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At least 19 records

The Vertical Structure of Turbulence Kinetic Energy Near the Arctic Sea‐Ice Surface

Atmospheric turbulence over the Arctic sea-ice surface has been understudied due to the lack of observational data. In this study, we focus on the turbulence kinetic energy (TKE) over sea ice and distinguish its two different vertical structures, the “Surface” type and the “Elevated” type, using observations during the Multidisciplinary drifting Observatory for the Study of Arctic Climate expedition (MOSAiC). The “Surface” type has the maximum TKE near the surface (at 2 m), while the “Elevated” type has the maximum TKE at a higher level (6 m). The TKE budget analysis indicates that the “Elevated” type is caused by the increased shear production of TKE at 6 m. In addition, spectral analysis reveals that the contribution to TKE by horizontal large eddies is enhanced in the “Elevated” type. Finally, how the vertical structure of TKE affects the parameterization of turbulent momentum flux is discussed.

54 ENVIRONMENTAL SCIENCES↗

Can machine learning improve the model representation of turbulent kinetic energy dissipation rate in the boundary layer for complex terrain?

Current turbulence parameterizations in numerical weather prediction models at the mesoscale assume a local equilibrium between production and dissipation of turbulence. As this assumption does not hold at fine horizontal resolutions, improved ways to represent turbulent kinetic energy (TKE) dissipation rate (ϵ) are needed. Here, we use a 6-week data set of turbulence measurements from 184 sonic anemometers in complex terrain at the Perdigão field campaign to suggest improved representations of dissipation rate. First, we demonstrate that the widely used Mellor, Yamada, Nakanishi, and Niino (MYNN) parameterization of TKE dissipation rate leads to a large inaccuracy and bias in the representation of ϵ. Next, we assess the potential of machine-learning techniques to predict TKE dissipation rate from a set of atmospheric and terrain-related features. We train and test several machine-learning algorithms using the data at Perdigão, and we find that the models eliminate the bias MYNN currently shows in representing ϵ, while also reducing the average error by up to almost 40 %. Of all the variables included in the algorithms, TKE is the variable responsible for most of the variability of ϵ, and a strong positive correlation exists between the two. These results suggest further consideration of machine-learning techniques to enhance parameterizations of turbulence in numerical weather prediction models.

58 GEOSCIENCES↗

Scaling Behavior of a Turbulent Kinetic Energy Closure Scheme for the Stably Stratified Atmosphere: A Steady-State Analysis

Abstract We present a turbulent kinetic energy (TKE) closure scheme for the stably stratified atmosphere in which the mixing lengths for momentum and heat are not parameterized in the same manner. The key difference is that, while the mixing length for heat tends toward the stability independent mixing length for momentum in neutrally stratified conditions, it tends toward one based on the Brunt–Väisälä time scale and square root of the TKE in the limit of large stability. This enables a unique steady-state solution for TKE to be obtained, which we demonstrate would otherwise be impossible if the mixing lengths were the same. Despite the model’s relative simplicity, it is shown to perform reasonably well with observational data from the 1999 Cooperative Atmosphere–Surface Exchange Study (CASES-99) using commonly employed model constants. Analyzing the scaling behavior of the nondimensional velocity and potential temperature gradients, or of the stability (correction) functions, reveals that for large stability the present model scales in the same manner as the first-order operational scheme of Viterbo et al. Alternatively, it appears as a blend of two cases of the TKE closure scheme of Baas et al. Critically, because a unique steady-state TKE can be obtained, the present model avoids the nonphysical behavior identified in one of the cases of Baas et al.

Meteorology & Atmospheric Sciences↗

Similarity of the turbulent kinetic energy dissipation rate distribution in the upper mixed layer of the tropical Indian Ocean

Turbulence within the upper ocean mixed layer plays a key role in various physical, biological, and chemical processes. Between September and November 2011, a dataset of 570 vertical profiles of the turbulent kinetic energy (TKE) dissipation rate, as well as conventional hydrological and meteorological data, were collected in the upper layer of the tropical Indian Ocean. These data were used to statistically analyze the vertical distribution of the TKE dissipation rate in the mixed layer. The arithmetic-mean method made the statistical TKE dissipation rate profile more scattered than the median and geometric-mean methods. The statistical TKE dissipation rate were respectively scaled by the surface buoyancy flux and the TKE dissipation rate at the mixed-layer base. It was found that the TKE dissipation rate scaled by that at the mixed-layer base exhibited better similarity characteristics than that scaled by the surface buoyancy flux, whether the stability parameter D/|L MO | was greater or less than 10, indicating that the TKE dissipation rate at the mixed-layer base is a better characteristic scaling parameter for reflecting the intrinsic structure of the TKE dissipation rate in the mixed layer, where D and L MO are respectively the mixed-layer thickness and the Monin-Obukhov length scale. The parameterization of the TKE dissipation rate at the mixed-layer base on the shear-driven dissipation rate and the surface buoyancy flux was further explored. It was found that the TKE dissipation rate at the mixed-layer base could be well fitted by a linear combination of three terms: the wind-shear-driven dissipation rate, the surface buoyancy flux, and a simple nonlinear coupling term of these two.

54 ENVIRONMENTAL SCIENCES↗

Profiling the molecular destruction rates of temperature and humidity as well as the turbulent kinetic energy dissipation in the convective boundary layer

A simultaneous deployment of Doppler, temperature, and water-vapor lidars is able to provide profiles of molecular destruction rates and turbulent kinetic energy (TKE) dissipation in the convective boundary layer (CBL). Horizontal wind profiles and profiles of vertical wind, temperature, and moisture fluctuations are combined, and transversal temporal autocovariance functions (ACFs) are determined for deriving the dissipation and molecular destruction rates. These are fundamental loss terms in the TKE as well as the potential temperature and mixing ratio variance equations. These ACFs are fitted to their theoretical shapes and coefficients in the inertial subrange. Error bars are estimated by a propagation of noise errors. Sophisticated analyses of the ACFs are performed in order to choose the correct range of lags of the fits for fitting their theoretical shapes in the inertial subrange as well as for minimizing systematic errors due to temporal and spatial averaging and micro- and mesoscale circulations. We demonstrate that we achieve very consistent results of the derived profiles of turbulent variables regardless of whether 1 or 10 s time resolutions are used. We also show that the temporal and spatial length scales of the fluctuations in vertical wind, moisture, and potential temperature are similar with a spatial integral scale of ≈160 m at least in the mixed layer (ML). The profiles of the molecular destruction rates show a maximum in the interfacial layer (IL) and reach values of ϵ m ≃ 7 x 10 -4 g 2 kg −2 s −1 for mixing ratio and ϵ θ ≃ 1.6 x 10 -3 K 2 s −1 for potential temperature. In contrast, the maximum of the TKE dissipation is reached in the ML and amounts to ≃ 10 -2 m 2 s −3 . We also demonstrate that the vertical wind ACF coefficient k w ∝ $\overline{w'^{2}}$ and the TKE dissipation ϵ ∝ ($\overline{w'^{2}}$) 3/2 . For the molecular destruction rates, we show that ϵ m ∝ $\overline{m'^{2}}$ ($\overline{w'^{2}}$) 1/2 and ϵ θ ∝ $\overline{θ'^{2}}$ ($\overline{w'^{2}}$) 1/2 . These equations can be used for parameterizations of ϵ, ϵ m , and ϵ θ . All noise error bars are derived by error propagation and are small enough to compare the results with previous observations and large-eddy simulations. The results agree well with previous observations but show more detailed structures in the IL. Consequently, the synergy resulting from this new combination of active remote sensors enables the profiling of turbulent variables such as integral scales, variances, TKE dissipation, and the molecular destruction rates as well as deriving relationships between them. The results can be used for the parameterization of turbulent variables, TKE budget analyses, and the verification of large-eddy simulations.

dissipation rate↗

Two-Phase Turbulent Kinetic Energy Budget Computation in Co-Current Taylor Bubble Flow

Simulation of two-phase flows is relevant for reactor design and safety at normal operation or during accident scenarios. Often, the two-phase flow is in a regime in which slugs are formed or where the flow stratifies. Modeling such situations using standard single-phase Reynolds-averaged Navier-Stokes (RANS) turbulence models fails due to an overestimation of the eddy viscosity at the resolved two-phase interface. To solve this, an ad hoc turbulence damping term has been proposed in the literature that reduces the turbulence production locally at a two-phase interface, analogously to turbulence wall functions. However, this approach must be tailored to the specific setting and does not consider physical contributions such as surface tension or flow topology. Therefore, the problem of two-phase interfacial turbulence must be studied more in-depth. In this work, we consider co-current turbulent Taylor bubble flow using high-fidelity numerical simulation. The Basilisk code is used to simulate a Taylor bubble rising in a vertical pipe. By simulating the bubble in a moving frame of reference, we may study the turbulent kinetic energy (TKE) budgets ahead of the bubble, in its wake, and across the interface. The implementation of the TKE budget computation and the underlying averaging techniques are validated for the single-phase region ahead of the Taylor bubble using reference direct numerical simulation data. The analysis of the TKE budgets in the setting of Taylor bubble flow allows for the study of how turbulence behaves due to the presence of a two-phase interface and, in turn, supports the improvement of two-phase RANS models.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Turbulent Kinetic Energy Budgets over Gentle Topography Covered by Forests

Large-eddy simulations of flow over a “horizontally” uniform model forest are used to investigate the effects of gentle topography on the turbulent kinetic energy (TKE) budget within the canopy roughness sublayer. Despite significant differences between simulations using idealized sinusoidal topography and real topography of the Amazon forest, results indicate that the effects of topography are located predominantly in the upper canopy and above, and are mostly caused by mean advection of TKE. The “horizontally” averaged TKE budget from idealized and real gentle topographies are almost identical to that for flat terrain, including a clear inertial layer above the roughness sublayer in which shear production is balanced by local dissipation. At topography crests, where observational towers are usually located, mean vertical advection of TKE can be as important as horizontal advection. Here, we propose the use on an approximate TKE balance equation to estimate mean advection from single tower measurements, and introduce a new advection index that can be used as a proxy to quantify the importance of the topography on the TKE budget.

54 ENVIRONMENTAL SCIENCES↗

Simulated meteorological impacts of offshore wind turbines and sensitivity to the amount of added turbulence kinetic energy

Offshore wind energy projects are currently in development off the east coast of the United States and may influence the local meteorology of the region. Wind power production and other commercial uses in this area are related to atmospheric conditions, and so it is important to understand how future wind plants may change the local meteorology. In the absence of measurements of potential wind plant impacts on meteorology, simulations offer the next-best possible insight into wake effects on boundary layer height, temperature, fluxes, and wind speeds. However, simulation tools that capture these effects offer multiple options for representing the amount of turbine-added turbulence that may impact assessments of micrometeorological effects. To explore this sensitivity, we compare 1 year of simulations from the Weather Research and Forecasting (WRF) model with and without wind plants incorporated, focusing on the lease area south of Massachusetts and Rhode Island. The simulations with wind plants are repeated to include both the maximum and minimum amounts of added turbulence to provide bounds on the potential impacts. We assess changes in wind speeds, 2 m temperature, surface heat flux, turbulence kinetic energy (TKE), and boundary layer height during different stability classifications and ambient wind speeds over the entire year and compare results for the degree of added turbulence in the wind plant simulations. Because the wake behavior may be a function of boundary layer stability, in this paper, we also present a machine learning algorithm to quantify the area and distance of the wake generated by the wind plant. This analysis enables us to identify the relationship between wake extent and boundary layer height. We find that hub-height wind speed is reduced within and downwind of the wind plant, with the strongest impacts occurring during stable conditions and faster wind speeds in region 3 of the turbine power curve, although impacts lessen as wind speeds increase past 15 m s−1. In contrast, wind speeds near the surface decrease when no turbine-added turbulence is included but can increase for stably stratified conditions when 100 % of possible TKE is included in the simulations. TKE increases at hub height in the simulations with added TKE for all stability classes, suggesting that atmospheric stability does not immediately modify the TKE generated by turbines. Negligible changes in hub-height TKE manifest in the simulations without the added TKE. At the surface, TKE increases in the simulations with maximum added turbulence only for unstable conditions. In the no-added-turbulence simulations, surface TKE decreases slightly in neutral and unstable simulations. Differences in 2 m temperatures and surface heat fluxes are small but vary considerably with atmospheric stability and the amount of added TKE. Boundary layer heights increase within the wind plant when turbine-added turbulence is included and decrease slightly downwind during stable conditions. In contrast, with no added turbulence, the boundary layer height is in general reduced in stable conditions with wind speeds less than 15 m s −1 and slightly increased in neutral conditions. Finally, shallower upwind boundary layer heights tend to correlate with larger wake areas and distances, though other factors likely also play a role in determining the extent of the wind plant wake. These simulation-based results provide a bound for micrometeorological impacts of wind plant wakes: simulations that couple the atmosphere to the ocean may reduce these impacts, and we await observational verification.

17 WIND ENERGY↗

Turbulent kinetic energy over large offshore wind farms observed and simulated by the mesoscale model WRF (3.8.1)

Abstract. Wind farms affect local weather and microclimates;hence, parameterizations of their effects have been developed for numerical weather prediction models.While most wind farm parameterizations (WFPs) include drag effects of wind farms, models differ on whether or not an additionalturbulent kinetic energy (TKE) source should be included in theseparameterizations to simulate the impact of wind farms on the boundary layer.Therefore, we use aircraft measurements above large offshore wind farms in stable conditions to evaluateWFP choices. Of the three case studies we examine, we find the simulated ambient backgroundflow to agree with observations of temperature stratification and winds. This agreement allows us toexplore the sensitivity of simulated wind farm effects with respect to modeling choicessuch as whether or not to include a TKE source, horizontal resolution, vertical resolutionand advection of TKE. For a stably stratified marine atmospheric boundary layer (MABL), a TKE source and a horizontal resolutionon the order of 5 km or finer are necessary to represent the impact of offshore wind farms on the MABL.Additionally, TKE advection results in excessively reduced TKE over the wind farms, which in turn causesan underestimation of the wind speed deficit above the wind farm. Furthermore, using fine verticalresolution increases the agreement of the simulated wind speed with satellite observations of surface wind speed.

17 WIND ENERGY↗

Dry Deposition Methods Based on Turbulence Kinetic Energy: 1. Evaluation of Various Resistances and Sensitivity Studies Using a Single‐Point Model

Different functions are used to account for turbulence strength in the atmospheric boundary layer for different stability regimes. These functions are one of the sources for differences among different atmospheric models' predictions and associated biases. Also, turbulence strength is underrepresented in some of the resistance formulations. Here, to address these issues with dry deposition, firstly we take advantage of three‐dimensional (3‐D) turbulence information in estimating resistances by proposing and validating a 3‐D turbulence velocity scale that is relevant for different stability regimes of boundary layer. Secondly, we hypothesize and validate that friction velocity measured by 3‐D sonic anemometer can be effectively replaced by the new turbulence velocity scale multiplied by the von Karman constant. Finally, we (a) present a set of resistance formulations for ozone (O 3 ) based on the 3‐D turbulence velocity scale; (b) intercompare estimations of such resistances with those obtained using existing formulations; and, (c) evaluate simulated O 3 fluxes using a single‐point dry deposition model against long‐term observations of O 3 fluxes at the Harvard Forest (MA) site. Results indicate that the new resistance formulations work very well in simulating surface latent heat and O 3 fluxes when compared to respective existing formulations and measurements at a decadal time scale. Findings from this research may help to improve the capability of dry deposition schemes for better estimation of dry deposition fluxes and create opportunities for the development of a community dry deposition model for use in regional/global air quality models.

54 ENVIRONMENTAL SCIENCES↗

Using Particle Image Velocimetry to Determine Turbulence Model Parameters

The primary parameter of a standard k-ϵ model, C μ , was calculated from stereoscopic particle image velocimetry (PIV) data for a supersonic jet exhausting into a transonic crossflow. This required the determination of turbulent kinetic energy, turbulent eddy viscosity, and turbulent energy dissipation rate. Image interrogation was optimized, with different procedures used for mean strain rates and Reynolds stresses, to produce useful turbulent eddy viscosity fields. The eddy viscosity was calculated by a least-squares fit to all components of the three-dimensional strain-rate tensor that were available from the PIV data. This eliminated artifacts and noise observed when using a single strain component. Local dissipation rates were determined via Kolmogorov’s similarity hypotheses and the second-order structure function. The eddy viscosity and dissipation rates were then combined to determine C μ . Considerable spatial variation was observed in C μ , with the highest values found in regions where turbulent kinetic energy was relatively low but where turbulent mixing was important, e.g., along the high-strain jet edges and in the wake region. This suggests that use of a constant C μ in modeling may lead to poor Reynolds stress predictions at mixing interfaces. A data-driven modeling approach that can predict this spatial variation of C μ based on known state variables may lead to improved simulation results without the need for calibration.

42 ENGINEERING↗

A Study of the Transition to Turbulence in a Bed of 67 Spherical Pebbles

Packed beds are commonly found in many engineering systems and have been widely studied for decades. A relatively new packed bed system is the Pebble Bed Reactor, a type of generation-IV nuclear reactor. Unlike many of the packed beds encountered in chemical and process engineering applications, Pebble Bed Reactors are larger and operate at significantly higher Reynolds numbers. As a result of these differences, there is a very limited amount of information on the detailed flow physics that exist in these complex geometries. This work seeks to contribute to a growing database of flow data for Pebble Bed Reactor systems by performing Direct Numerical Simulations of the flow in an experimental bed of 67 pebbles for a range of conditions. Simulations are performed at a Prandtl number of 0.66 and Reynolds numbers from 300–600. These Reynolds numbers are chosen to gain additional knowledge on the spatial development of turbulence in these systems. Analysis of the Turbulent Kinetic Energy, turbulence anisotropy, and Turbulent Heat Flux is performed. Results demonstrate significant development of the TKE across the tested range of Reynolds numbers. Examination of both the TKE and THF reveal that development first occurs near the center of the bed and propagates radially as the flow moves further into the bed. Notable regions of negative production of turbulent kinetic energy are observed in regions where flow accelerates around pebble contact points. Furthermore, these regions are found to coincide with regions of 1-component turbulence.Kindly check and confirm, all authors email id is correctly identified.These are correct

Direct numberical simulation↗

Simultaneous velocity and density measurements of fully developed Rayleigh-Taylor mixing

Here, the dynamics of molecular mixing and the energy transfer process in the Rayleigh-Taylor instability (RTI) are studied through the collection of simultaneous density-velocity measurements. These experiments provide simultaneous density-velocity field measurements, in contrast to previous point measurements. Statistically stationary experiments are performed in a “convective-type” gas tunnel facility, with density contrast achieved through the injection of helium into the bottom stream. Three experiments at Atwood number ≈ 0.1 are captured at three outer scale Reynolds numbers Re = 520, 2260, and 4050. Particle image velocimetry and laser induced fluorescence are employed simultaneously. Statistics of the density and velocity show self-similar collapse of RTI profiles at large Reynolds number Re >2000. Flat velocity profiles indicate homogeneous turbulence characteristics in the core of the mixing region. Significant anisotropy develops in the flow, with horizontal velocity fluctuations being only 60% of the vertical velocity fluctuations. The turbulent mass flux is found to be asymmetric about the centerline, with increased peak towards the spike. Measurements of the molecular mixing show that mixing is maximized at the core of the flow and increases with increased Reynolds number. The transport equation of density-specific-volume correlation b shows that it is mostly produced in the core of the mixing region, and that the spatial evolution of its profile is the result of transport by bulk motion of the bubble and spike. Energy transfer from gravitational potential energy to turbulent kinetic energy and viscous dissipation is observed to occur in the experiment with a ratio of dissipated energy to potential energy released of 38%. The analysis of the turbulent kinetic energy transport equation budget reveals that production is the primary mechanism towards the growth of turbulent kinetic energy in the core of the flow, and is asymmetrically slightly skewed towards the spike. However, it is through the transport that the strong advection at the edges of the mixing region is maintained.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Dynamic Wind Loading on CSP Collectors Caused by Turbulent Wind Fluctuations: Insights from a 2-Year Field Campaign

Concentrating Solar Power (CSP) is a promising solar technology for electricity generation with thermal energy storage and with the additional benefit of industrial heat production. Wind loading on CSP collector structures, such as parabolic troughs or heliostats, is one of the primary drivers of their structural design costs. In particular, dynamic wind loading is a major source of uncertainty in the collector design process, which heavily relies on wind tunnel testing. In the field, the turbulent nature of the incoming wind creates fluctuating loads (support structure loads and resulting mirror deflections) on the collectors, with impacts on fatigue lifetime and optical performance. As is well known, wind tunnel tests cannot entirely reproduce the complex turbulent wind conditions typically observed at full-scale plants. To shed light on this topic, NREL initiated a field campaign at the operational Nevada Solar One (NSO) powerplant that uses parabolic troughs as solar collectors. The aim of the project is a detailed characterization of prevailing wind and turbulence conditions and resulting operational loads on parabolic troughs. We use the published 2-year dataset of high-resolution combined wind and structural loads measurements [1] to characterize the dynamic structural wind response. For quantifying dynamic wind loading, we apply the concept of admittance functions, which are spectral transfer functions that couple the turbulent wind to resulting structural loads (aerodynamic admittance), and to the structural response (mechanical admittance). In practice, aerodynamic admittance describes which turbulent eddy sizes are effective in creating structural loads. The mechanical admittance describes in which frequency ranges these loads are reinforced or dampened by the structure. While these functions are an established concept in civil engineering, their recent application to a single full-scale heliostat [2] proved their broader applicability to CSP collectors. Here, we present a characterization of admittance functions for full-scale parabolic trough collectors and show how wind characteristics (mean wind speed and direction, turbulent kinetic energy, turbulent length scales), the sun-tracking trough angle, and row position alter the admittance functions. Further, we study to which extent the admittance functions are universal for a specific trough geometry and how our findings compare to reported heliostat results. References [1] https://data.openei.org/submissions/5938. [2] Blume, K., Roger, M., and Pitz-Paal, R. 2023b. "Simplified analytical model to describe wind loads and wind-induced tracking deviations of heliostats." Solar Energy, 256, 96-109. https://doi.org/10.1016/j.solener.2023.03.055.

admittance functions↗

Observations of the Marine Atmospheric Boundary Layer’s Response to a Solar Eclipse

The atmospheric response to the solar eclipse of 8 April 2024 in North America is investigated with a specific focus on the marine atmospheric boundary layer (MABL). We leverage measurements collected during the Third Wind Forecast Improvement Project (WFIP3), including Doppler lidars, sonic anemometers, and thermodynamic profiler data to investigate the atmospheric response across sites that experienced partial eclipse conditions with nearly 90% obscuration. Using these measurements, we examine eclipse-induced changes in key meteorological parameters, such as temperature, wind speed, and turbulent fluxes. Most previous eclipse studies have been conducted over land, whereas this study provides new observations for both coastal and marine environments, offering additional insight into eclipse-driven variability in the MABL. The findings confirm a notable decrease in downwelling shortwave radiation during the eclipse, which results in rapid cooling of surface air. The temperature reduction ranges from $1.2^\circ \text {C}$ to $1.4^\circ \text {C}$ in coastal regions and from $0.3^\circ \text {C}$ to $0.5^\circ \text {C}$ over the ocean. This analysis suggests that the MABL’s higher thermal inertia compared to coastal regions moderates the temperature decrease during the eclipse. Wind speed exhibits a more complex behavior, as it is influenced by both the MABL and preexisting synoptic conditions. Although a reduction in wind speed is observable up to approximately 140 m above ground level (AGL) at more inland sites, at other locations closer to the coast, this reduction is constrained to the lowest 100 m AGL. Turbulence parameters retrieved from sonic anemometers, such as turbulence kinetic energy, turbulent heat flux, and friction velocity, decrease during the eclipse at coastal sites, accompanied by a brief transition of atmospheric stability from unstable to neutral or weakly stable conditions. For the open-ocean sites, the variability in turbulence statistics and atmospheric stability is minimal during the occurrence of the eclipse.

16 TIDAL AND WAVE POWER↗

Mass and momentum transport in the Tilted Rocket Rig experiment

Here, high-fidelity large eddy simulations of the inclined Rayleigh-Taylor instability in the Tilted Rocket Rig experimental configuration [Smeeton and Youngs, AWE Report No. O 35/87 (1987)] are performed using a tenth-order compact finite difference code. These simulations are analyzed for spatial distributions of turbulent kinetic energy, turbulent mass flux velocity, species mass fraction flux, species mass fraction variance, and Favre-averaged Reynolds stresses at two time instances, t = 37 ms and t = 52 ms. Additionally, the vertical distribution of the components of the unclosed budget equations over the center of the domain for these quantities are examined. The dominant terms of these budget equations are further decomposed to examine the principal contributions to these terms in each axis. Notably, the principal contribution to the horizontal turbulent mass flux velocity budget is found to be from a term which is commonly neglected in many Reynolds-averaged Navier-Stokes models.

42 ENGINEERING↗