Large Eddy Simulation Results Research Articles

Background-oriented schlieren experimental and simulation study of the effect of sidewalls on optical turbulence anisotropy in a thermal convection turbulence simulator

The anisotropic optical structure characteristics within the Rayleigh-Bénard (RB) turbulence simulator have been investigated through experiment and simulation. We collected data using background-oriented schlieren technology and extracted displacements using optical flow algorithms. The wavefront phase can be recovered using the conjugate gradient iterative algorithm. We analyzed the optical structural characteristics within the turbulence simulator under different temperature differences. It is observed that with an increased temperature difference, the spatial correlation of the refractive index field decreases at an accelerated rate as the separation distance increases, and the degree of anisotropy characterized by the phase structure function increases. Large eddy simulation and split-step beam propagation method complement experimental results. Numerical simulations demonstrate consistency with experimental data. The results show that the von Karman power spectral density fits the simulation and experimental phase structure function very well relative to the Kolmogorov power spectral density, which demonstrates that the simulation system combining dynamics simulation and optical simulation can achieve power spectral characteristics that are consistent with reality. The experimental and simulation results are crucial for understanding the flow field's optical structural properties inside the turbulence simulator. They will help to construct a suitable turbulence simulator for optical engineering applications and establish a rational scheme for analyzing its internal optical structural properties.

Large-Eddy vs. Reynolds-Averaged Navier–Stokes Simulations of Flow and Heat Transfer in a U-Duct with Unsteady Flow Separation

Large-eddy simulation (LES) and Reynolds-Averaged Navier–Stokes (RANS) equations were used to study incompressible flow and heat transfer in a U-duct with a high-aspect-ratio trapezoidal cross section. For the LES, the WALE subgrid-scale model was employed, and its inflow boundary condition was provided by a concurrent LES of incompressible fully-developed flow in a straight duct with the same cross section and flow conditions as the U-duct. LES results are presented for turbulent kinetic energy, Reynolds stresses, pressure–strain rate, turbulent diffusion, turbulent transport, and velocity–temperature correlations, with a focus on how they are affected by the U-turn region of the U-duct. The LES results were also used to assess three commonly used RANS models: the realizable k-ε with the two-layer model in the near-wall region, the two-equation shear-stress transport model, and the seven-equation stress-omega Reynolds stress model. Results obtained show steady and unsteady RANS to incorrectly predict the effects of unsteady flow separation. The results obtained also identified the terms in the RANS models that need to be modified and suggested how turbulent diffusion should be modeled when there is unsteady flow separation.

The multi-scale coupled model: a new framework capturing wind farm–atmosphere interaction and global blockage effects

Abstract. The growth in the number and size of wind energy projects in the last decade has revealed structural limitations in the current approach adopted by the wind industry to assess potential wind farm sites. These limitations are the result of neglecting the mutual interaction of large wind farms and the thermally stratified atmospheric boundary layer. While currently available analytical models are sufficiently accurate to conduct site assessments for isolated rotors or small wind turbine clusters, the wind farm's interaction with the atmosphere cannot be neglected for large-size arrays. Specifically, the wind farm displaces the boundary layer vertically, triggering atmospheric gravity waves that induce large-scale horizontal pressure gradients. These perturbations in pressure alter the velocity field at the turbine locations, ultimately affecting global wind farm power production. The implication of such dynamics can also produce an extended blockage region upstream of the first turbines and a favorable pressure gradient inside the wind farm. In this paper, we present the multi-scale coupled (MSC) model, a novel approach that allows the simultaneous prediction of micro-scale effects occurring at the wind turbine scale, such as individual wake interactions and rotor induction, and meso-scale phenomena occurring at the wind farm scale and larger, such as atmospheric gravity waves. This is achieved by evaluating wake models on a spatially heterogeneous background velocity field obtained from a reduced-order meso-scale model. Verification of the MSC model is performed against two large-eddy simulations (LESs) with similar average inflow velocity profiles and a different capping inversion strength, so that two distinct interfacial gravity wave regimes are produced, i.e. subcritical and supercritical. Interfacial waves can produce high blockage in the first case, as they are allowed to propagate upstream. On the other hand, in the supercritical regime their propagation speed is less than their advection velocity, and upstream blockage is only operated by internal waves. The MSC model not only proves to successfully capture both local induction and global blockage effects in the two analyzed regimes, but also captures the interaction between the wind farm and gravity waves, underestimating wind farm power by about only 2 % compared with the LES results. Conversely, wake models alone cannot distinguish between differences in thermal stratification, even if combined with a local induction model. Specifically, they are affected by a first-row overprediction bias that leads to an overestimation of the wind farm power by 13 % to 20 % for the modeled regimes.

An Open–Closed Flow Separation in a Compressor Radial Diffuser

Abstract Large eddy simulations (LES) results are used to track flow separation zones in a splittered vaned radial diffuser near the compressor best efficiency at high rotation speed. The topology analysis reveals some closed separations at the corner of the blade and hub or shroud surface. In addition, an open–closed flow separation at the main blade pressure side is observed for the first time. The surface separation has the shape of a sheet at the blade mid-span, and the associated separation line is delimited only at its downstream extremity by a trailing edge node. This flow separation process is robust to a small shift in operating condition, and the separation surface remains essentially unchanged. A large flowrate variation converts the open–closed separation into a more classic closed separation. The evolution in time of the separation surface is also observed, and the authors conclude to the unsteady existence of the open–closed separation.

Ice base slope effects on the turbulent ice shelf-ocean boundary current

Abstract Efforts to parameterize ice shelf basal melting within climate models are limited by an incomplete understanding of the influence of ice base slope on the turbulent ice shelf-ocean boundary current (ISOBC). Here we examine the relationship between ice base slope, boundary current dynamics, and melt rate using 3-D, turbulence-permitting large-eddy simulations (LES) of an idealized ice shelf-ocean boundary current forced solely by melt-induced buoyancy. The range of simulated slopes (3-10%) is appropriate to the grounding zone of small Antarctic ice shelves and to the flanks of relatively wide ice base channels, and the initial conditions are representative of warm-cavity ocean conditions. In line with previous studies, the simulations feature the development of an Ekman boundary layer adjacent to the ice, overlaying a broad pycnocline. The time-averaged flow within the pycnocline is in thermal wind balance, with a mean shear that is only weakly dependent on the ice base slope angle α, resulting in a mean gradient Richardson number 〈Rig〉 that decreases approximately linearly with sinα. Combining this inverse relationship with a linear approximation to the density profile, we derive formulations for the friction velocity, thermal forcing, and melt rate in terms of slope angle and total buoyancy input. This theory predicts that melt rate varies like the square root of slope, which is consistent with the LES results and differs from a previously proposed linear trend. The derived scalings provide a potential framework for incorporating slope-dependence into parameterizations of mixing and melting at the base of ice shelves.

Derivation of “Double-Loop” Theory and Mechanism of Cavitation-Vortex Interaction in Turbulent Cavitation Boundary Layer

Abstract “Double-loop” theory was determined by deriving a correlation between turbulent fluctuating kinetic energy and water vapor volume fraction from the momentum equation, which further logically revealed the mystery of cavitation breaking around a three-dimensional symmetry hydrofoil based on the numerical results of large eddy simulation and Zwart–Gerber–Belamri cavitation model. When the second-order fluctuation moment Vx′Vx′ and the streamwise velocity Vx are depleted, a vortex is generated, leading to alternating cavitation interface fluctuations. In one state, cavitation naturally breaks outward from the inner zone, triggering an up-and-down fluctuation in the normal velocity in the gap vortex and transferring external energy to the inner zone. In another state, cavitation collapse caused by a reentrant jet stagnates the reverse Vx so that Vx′Vx′ tends to zero. It triggers a rise in an upward normal velocity in the attached vortex, creating an exchange of energy through the wake. The pressure implosion resulting from the Shrinkage of the “Like-Rayleigh–Plesset” cavity at the cavitation onset is stronger than the pressure implosion created by the vortex field during cavitation breaking.

A one-dimensional urban flow model with an eddy-diffusivity mass-flux (EDMF) scheme and refined turbulent transport (MLUCM v3.0)

Abstract. In recent years, urban canopy models (UCMs) have been used as fully coupled components of mesoscale atmospheric models as well as offline tools to estimate temperature and surface fluxes using atmospheric forcings. Examples include multi-layer urban canopy models (MLUCMs), where the vertical variability of turbulent fluxes is calculated by solving prognostic momentum and turbulent kinetic energy (TKE, k) using mixing length scale (l) and drag parameterizations. These parameterizations are based on the well-established 1.5-order k−l turbulence closure theory and are often informed by microscale fluid dynamics simulations. However, this approach can include simplifications such as assuming the same diffusion coefficient for momentum, TKE, and scalars. In addition, the dispersive stresses arising from spatially averaged flow properties have been parameterized together with the turbulent fluxes despite being controlled by different mechanisms. Both of these assumptions impact the quantification of the turbulent exchange of flow properties and subsequent air temperature predictions in urban canopies. To assess these assumptions and improve corresponding parameterization, we analyzed 49 large-eddy simulations (LES) for idealized urban arrays, encompassing variable building height distributions and a comprehensive range of urban densities (λp∈[0.0625,0.64]) seen in global cities. We find that the efficiency of turbulent transport (numerically described via diffusion coefficients) is similar for scalars and momentum but is 3.5 times higher for TKE. Additionally, parameterizing the dispersive momentum flux using the k−l closure was a source of error, while scaling with the pressure gradient and urban morphological parameters appears more appropriate. In response to these findings, we propose two changes to the previous version of MLUCM: (a) separate characterization for turbulent diffusion coefficient for momentum and TKE and (b) introduction of an explicit physics-based “mass-flux” term to represent the fraction of the dispersive momentum transport directly induced from buildings as an amendment to the existing “eddy-diffusivity” framework. The updated one-dimensional model, after being tuned for building height variability, is further compared against the original LES results and demonstrates improved performance in predicting vertical turbulent exchange in urban canopies.

Modelling Turbulent Flows near Coastal Structures Using Various Turbulence Models

Introduction. The reduction in beach width due to erosion is a significant issue that can either be mitigated or exacerbated by coastal protection structures. Modelling breaking waves near the coast and around coastal structures can be used to determine their impact on the dynamics of the coastal zone. The objective of this study is to model and analyze the dynamics of turbulent structures around a single breakwater, obtained using two turbulence modelling schemes: RANS and LES.Materials and Methods. Turbulence induced by breaking waves was investigated. The modelling was based on bathymetric measurements conducted along the Azov Sea coast and a three-dimensional wave hydrodynamics model supplemented with various turbulence calculation configurations.Results. Modelling results of wave processes generating turbulent flows in the presence of coastal protection structures using different turbulence models were obtained. Results obtained based on Reynolds-averaged Navier-Stokes (RANS) equations are compared with the results of Large Eddy Simulation (LES) approach with Smagorinsky dynamic subgrid-scale model (DSM).Discussion and Conclusions. The results showed that wave heights simulated by LES were higher than those simulated by RANS in the front and leeward regions of the coastal protection structure and were lower in its upper part. Thus, according to LES, a greater amount of wave energy was preserved after passing over the breakwater. Velocity vectors of the water medium showed the formation of a vortex when LES was used, whereas no evidence of such turbulent vortices was detected in the case of RANS, confirming the better performance of LES for turbulence modelling in the coastal zone. According to the presented results, LES is the preferred tool for generating turbulence under incoming wave conditions in engineering practices.

Predicting turbulent wake flow of marine hydrokinetic turbine arrays in large-scale waterways via physics-enhanced convolutional neural networks

We present a physics-enhanced convolutional neural network (PECNN) algorithm for reconstructing the mean flow and turbulence statistics in the wake of marine hydrokinetic (MHK) turbine arrays installed in large-scale meandering rivers. The algorithm embeds the mass and momentum conservation equations into the loss function of the PECNN algorithm to improve the physical realism of the reconstructed flow fields. The PECNN is trained using large eddy simulation (LES) results of the wake flow of a single row of turbines in a virtual meandering river. Subsequently, the trained PECNN is applied to predict the wake flow of MHK turbines with arrangements and positionings different than those considered during the training process. The PECNN predictions are validated using the results of separately performed LES. The results show that the PECNN algorithm can accurately predict the wake flow of MHK turbine farms at a small fraction of the cost of LES. The PECNN can improve the accuracy by around 1% and reduce the physical constraint indices by around 50% compared to the CNN without physical constraints. This work underscores the potential of PECNN to develop reduced-order models for control co-design and optimization of MHK turbine arrays in natural riverine environments.

Turbulence calculation based on the extended Navier–Stokes equations

In this study, phenomenological observations and the Kreuer interpretation of the origin of viscosity were used to develop a computational method for solving the turbulence problem of incompressible viscous Newtonian fluids based on extended Navier–Stokes (N–S) equations. The shear process in fluid flow was hypothesized to be accompanied by eddy formation, and the effects of eddies on the convection and diffusion were considered. The classical N–S equations were improved to obtain extended N–S equations. The extended equations are closed, and the sources of the velocity fluctuations are explicitly considered to be additional convection and diffusion. The extended equations are compatible with the classical N–S equations; thus, they can describe laminar and turbulent flows in a unified manner. In fluid flow simulations, the equations describing the mean flow quantities could be directly obtained from the extended N–S equations without any additional turbulence models. A numerical investigation was carried out to verify the extended equations by exploring the flow over a cube placed in a channel. The simulation results were compared with both the large eddy simulation and experimental results.

Using EUREC4A/ATOMIC field campaign data to improve trade wind regimes in the Community Atmosphere Model

Abstract. Improving the prediction of clouds in shallow-cumulus regimes via turbulence parameterization in the planetary boundary layer (PBL) will likely increase the global skill of global climate models (GCMs) because this cloud regime is common over tropical oceans where low-cloud fraction has a large impact on Earth's radiative budget. This study attempts to improve the prediction of PBL structure in tropical trade wind regimes in the Community Atmosphere Model (CAM) by updating its formulation of momentum flux in CLUBB (Cloud Layers Unified by Binormals), which currently does not by default allow for upgradient momentum fluxes. Hindcast CAM output from custom CLUBB configurations which permit countergradient momentum fluxes are compared to in situ observations from weather balloons collected during the ElUcidating the RolE of Cloud–Circulation Coupling in ClimAte and Atlantic Tradewind Ocean–Atmosphere Mesoscale Interaction Campaign (EUREC4A/ATOMIC) field campaign in the tropical Atlantic in early 2020. Comparing a version with CAM–CLUBB with a prognostic treatment of momentum fluxes results in vertical profiles that better match large-eddy simulation results. Countergradient fluxes are frequently simulated between 950 and 850 hPa over the EUREC4A/ATOMIC period in CAM–CLUBB. Further modification to the planetary boundary layer (PBL) parameterization by implementing a more generalized calculation of the turbulent length scale reduces model bias and root mean squared error (RMSE) relative to sounding data when coupled with the prognostic momentum configuration. Benefits are also seen in the diurnal cycle, although more systematic model errors persist. A cursory budget analysis suggests the buoyant production of momentum fluxes, both above and below the jet maximum, significantly contributes to the frequency and depth of countergradient vertical momentum fluxes in the study region. This paper provides evidence that higher-order turbulence parameterizations may offer pathways for improving the simulation of trade wind regimes in global models, particularly when evaluated in a process study framework.

Energy Exascale Computational Fluid Dynamics Simulations With the Spectral Element Method

Abstract Development and application of the open-source GPU-based fluid-thermal simulation code, NekRS, are described. Time advancement is based on an efficient kth-order accurate timesplit formulation coupled with scalable iterative solvers. Spatial discretization is based on the high-order spectral element method (SEM), which affords the use of fast, low-memory, matrix-free operator evaluation. Recent developments include support for nonconforming meshes using overset grids and for GPU-based Lagrangian particle tracking. Results of large-eddy simulations of atmospheric boundary layers for wind-energy applications as well as extensive nuclear energy applications are presented.

Large eddy simulation of a turbulent flow in a 5 x 5 rod bundle with a mixing vane spacer grid

In fuel assemblies of pressurized water reactors (PWRs), mixing-vane spacer grids are extensively employed to array fuel rods and enhance inter- and intra-subchannel mixing. The turbulent flow downstream of spacer grids is essential knowledge to support the design of spacer grids and mixing vanes. As a high-fidelity approach for turbulence simulation, large eddy simulation (LES) results are assessed with the high-resolution flow field measured with particle image velocimetry (PIV). The LES results reveal a mixing vane effect on vortex structures and Reynolds stresses. The mechanism of vortex generation at the mixing vanes and the development downstream of the spacer grid are visualized by the Q-criterion. The distributions of the root mean square fluctuating velocity and Reynolds stresses decay rapidly downstream of the spacer grid. The secondary flow intensity downstream of the spacer grid predicted by LES is evaluated and follows an exponentially decaying law with distance from the spacer grid.

A wall model for large-eddy simulation of highly compressible flows based on a new scaling of the law of the wall

Wall modelling in large-eddy simulation (LES) is of high importance to allow scale resolving simulations of industrial applications. Numerous models were developed and validated for incompressible flows, including a simple quasi-analytical model based on Reichardt's formula that approximates the law of the wall. In this paper, a scaling is proposed to generalize this wall model to highly compressible flows. First, the results of wall-resolved LES (wrLES) of adiabatic compressible turbulent channel flows at $Re_\tau = 1000$ and at centreline Mach numbers of $M_c= 0.76$ and $1.5$ are presented. Then, three potential scalings of the incompressible wall model are proposed, and their a priori performance is evaluated : (i) the Howarth–Stewartson scaling, (ii) an improved Van Driest scaling and (iii) a new scaling obtained from a blending of those two. The results of wall-modelled LES (wmLES) of compressible channel flows using these three models are compared with the reference wrLES data, showing the superior accuracy of the hybrid scaling. The consistency of the new wall model at low Mach numbers is also verified by comparing the results of a wmLES at $M_c= 0.25$ with those of reference incompressible DNS data at $Re_\tau = 1000$ and $5200$ . Finally, the proposed wall model is also applied to a turbulent channel flow at $M_c=1.5$ and $Re_\tau =5200$ .

A parametric large-eddy simulation study of wind-farm blockage and gravity waves in conventionally neutral boundary layers

We present a suite of large-eddy simulations (LES) of a wind farm operating in conventionally neutral boundary layers. A fixed 1.6 GW wind farm is considered for 40 different atmospheric stratification conditions to investigate effects on wind-farm efficiency and blockage, as well as related gravity-wave excitation. A tuned Rayleigh damping layer and a wave-free fringe-region method are used to avoid spurious excitation of gravity waves, and a domain-size study is included to evaluate and minimize effects of artificial domain blockage. A fully neutral reference case is also considered, to distinguish between a case with hydrodynamic blockage only, and cases that include hydrostatic blockage induced by the air column above the boundary layer and the excitation of gravity waves therein. We discuss in detail the dependence of gravity-wave excitation, flow fields and wind-farm blockage on capping-inversion height, strength and free-atmosphere lapse rate. In all cases, an unfavourable pressure gradient is present in front of the farm, and a favourable pressure gradient in the farm, with hydrostatic contributions arising from gravity waves at least an order of magnitude larger than hydrodynamic effects. Using respectively non-local and wake efficiencies $\eta _{nl}$ and $\eta _{w}$ , we observe a strong negative correlation between the unfavourable upstream pressure rise and $\eta _{nl}$ , and a strong positive correlation between the favourable pressure drop in the farm and $\eta _{w}$ . Using a simplified linear gravity-wave model, we formulate a simple scaling for the ratio $(1-\eta _{nl})/\eta _{w}$ , which matches reasonably well with the LES results.

Large-Eddy Simulations of a Hypersonic Re-Entry Capsule Coupled with the Supersonic Disk-Gap-Band Parachute

The goal of this paper is to investigate the aerodynamic and aerothermodynamic behavior of the Schiaparelli capsule after the deployment of a supersonic disk-gap-band (DGB) parachute during its re-entry phase into the Martian atmosphere. The novelty of this work lies in the investigation by LES (large-eddy simulations) of the coupled interaction of the flow field generated behind the capsule and that in front of the flexible DGB parachute. These simulations are performed at an altitude of 10 km and a Mach number around 2, i.e., a regime in which large canopy-area oscillations are observed. LES results have shown a strong interaction between the bow shock, the recompression and expansion waves, high pressure, density and temperature gradients, heat flux towards the airstream and the body implying turbulence generation, ingestion, and amplification through the shock waves. Vortices released from the capsule at a frequency of about 52 Hz and 159 Hz, corresponding to Strouhal numbers of ~0.2 and 0.75, respectively, are the main factors responsible for the instabilities of the hypersonic re-entry capsule and the disk-gap-band parachute coupled system. The nonlinear turbulence flow field generated at the capsule back is amplified when passing the parachute bow shock, and this is responsible for the non-axisymmetric behavior around and behind the parachute that caused the uncontrolled capsule oscillations and the Schiaparelli mission failure. In fact, an LES of the parachute without the capsule, for the same conditions, show a completely axisymmetric field, varying in time, but axisymmetric. In order to avoid this turbulence amplification, dampening of the vortex shedding is critical. Different techniques have been already proposed for other applications. In the case of capsule re-entry, due to the high temperatures in front of the capsule behind the bow shock since air plasma is generated, damping of the vortex shedding could be achieved by means of magnetohydrodynamic (MHD) control.

Advanced Modeling of Flow and Heat Transfer in Rotating Disk Cavities Using Open-Source Computational Fluid Dynamics

Abstract Code_Saturne, an open-source computational fluid dynamics (CFD) code, has been applied to a range of problems related to turbomachinery internal air systems. These include a closed rotor–stator disk cavity, a co-rotating disk cavity with radial outflow and a co-rotating disk cavity with axial throughflow. Unsteady Reynolds-averaged Navier–Stokes (RANS) simulations and large eddy simulations (LES) are compared with experimental data and previous direct numerical simulation and LES results. The results demonstrate Code_Saturne's capabilities for predicting flow and heat transfer inside rotating disk cavities. The Boussinesq approximation was implemented for modeling centrifugally buoyant flow and heat transfer in the rotating cavity with axial throughflow. This is validated using recent experimental data and CFD results. Good agreement is found between LES and RANS modeling in some cases, but for the axial throughflow cases, advantages of LES compared to URANS are significant for a high Reynolds number condition. The wall-modeled large eddy simulation (WMLES) method is recommended for balancing computational accuracy and cost in engineering applications.

Designing a Convection‐Cloud Chamber for Collision‐Coalescence Using Large‐Eddy Simulation With Bin Microphysics

AbstractCollisional growth of cloud droplets is an essential yet uncertain process for drizzle and precipitation formation. To improve the quantitative understanding of this key component of cloud‐aerosol‐turbulence interactions, observational studies of collision‐coalescence in a controlled laboratory environment are needed. In an existing convection‐cloud chamber (the Pi Chamber), collisional growth is limited by low liquid water content and short droplet residence times. In this work, we use numerical simulations to explore various configurations of a convection‐cloud chamber that may intensify collision‐coalescence. We employ a large‐eddy simulation (LES) model with a size‐resolved (bin) cloud microphysics scheme to explore how cloud properties and the intensity of collision‐coalescence are affected by the chamber size and aspect ratio, surface roughness, side‐wall wetness, side‐wall temperature arrangement, and aerosol injection rate. Simulations without condensation and evaporation within the domain are first performed to explore the turbulence dynamics and wall fluxes. The LES wall fluxes are used to modify the Scalar Flux‐budget Model, which is then applied to demonstrate the need for non‐uniform side‐wall temperature (two side walls as warm as the bottom and the two others as cold as the top) to maintain high supersaturation in a tall chamber. The results of LES with full cloud microphysics reveal that collision‐coalescence is greatly enhanced by employing a taller chamber with saturated side walls, non‐uniform side‐wall temperature, and rough surfaces. For the conditions explored, although lowering the aerosol injection rate broadens the droplet size distribution, favoring collision‐coalescence, the reduced droplet number concentration decreases the frequency of collisions.

Generalized wall-modeled large eddy simulation model for industrial applications

In this work, a generalized wall-modeled large eddy simulation model (GWMLES) is presented. An extended formulation of the classical WMLES approach is proposed that also enables the modeling of the entire log-layer by using a Reynolds-averaged Navier–Stokes (RANS) model. GWMLES is validated against direct numerical simulations, large eddy simulations (LES), WMLES, hybrid RANS/LES, unsteady RANS (URANS), and experimental data of test cases featuring industrial flows. It is demonstrated that GWMLES does not share the main shortcoming of current WMLES models. When the entire log-layer is solved with a RANS model, GWMLES gives a level of accuracy similar to recent LES results, as well as computational cost savings that are proportional to the Reynolds number in wall-bounded flows. The model shows superior performance than URANS even when the resolved portion of the energy spectrum is reduced. Motivated by the different time scales of the flow and RANS variables, it requires approximately 30% lower computational costs than the detached eddy simulation family models in the turbulent flows considered. These features represent significant advancements in the simulation of wall-bounded flows at high Reynolds numbers, particularly in industrial applications.

A New Hybrid Mass‐Flux/High‐Order Turbulence Closure for Ocean Vertical Mixing

AbstractWhile various parameterizations of vertical turbulent fluxes at different levels of complexity have been proposed, each has its own limitations. For example, simple first‐order closure schemes such as the K‐Profile Parameterization (KPP) lack energetic constraints; two‐equation models like directly solve an equation for the turbulent kinetic energy but do not account for non‐diffusive fluxes, and high‐order closures that include the high‐order transport terms are computationally expensive. To address these, we extend the Assumed‐Distribution Higher‐Order Closure (ADC) framework originally proposed for the atmospheric boundary layer and apply it to the ocean surface boundary layer. By assuming a probability distribution function relationship between the vertical velocity and tracers, all second‐order and higher‐order moments are exactly constructed and turbulence closure is achieved in the ADC scheme. In addition, this ADC parameterization has full energetic constraints and includes non‐diffusive fluxes without the computational cost of a full higher‐order closure scheme. We have tested the ADC scheme against a combination of large eddy simulation (LES), KPP, and for surface buoyancy‐driven convective mixing and found that the ADC scheme is robust with different vertical resolutions and compares well to the LES results.