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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Topography-Induced TKE Budget Behavior Over an Amazon Forest

Data from three different heights (35, 50 and 81 m) of one of the ATTO Project towers in the Amazon forest were used to calculate the TKE (turbulence kinetic energy) budget and some other statistics within the RSL (roughness sublayer). The statistical analyses were carried out for unstable and stable cases. The vertical transport and the vertical advection terms do not explain the imbalances found in the TKE budget, highlighting the impor- tance of horizontal terms in complex terrain. Indeed, patterns independent of the time of day were found for vertical transport, horizontal and vertical velocity skewness, the mean vertical component velocity, and momentum and vertical TKE flux. Here, the highest values of mean vertical velocity were observed from the direction where there is a valley near the tower, which may indicate a topographical effect. Monin-Obukhov Similarity Theory (MOST) predictions for the mean velocity gradient, strictly applicable only in the inertial sublayer (ISL), gave reasonable predictions at 35 and 50 m, but dimensionless dissipation rates displayed large scatter. At 81 m, there were clear deviations from MOST for the two functions, disclosing the effect of topography. In addition, a neutral LES (large-eddy simu- lation) study showed good agreement with tower data for the same general wind direction.

ATTO project↗
DOE OSTI2024

$\overline{TKE}$ Parameterization and $\bar{v}$ Uncertainty Analysis for CGMF

Previous work was performed on tuning CGMF parameters for 235 U, 238 U, and Plutonium isotopes. Now work is being done to tune minor uranium isotopes. However, uranium isotopes like 232 U and 236 U have almost no experimental data. We are applying cross-isotope models to extrapolate and tune CGMF on isotopes that lack experimental data. There exist several internal CGMF physics quantities that affect the output of CGMF—multi-chance fission probability, excitation energy sharing, spin-cutoff factor, spin scaling, and fragment total kinetic energy to name a few. The mean fragment total kinetic energy, $\overline{TKE}$, is particularly interesting because of its strong anti-correlation with $\bar{v}$. We are most interested in the mean fragment total kinetic energy before neutron emissions. $\overline{TKE}$ is assumed to be pre-neutron emission unless otherwise stated. Currently in CGMF, the $\overline{TKE}$ model for 233,234,235,238 U are tuned independently to reproduce ν for the associated isotopes. In this report, we will tune a cross-isotope $\overline{TKE}$ model to experimental $\overline{TKE}$ data for 232,233,234,235,236,238 U. Because of the unreliable and sparse nature of $\overline{TKE}$ experimental data, future work will use more reliable experimental $\bar{v}$ data to infer the $\overline{TKE}$ model (and likely other internal CGMF parameters) for uranium isotopes. Such work has been performed previously using a sensitivity analysis and Kalman filter methods.

07 ISOTOPE AND RADIATION SOURCES↗
NASA NTRS2001

Preprocessing for Eddy Dissipation Rate and TKE Profile Generation

The Aircraft Vortex Spacing System (AVOSS), a set of algorithms to determine aircraft spacing according to wake vortex behavior prediction, requires turbulence profiles to appropriately determine arrival and departure aircraft spacing. The ambient atmospheric turbulence profile must always be produced, even if the result is an arbitrary (canned) profile. The original turbulence profile code was generated By North Carolina State University and used in a non-real-time environment in the past. All the input parameters could be carefully selected and screened prior to input. Since this code must run in real-time using actual measurements in the field as input, it became imperative to begin a data checking and screening process as part of the real-time implementation. The process described herein is a step towards ensuring that the best possible turbulence profile is always provided to AVOSS. Data fill-ins, constant profiles and arbitrary profiles are used only as a last resort, but are essential to ensure uninterrupted application of AVOSS.

Zak, J. Allen↗
DOE OSTI2022

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↗
DOE OSTI2025

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↗
NASA NTRS2005

Interannual Variability of Seasonal Pblooms in the North Polar Atlantic in Response to Atmospheric Forcing

The year-to-year variability of timing, intensity, and spatial distribution of surface phytoplankton during spring-summer seasons is examined in the north polar region of the Atlantic using satellite-derived chlorophyll a concentration (Chl) over 7 years (1998 2004). Each year phytoplankton bloom differed in onset, temporal evolution, and intensity. This interannual variability is to a large degree controlled by local weather, as indicated by the analysis of coincident meteorological data. The atmospheric forcing was parameterized in terms of the generation rate of turbulent kinetic energy (TKE(sub RT)) supplied from the atmosphere to the ocean. Timing of the bloom is delayed in years with high TKE(sub RT) supplied to the ocean in March. In April, Chl (local and regionally averaged) and TKE(sub RT) are inversely related to one another. The late winter and early spring atmospheric conditions influence the seasonal Chl patterns. The seasonal (April-August) Chl correlates well with net heat flux, wind energy, and TKE(sub RT) in March and April, but the correlation can be negative or positive in different areas of the north polar Atlantic. The correlation between TKE(sub RT) and seasonal Chl is positive in the Greenland Gyre (higher seasonal Chl corresponds to higher TKE(sub RT) in March April) and negative in the regions of East Greenland and North Atlantic/West Spitsbergen Currents. The most likely explanation for the positive correlation between TKE(sub RT) and Chl within the Greenland Gyre is that higher TKE(sub RT) in spring increases the seasonal supply of nutrients into surface waters.

Stramska, Malgorzata↗
DOE OSTI2024

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↗
DOE OSTI2022

Fast-neutron-induced fission of Pu 240 and Pu 242

Herein we report the measurement of the total kinetic energy (TKE) release in the fast neutron induced fission of 240 Pu and 242 Pu. The results are compared to the predictions of the GEF model, the CGMF model, and the model of Denisov and Sedykh as well as previous exptl. work on these reactions. Our absolute measurements of the TKE release are in good agreement with the previous measurements of Nethaway et al. for the interaction of 14.8 MeV neutrons with 240 Pu [Phys. Rev. C16, 1907 (1977)] and of Winkelmann and Aumann for the interaction of 15 MeV neutrons with 242 Pu [Phys. Rev. C30, 934 (1984)]. The general trends of the measured TKE values agree with phenomenol. models but the variances of the TKE distributions are significantly less than predicted by various models. The mean postneutron emission TKE release decreases nonlinearly with increasing neutron energy and can be represented as TKE(MeV) = 175.8 ± 0.3 - (2.4 ± 0.8) lo g 10 E n - (1.4 ± 0.4) lo g 10 $E^{2}_{n}$ for 240 Pu and TKE(MeV) = 177.1 ± 0.3 - (1.2 ± 0.9) lo g 10 E n - (1.8 ± 0.5)lo g 10 $E_{n}^{2}$ for 242 Pu.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Compare $\overline{ν}$ parameterizations for 235 U(n,f) with fitted fission barriers

In this document, we compare observables computed with CGMF to some available data for 235 U(n,f), to investigate the multi-chance fission probabilities (fission barriers from CoH were refit) and two TKE parametrization. The four parametrizations include i) default CGMF multi-chance fission probabilities with bends in TKE for all fission chances, ii) default CGMF multi-chance fission probabilities with a TKE bend in only first-chance fission iii) refitted multi-chance fission probabilities with bends in TKE for all fission chances, and iv) refitted multi-chance fission probabilities with a bend in TKE for only first-chance fission. In all figures where the four parametrizations are on the same plot, the ones with bends in TKE for all chance fission are in black, with only first-chance bend in red, the default multi-chance fission probabilities are dashed and the new multi-chance fission probabilities are the solid lines.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Impact of Momentum Perturbation on Convective Boundary Layer Turbulence

Mesoscale-to-microscale coupling is an important tool for conducting turbulence-resolving multiscale simulations of realistic atmospheric flows, which are crucial for applications ranging from wind energy to wildfire spread studies. Different techniques are used to facilitate the development of realistic turbulence in the large-eddy simulation (LES) domain while minimizing computational cost. Here, we explore the impact of a simple and computationally efficient Stochastic Cell Perturbation method using momentum perturbation (SCPM-M) to accelerate turbulence generation in boundary-coupled LES simulations using the Weather Research and Forecasting model. We simulate a convective boundary layer (CBL) to characterize the production and dissipation of turbulent kinetic energy (TKE) and the variation of TKE budget terms. Furthermore, we evaluate the impact of applying momentum perturbations of three magnitudes below, up to, and above the CBL on the TKE budget terms. Momentum perturbations greatly reduce the fetch associated with turbulence generation. When applied to half the vertical extent of the boundary layer, momentum perturbations produce an adequate amount of turbulence. However, when applied above the CBL, additional structures are generated at the top of the CBL, near the inversion layer. The magnitudes of the TKE budgets produced by SCPM-M when applied at varying heights and with different perturbation amplitudes are always higher near the surface and inversion layer than those produced by No-SCPM, as are their contributions to the TKE. This study provides a better understanding of how SCPM-M reduces computational costs and how different budget terms contribute to TKE in a boundary-coupled LES simulation.

17 WIND ENERGY↗
DOE OSTI2023

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↗
DOE OSTI2024

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↗
NASA NTRS2014

Flow Field and Acoustic Predictions for Three-Stream Jets

Computational fluid dynamics was used to analyze a three-stream nozzle parametric design space. The study varied bypass-to-core area ratio, tertiary-to-core area ratio and jet operating conditions. The flowfield solutions from the Reynolds-Averaged Navier-Stokes (RANS) code Overflow 2.2e were used to pre-screen experimental models for a future test in the Aero-Acoustic Propulsion Laboratory (AAPL) at the NASA Glenn Research Center (GRC). Flowfield solutions were considered in conjunction with the jet-noise-prediction code JeNo to screen the design concepts. A two-stream versus three-stream computation based on equal mass flow rates showed a reduction in peak turbulent kinetic energy (TKE) for the three-stream jet relative to that for the two-stream jet which resulted in reduced acoustic emission. Additional three-stream solutions were analyzed for salient flowfield features expected to impact farfield noise. As tertiary power settings were increased there was a corresponding near nozzle increase in shear rate that resulted in an increase in high frequency noise and a reduction in peak TKE. As tertiary-to-core area ratio was increased the tertiary potential core elongated and the peak TKE was reduced. The most noticeable change occurred as secondary-to-core area ratio was increased thickening the secondary potential core, elongating the primary potential core and reducing peak TKE. As forward flight Mach number was increased the jet plume region decreased and reduced peak TKE.

RANS CFD↗
DOE OSTI2023

New insights on wind turbine wakes from large‐eddy simulation: Wake contraction, dual nature, and temperature effects

Abstract Large‐eddy simulation (LES) has been adopted to study wind turbine wakes because it can capture fine‐scale details of turbulent wind flows and interactions with wind turbines. Here, we use the LES version of the Weather Research and Forecasting (WRF) model with an actuator disk model to gain insights on several wake effects that have been traditionally difficult to measure. The first finding is that the wake has a “dual nature,” meaning that the wind speed deficit behaves differently from the added turbulent kinetic energy (TKE) and the two are not co‐located in space. For example, the wind speed deficit peaks at hub height and reaches the ground within 8D (D is the rotor diameter), but added TKE peaks near the rotor tip and generally remains aloft. Second, temperature changes near the ground are driven by the added TKE in the rotor area and by atmospheric stability. The combination of these two factors determines the sign and intensity of the vertical heat flux divergence below the rotor, with convergence and warming associated with stable conditions and weak divergence and modest cooling with unstable conditions. Third, wakes do not expand indefinitely, as suggested by similarity theory applied to the wind speed deficit, but eventually stop expanding and actually contract, at different rates depending on atmospheric stability. The implication of these findings is that, in order to study wakes, it is not sufficient to focus on wind speed deficit alone, because TKE is also important and yet behaves differently from the wind speed deficit.

17 WIND ENERGY↗
DOE OSTI2022

Analysis of scale-dependent kinetic and potential energy in sheared, stably stratified turbulence

Budgets of turbulent kinetic energy (TKE) and turbulent potential energy (TPE) at different scales $\ell$ in sheared, stably stratified turbulence are analysed using a filtering approach. Competing effects in the flow are considered, along with the physical mechanisms governing the energy fluxes between scales, and the budgets are used to analyse data from direct numerical simulation at buoyancy Reynolds number $Re_b=O(100)$ . The mean TKE exceeds the TPE by an order of magnitude at the large scales, with the difference reducing as $\ell$ is decreased. At larger scales, buoyancy is never observed to be positive, with buoyancy always converting TKE to TPE. As $\ell$ is decreased, the probability of locally convecting regions increases, though it remains small at scales down to the Ozmidov scale. The TKE and TPE fluxes between scales are both downscale on average, and their instantaneous values are correlated positively, but not strongly so, and this occurs due to the different physical mechanisms that govern these fluxes. Moreover, the contributions to these fluxes arising from the sub-grid fields are shown to be significant, in addition to the filtered scale contributions associated with the processes of strain self-amplification, vortex stretching and density gradient amplification. Probability density functions (PDFs) of the $Q,R$ invariants of the filtered velocity gradient are considered and show that as $\ell$ increases, the sheared-drop shape of the PDF becomes less pronounced and the PDF becomes more symmetric about $R=0$ .

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

A mesoscopic device for a realization of the topological Kondo effect

The search for anyons is a field of immense interest owing to its potential application in the field of quantum information. Quantum critical Kondo impurities constitute one possible platform for their realization and topological Kondo effect (TKE) by virtue of remaining critical in the presence of perturbations, seems to be especially promising in this regard. In this paper we discuss practical steps for a realization of TKE with a relatively high Kondo temperature $\mathbf{T}$ k . Its central feature is the so-called Majorana-Cooper box (MCB) and we argue that a particular type of iron-based topological superconductor is especially suitable for realization of TKE. Once MCB is available one needs to connect it to external metallic leads to produce TKE. A relatively high value of the Kondo temperature $\mathbf{T}$ k is then aided by a large superconducting gap of the iron-based superconductor. We give estimates for $\mathbf{T}$ k , for the cases of both isotropic and anisotropic exchange couplings of MCB with the leads.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Evaluation of the Fitch Wind-Farm Wake Parameterization with Large-Eddy Simulations of Wakes Using the Weather Research and Forecasting Model

Abstract Wind-farm parameterizations in weather models can be used to predict both the power output and farm effects on the flow; however, their correctness has not been thoroughly assessed. We evaluate the wind-farm parameterization of the Weather Research and Forecasting Model with large-eddy simulations (LES) of the wake performed with the same model. We study the impact on the velocity and turbulence kinetic energy (TKE) of inflow velocity, roughness, resolution, number of turbines (one or two), and inversion height and strength. We compare the mesoscale with the LES by spatially averaging the LES within areas correspondent to the mesoscale horizontal spacing: one covering the turbine area and two downwind. We find an excellent agreement of the velocity within the turbine area between the two types of simulations. However, within the same area, we find the largest TKE discrepancies because in mesoscale simulations, the turbine-added TKE has to be highest at the turbine position to be advected downwind. Within the downwind areas, differences between velocities increase as the wake recovers faster in the LES, whereas for the TKE both types of simulations show similar levels. From the various configurations, the impact of inversion height and strength is small for these heights and inversion levels. The highest impact for the one-turbine simulations appears under the low-speed case due to the higher thrust, whereas the impact of resolution is low for the large-eddy simulations but high for the mesoscale simulations. Our findings demonstrate that higher-fidelity simulations are needed to validate wind-farm parameterizations.

17 WIND ENERGY↗
NASA NTRS1984

Problems with the process partitioning theory of stratocumulus entrainment

Three different approaches to partitioning were proposed. Ball (1960), Lilly (1968), and Deardorff et al. (1969, 1974) considered the sign of the net buoyancy flux at each level. If the net flux is positive, it is counted as TKE producing; otherwise, it is counted as TKE consuming. This approach can be called Eulerian partitioning. The second approach can be called process partitioning. It is assumed that the various processes acting in concert each produce and consume the same energy as if they acted independently (Manins and Turner, 1978). The total rates of TKE production and consumption are obtained by summing the effects of all the forcing processes. The third approach is Lagrangian partitioning. Each air parcel is considered as either producing or consuming TKE, according to the sign of the product of its density and vertical velocity anomalies. Stage and Businger (1981a,b) have applied process partitioning to the cloud topped mixed layer. One of the most important processes influencing entrainment into such a layer is cloud top radiative cooling. The production and consumption due to entrainment and radiative cooling are thus closely related. Model results are sensitive to the choice of formulation.

Randall, D. A.↗