertical mixing in the Bohai Strait is analyzed through field observations conducted using the Turbulence Ocean Microstructure Acquisition Profiler in summer. Based on the measured temperature and mixing data, three-dimensional numerical models are established with various temperature distribution and turbulence closure schemes. It is concluded that the vertical eddy viscosity Km and the thermal-diffusion coefficient Kh, using the Mellor and Yamada level 2.5 (MY-2.5) and the k-e turbulen...

ASSESSMENT OF THE EFFECT OF DIFFERENT TURBULENT CLOSURE SCHEMES ON SIMULATING THE SEA SURFACE TEMPERATURE IN THE CENTRAL REGION OF VIETNAM’S EAST SEA

In this paper, the ROMS model was used to simulate the sea surface temperature (SST) in the central region of Vietnam’s East Sea. Two turbulent closure schemes: Brunt-Vaisala and KPP were applied with the same conditions in order to compare the differences and the ability for using them. The simulated SST fields were compared and in good agreement with the mechanism maps of SST. The suggestions for using these schemes were analyzed. This result raises a question and answers how to choose a better closure scheme to apply in simulating SST. The solved problem is very necessary for applying numerical models to simulate SST field.

Wave-induced seabed response around an offshore pile foundation platform

In this paper, a three-dimensional integrated numerical model including the wave and seabed sub-model is developed to investigate the wave induce seabed response around a pile foundation platform. The wave sub-model is based on Volume-Averaged Reynolds-Averaged Naiver-Stokes (VARANS) equations with k-ε turbulence closure scheme, and the volume of fluid (VOF) method is applied to track water free surface. The seabed is treated as an isotropic and homogeneous porous medium and characterized by Biot's partly dynamic equations (u-p model). The proposed model is verified with the previous analytical results. Based on the numerical results, the distribution of flow field around pile foundation will be investigated. Then, a comprehensive comparison between a pile foundation platform model and a pile foundation without platform model will be performed to examine the effects of platform to the pile foundation. Finally, the effects of wave, pile foundation, and seabed characteristics, such as wave depth, wave height, pile diameter, pile insertion ratio, soil permeability and degree of saturation on the wave-induced seabed and pile foundation platform response will be studied.

Closure Schemes for Stably Stratified Atmospheric Flows without Turbulence Cutoff

Abstract Two recently proposed turbulence closure schemes are compared against the conventional Mellor–Yamada (MY) model for stably stratified atmospheric flows. The Energy- and Flux-Budget (EFB) approach solves the budgets of turbulent momentum and heat fluxes and turbulent kinetic and potential energies. The Cospectral Budget (CSB) approach is formulated in wavenumber space and integrated across all turbulent scales to obtain flow variables in physical space. Unlike the MY model, which is subject to a “critical gradient Richardson number,” both EFB and CSB models allow turbulence to exist at any gradient Richardson number and predict a saturation of flux Richardson number () at sufficiently large . The CSB approach further predicts the value of and reveals a unique expression linking the Rotta and von Kármán constants. Hence, all constants in the CSB model are nontunable and stability independent. All models agree that the dimensionless sensible heat flux decays with increasing . However, the decay rate and subsequent cutoff in the MY model appear abrupt. The MY model further exhibits an abrupt cutoff in the turbulent stress normalized by vertical velocity variance, while the CSB and EFB models display increasing trends. The EFB model produces a rapid increase in the ratio of turbulent potential energy and vertical velocity variance as is approached, suggesting a strong self-preservation mechanism. Vertical anisotropy in the turbulent kinetic energy is parameterized in different ways in MY and EFB, but this consideration is not required in CSB. Differences between EFB and CSB model predictions originate from how the vertical anisotropy is specified in the EFB model.

Turbulence-particle interactions under surface gravity waves

Abstract The dispersion and transport of single inertial particles through an oscillatory turbulent aquatic environment are examined numerically by a Lagrangian particle tracking model using a series of idealised test cases. The turbulent mixing is incorporated into the Lagrangian model by the means of a stochastic scheme in which the inhomogeneous turbulent quantities are governed by a one-dimensional k- ε turbulence closure scheme. This vertical mixing model is further modified to include the effects of surface gravity waves including Coriolis-Stokes forcing, wave breaking, and Langmuir circulations. To simplify the complex interactions between the deterministic and the stochastic phases of flow, we assume a time-invariant turbulent flow field and exclude the hydrodynamic biases due to the effects of ambient mean current. The numerical results show that the inertial particles acquire perturbed oscillations traced out as time-varying sinking/rising orbits in the vicinity of the sea surface under linear and cnoidal waves and acquire a non-looping single arc superimposed with the high-frequency fluctuations beneath the nonlinear solitary waves. Furthermore, we briefly summarise some recipes through the course of this paper on the implementation of the stochastic particle tracking models to realistically describe the drift and suspension of inertial particles throughout the water column.

CFD modelling approaches against single wind turbine wake measurements using RANS

Numerical simulations of two wind turbine generators including the exact geometry of their blades and hub are compared against a simplified actuator disk model (ADM). The wake expansion of the upstream rotor is investigated and compared with measurements. Computational Fluid Dynamics (CFD) simulations have been performed using the open-source platform OpenFOAM [1]. The multiple reference frame (MRF) approach was used to model the inner rotating reference frames in a stationary computational mesh and outer reference frame for the full wind turbine rotor simulations. The standard k — ε and k — ω turbulence closure schemes have been used to solve the steady state, three dimensional Reynolds Averaged Navier- Stokes (RANS) equations. Results of near and far wake regions are compared with wind tunnel measurements along three horizontal lines downstream. The ADM under-predicted the velocity deficit at the wake for both turbulence models. Full wind turbine rotor simulations showed good agreement against the experimental data at the near wake, amplifying the differences between the simplified models.