Temperature Variance Budgets Research Articles

Observed Influences of Subpolar Front in the Japan/East Sea on Winter and Spring North Pacific Storm Track Activity

AbstractThis study investigated the response of the North Pacific storm track (NPST) activity to the meridional shift of the Japan/East Sea subpolar front during the cold season using a statistical method called generalized equilibrium feedback analysis. Results showed that the NPST response exhibits a basin‐wide anomaly in winter but a north‐south dipole in spring. Synoptic eddy temperature variance budget was employed to explore possible mechanisms from the perspective of eddy available potential energy (EAPE) generation. In winter, the baroclinic conversion directly induced by baroclinicity changes drives EAPE generation, and then, the positive eddy feedback reinforces this EAPE generation, giving rise to an intensified NPST. In spring, poleward‐shifted baroclinicity drives a displaced EAPE generation, leading to the poleward displacement of NPST. The shifted baroclinicity is caused by a basin‐scale warm air temperature anomaly, which is coherent with the anticyclone anomaly induced by the divergence of synoptic eddy heat and vorticity fluxes.

Assessing Modeled Mesoscale Stirring Using Microscale Observations

Abstract We assess the representation of mesoscale stirring in a suite of models against an estimate derived from microstructure data collected during the North Atlantic Tracer Release Experiment (NATRE). We draw heavily from the approximate temperature variance budget framework of Ferrari and Polzin. This framework assumes two sources of temperature variance away from boundaries: first, the vertical stirring of the large-scale mean vertical gradient by small-scale turbulence; and second, the lateral stirring of large-scale mean along-isopycnal gradients by mesoscale eddies. Temperature variance so produced is transformed and on average transferred down scales for ultimate dissipation at the microscale at a rate χ estimated using microstructure observations. Ocean models represent these pathways by a vertical mixing parameterization, and an along-isopycnal lateral mixing parameterization (if needed). We assess the rate of variance production by the latter as a residual from the NATRE dataset and compare against the parameterized representations in a suite of model simulations. We find that variance production due to lateral stirring in a Parallel Ocean Program version 2 (POP2) 1/10° simulation agrees well, to within the estimated error bars, with that inferred from the NATRE estimate. A POP2 1° simulation and the Estimating the Circulation and Climate of the Ocean Version 4 release 4 (ECCOV4r4) simulation appear to dissipate an order of magnitude too much variance by applying a lateral diffusivity, when compared to the NATRE estimate, particularly below 1250 m. The ECCOV4r4-adjusted lateral diffusivities are elevated where the microstructure suggests elevated χ sourced from mesoscale stirring. Such elevated values are absent in other diffusivity estimates suggesting the possibility of compensating errors and caution in interpreting ECCOV4r4’s adjusted lateral diffusivities. Significance Statement We look at whether microstructure turbulence observations can provide a useful metric for judging the fidelity of representation of mesoscale stirring in a suite of models. We focus on the region of the North Atlantic Tracer Release Experiment (NATRE), the site of a major ocean turbulence observation campaign, and use an approximate variance budget framework for the region with observational estimates from Ferrari and Polzin (2005). The approach provides a novel framework to evaluate the approximate representation of mesoscale stirring in a variety of models.

Numerical study of thermally developing turbulent internal flows

The effect of fluid Prandtl number on the thermal characteristics of the flow at the thermal-entry region of a hydrodynamically fully developed turbulent channel flow at a friction Reynolds number of Reτ=180 is investigated using direct numerical simulation. Four test cases with molecular Prandtl numbers of Pr = 0.71, 1, 3, 7 are considered. The numerical results confirm that in contrast to laminar flows, where the thermal entry length increases with the increase of the Prandtl number, for turbulent flows the increase of the Prandtl number accelerates the thermal development of the flow toward its asymptotic fully developed state. The variations of the Nusselt number, and the mean and rms temperature profiles are reported in the streamwise direction. It is shown that at highest Prandtl number considered in this study (Pr =7 ), while the mean temperature profile in the logarithmic region is still developing, the temperature profile in the conductive sublayer and the Nusselt number approach their fully developed values, confirming the dependence of the Nusselt number of turbulent flows to the development of the conductive sublayer. The development of the rms temperature profiles in the streamwise direction is also shown to be a good indicator for the flow reaching its thermally fully developed condition. The temperature-velocity correlations, temperature variance budgets, and contours of temperature are also reported at different streamwise locations for different Prandtl numbers.

Drivers of Atmospheric and Oceanic Surface Temperature Variance: A Frequency Domain Approach

AbstractOcean–atmosphere coupling modifies the variability of Earth’s climate over a wide range of time scales. However, attribution of the processes that generate this variability remains an outstanding problem. In this article, air–sea coupling is investigated in an eddy-resolving, medium-complexity, idealized ocean–atmosphere model. The model is run in three configurations: fully coupled, partially coupled (where the effect of the ocean geostrophic velocity on the sea surface temperature field is minimal), and atmosphere-only. A surface boundary layer temperature variance budget analysis computed in the frequency domain is shown to be a powerful tool for studying air–sea interactions, as it differentiates the relative contributions to the variability in the temperature field from each process across a range of time scales (from daily to multidecadal). This method compares terms in the ocean and atmosphere across the different model configurations to infer the underlying mechanisms driving temperature variability. Horizontal advection plays a dominant role in driving temperature variance in both the ocean and the atmosphere, particularly at time scales shorter than annual. At longer time scales, the temperature variance is dominated by strong coupling between atmosphere and ocean. Furthermore, the Ekman transport contribution to the ocean’s horizontal advection is found to underlie the low-frequency behavior in the atmosphere. The ocean geostrophic eddy field is an important driver of ocean variability across all frequencies and is reflected in the atmospheric variability in the western boundary current separation region at longer time scales.

Direct numerical simulation of turbulent particle-laden flows: effects of Prandtl and Stokes numbers

The effect of molecular Prandtl number on the turbulent heat transfer of a non-isothermal turbulent channel flow laden with particles with four different Stokes number is investigated using direct numerical simulation coupled with a Lagrangian particle tracking. The flow configuration is a downward vertical channel with side walls kept at constant temperature. A total of 16 test cases with four different Prandtl numbers of Pr = 0.71, 1, 3, 7, and four particle sizes with the Stokes numbers of St= 40, 60, 100, 190 are considered. The mass loading, particle-to-fluid density ratio, and specific heat ratio are constant for all cases and they are equal to 0.57, 7298, and 0.39, respectively. It is shown that by the addition of particles, the heat transfer rate decreases and the thickness of the conductive sublayer thickness increases for all cases. The percentage of heat transfer modulation resulting from the addition of particles is almost independent of the Prandtl number but it slightly depends on the size of the particles, with the maximum being for smaller particles. The mean and rms values of temperature, temperature-velocity correlations, mean energy equation, and temperature variance budgets are presented. Contours of temperature in planes parallel to the wall and normal to the streamwise direction are also reported. At higher Prandtl numbers, the temperature contours clearly visualize the mushroom shaped structures formed as a result of the ejection of low-speed fluid from the wall.

Resolved and subgrid dynamics of Rayleigh–Bénard convection

In this work we present and demonstrate the reliability of a theoretical framework for the study of thermally driven turbulence. It consists of scale-by-scale budget equations for the second-order velocity and temperature structure functions and their limiting cases, represented by the turbulent kinetic energy and temperature variance budgets. This framework represents an extension of the classical Kolmogorov and Yaglom equations to inhomogeneous and anisotropic flows, and allows for a novel assessment of the turbulent processes occurring at different scales and locations in the fluid domain. Two relevant characteristic scales, $\ell _{c}^{u}$ for the velocity field and $\ell _{c}^{\unicode[STIX]{x1D703}}$ for the temperature field, are identified. These variables separate the space of scales into a quasi-homogeneous range, characterized by turbulent kinetic energy and temperature variance cascades towards dissipation, and an inhomogeneity-dominated range, where the production and the transport in physical space are important. This theoretical framework is then extended to the context of large-eddy simulation to quantify the effect of a low-pass filtering operation on both resolved and subgrid dynamics of turbulent Rayleigh–Bénard convection. It consists of single-point and scale-by-scale budget equations for the filtered velocity and temperature fields. To evaluate the effect of the filter length $\ell _{F}$ on the resolved and subgrid dynamics, the velocity and temperature fields obtained from a direct numerical simulation are split into filtered and residual components using a spectral cutoff filter. It is found that when $\ell _{F}$ is smaller than the minimum values of the cross-over scales given by $\ell _{c,min}^{\unicode[STIX]{x1D703}\ast }=\ell _{c,min}^{\unicode[STIX]{x1D703}}Nu/H=0.8$, the resolved processes correspond to the exact ones, except for a depletion of viscous and thermal dissipations, and the only role of the subgrid scales is to drain turbulent kinetic energy and temperature variance to dissipate them. On the other hand, the resolved dynamics is much poorer in the near-wall region and the effects of the subgrid scales are more complex for filter lengths of the order of $\ell _{F}\approx 3\ell _{c,min}^{\unicode[STIX]{x1D703}}$ or larger. This study suggests that classic eddy-viscosity/diffusivity models employed in large-eddy simulation may suffer from some limitations for large filter lengths, and that alternative closures should be considered to account for the inhomogeneous processes at subgrid level. Moreover, the theoretical framework based on the filtered Kolmogorov and Yaglom equations may represent a valuable tool for future assessments of the subgrid-scale models.

Quantifying the Role of Oceanic Feedbacks on ENSO Asymmetry

AbstractThe role of oceanic feedbacks in determining the asymmetry of El Niño–Southern Oscillation (ENSO) magnitude, spatial structure, and duration is quantified on the basis of a novel temperature variance budget. Results confirm previous studies that in the eastern Pacific, El Niño warm temperature anomalies are larger in magnitude than La Niña cold temperature anomalies mainly due to stronger positive oceanic feedbacks for El Niño. We find that La Niña cold anomalies are typically stronger than El Niño warm anomalies in the central Pacific with a faster growth rate for cold anomalies, due to a stronger positive thermocline feedback and weaker nonlinear damping. The thermocline feedback related to recharge oscillator dynamics plays a dominate role and leads to asymmetry in the duration of El Niño and La Niña events. In particular, the thermocline feedback becomes significantly negative during the late decaying phase of El Niño and speeds up its demise.

A comparison of near-surface potential temperature variance budgets for unstable atmospheric flows with contrasting vegetation cover flat surfaces and a gentle slope

Over the past decades, researchers have made significant progress toward a fundamental understanding of the budgets of turbulence variables over flat and homogeneous terrain, and only more recently over complex terrain. However, temperature variance budgets, which are parameterized in most meteorological models, are still poorly understood even under relatively idealized conditions. The objective of this study is to analyze the near-surface potential temperature variance budget over contrasting surfaces. To do this, we rely on profiles of near-surface turbulence variables collected as part of the Mountain Terrain Atmospheric Modeling and Observations program. Daytime observations collected in May 2013 in western Utah at three field sites subjected to similar large-scale forcing are analyzed: a desert playa (i.e., dry lakebed), characterized by a flat surface devoid of vegetation; a vegetated site, characterized by a flat valley floor covered with greasewood vegetation, and a slope site with a local slope angle of 2°–4° and covered by 1-m tall sparse desert steppe vegetation. The observations indicate a persistent 5-m surface layer across all three sites, where the flow is equilibrium due to the balance between dominant production and dissipation terms in the potential temperature variance equation. The temperature variances in this layer are well predicted by Monin–Obukhov similarity theory. During convective periods at the Playa and Slope sites, $$\approx 60\%$$ of the data show a ratio of turbulent transport to production greater than 0.1. Within the surface layer, turbulent transport of potential temperature variance acts as a sink term at all three sites. Neither the ratio of turbulent transport to production nor the ratio of production to dissipation show a dependence on atmospheric stability during the unstable periods studied. A short-period comparison of dissipation rates calculated using dissipation-scale resolving cold-wire anemometry and several common indirect methods using sonic anemometry is presented for data acquired at Playa site. The results indicate that the dissipation rates from all methods follow similar trends, however the values can differ by a factor of 2–3.

Direct Numerical Simulation of an air-filled differentially heated square cavity with Rayleigh numbers up to [formula omitted

A set of Direct Numerical Simulations in a heated square cavity invoking the Boussinesq approximation was carried out at Rayleigh numbers ranging between 108 and 1011 and Prandtl number of 0.71. The three dimensional configurations studied represent an infinitely deep cavity, thus corresponding to a statistically two-dimensional flow with an imposed temperature varying linearly on the horizontal walls. In such configuration, the Rayleigh number, and therefore turbulence intensity, is the highest ever reached. The database presented herein includes first and second order statistical moments as well as full Reynolds stresses, turbulent heat fluxes and temperature variance budgets. The latter are extremely rare for buoyancy driven flow configurations and are therefore believed to be valuable to the turbulence modelling community. The analysis of the data collected thus focuses on aspects of relevance to the Reynolds averaged modelling of such flows. The effect of increasing the Rayleigh number on the flow statistics, Nusselt number predictions and thermal stratification is investigated. The most important aspect influencing the behaviour of the budgets was found to be the displacement of the position of the maximum of temperature variance towards the inner zone of the boundary layer. Such difference in behaviour between the thermal and velocity boundary layers introduces regions of negative production in the budgets that tend to increase with the Rayleigh number. The production of turbulence by buoyancy is also found to be of the same order of magnitude as other budget terms at all Rayleigh numbers.

Ocean Processes Affecting the Twenty-First-Century Shift in ENSO SST Variability

Abstract Sea surface temperature (SST) variability associated with El Niño–Southern Oscillation (ENSO) slightly increased in the central Pacific Ocean but weakened significantly in the eastern Pacific at the beginning of twenty-first century relative to 1980–99. This decadal shift led to the greater prominence central Pacific (CP) El Niño events during the 2000s relative to the previous two decades, which were dominated by eastern Pacific (EP) events. To expand upon previous studies that have examined this shift in ENSO variability, temperature and temperature variance budgets are examined in the mixed layer of the Niño-3 (5°S–5°N, 150°–90°W) and Niño-4 (5°S–5°N, 160°E–150°W) regions from seven ocean model products spanning the period 1980–2010. This multimodel-product-based approach provides a robust assessment of dominant mechanisms that account for decadal changes in two key index regions. A temperature variance budget perspective on the role of thermocline feedbacks in the ENSO cycle based on recharge oscillator theory is also presented. As found in previous studies, thermocline and zonal advective feedbacks are the most important positive feedbacks for generating ENSO SST variance, and thermodynamic damping is the largest negative feedback for damping ENSO variance. Consistent with the shift toward more CP El Niños after 2000, thermocline feedbacks experienced a substantial reduction from 1980 to 1999 and into the 2000s, while zonal advective feedbacks were less affected. Negative feedbacks likewise weakened after 2000, particularly thermal damping in the Niño-3 region and the nonlinear sink of variance in both regions.

Physical and scale-by-scale analysis of Rayleigh–Bénard convection

A novel approach for the study of turbulent Rayleigh–Bénard convection (RBC) in the compound physical/scale space domain is presented. All data come from direct numerical simulations of turbulent RBC in a laterally unbounded domain confined between two horizontal walls, for Prandtl number $0.7$ and Rayleigh numbers $1.7\times 10^{5}$, $1.0\times 10^{6}$ and $1.0\times 10^{7}$. A preliminary analysis of the flow topology focuses on the events of impingement and emission of thermal plumes, which are identified here in terms of the horizontal divergence of the instantaneous velocity field. The flow dynamics is then described in more detail in terms of turbulent kinetic energy and temperature variance budgets. Three distinct regions where turbulent fluctuations are produced, transferred and finally dissipated are identified: a bulk region, a transitional layer and a boundary layer. A description of turbulent RBC dynamics in both physical and scale space is finally presented, completing the classic single-point balances. Detailed scale-by-scale budgets for the second-order velocity and temperature structure functions are shown for different geometrical locations. An unexpected behaviour is observed in both the viscous and thermal transitional layers consisting of a diffusive reverse transfer from small to large scales of velocity and temperature fluctuations. Through the analysis of the instantaneous field in terms of the horizontal divergence, it is found that the enlargement of thermal plumes following the impingement represents the triggering mechanism which entails the reverse transfer. The coupling of this reverse transfer with the spatial transport towards the wall is an interesting mechanism found at the basis of some peculiar aspects of the flow. As an example, it is found that, during the impingement, the presence of the wall is felt by the plumes through the pressure field mainly at large scales. These and other peculiar aspects shed light on the role of thermal plumes in the self-sustained cycle of turbulence in RBC, and may have strong repercussions on both theoretical and modelling approaches to convective turbulence.

Budgets of turbulent kinetic energy, Reynolds stresses, variance of temperature fluctuations and turbulent heat fluxes in a round jet

The self-preserving region of a free round turbulent air jet at high Reynolds number is investigated experimentally (at$x/D=30$,$\mathit{Re}_{D}=1.4\times 10^{5}$and$\mathit{Re}_{{\it\lambda}}=548$). Air is slightly heated ($20\,^{\circ }\text{C}$above ambient) in order to use temperature as a passive scalar. Laser doppler velocimetry and simultaneous laser doppler velocimetry–cold-wire thermometry measurements are used to evaluate turbulent kinetic energy and temperature variance budgets in identical flow conditions. Special attention is paid to the control of initial conditions and the statistical convergence of the data acquired. Measurements of the variance, third-order moments and mixed correlations of velocity and temperature are provided (including$\overline{vw^{2}}$,$\overline{u{\it\theta}^{2}}$,$\overline{v{\it\theta}^{2}}$,$\overline{u^{2}{\it\theta}}$,$\overline{v^{2}{\it\theta}}$and$\overline{uv{\it\theta}}$). The agreement of the present results with the analytical expressions given by the continuity, mean momentum and mean enthalpy equations supports their consistency. The turbulent kinetic energy transport budget is established using Lumley’s model for the pressure diffusion term. Dissipation is inferred as the closing balance. The transport budgets of the$\overline{u_{i}u_{j}}$components are also determined, which enables analysis of the turbulent kinetic energy redistribution mechanisms. The impact of the surrogacy$\overline{vw^{2}}=\overline{v^{3}}$is then analysed in detail. In addition, the present data offer an opportunity to evaluate every single term of the passive scalar transport budget, except for the dissipation, which is also inferred as the closing balance. Hence, estimates of the dissipation rates of turbulent kinetic energy and temperature fluctuations (${\it\epsilon}_{k}$and${\it\epsilon}_{{\it\theta}}$) are proposed here for use in future studies of the passive scalar in a turbulent round jet. Finally, the budgets of turbulent heat fluxes ($\overline{u_{i}{\it\theta}}$) are presented.

Direct numerical simulations of turbulent Ekman layers with increasing static stability: modifications to the bulk structure and second-order statistics

AbstractDirect numerical simulations of stably stratified Ekman layers are conducted to study the effect of increasing static stability on turbulence dynamics and modelling in wall-bounded flows at three moderate Reynolds numbers. The flow field is analysed by examining the mean profiles of wind speed, potential temperature and momentum flux, as well as streamwise velocity and temperature spectra. The maximum stabilizing buoyancy flux that a flow can sustain while remaining fully turbulent is found to depend on the Reynolds number. The flows with the highest Reynolds number display a relatively well-developed inertial range and logarithmic layer, and are found to bear similarities to much higher-Reynolds-number flows like the ones encountered in the atmospheric boundary layer. In particular, the near-wall mean profiles follow the Monin–Obukhov similarity theory. However, several flow features, such as the critical Richardson number and the stress–strain alignment, are found to maintain significant dependence on the Reynolds number. The budgets of turbulence kinetic energy (TKE), vertical velocity variance, momentum and buoyancy fluxes, and temperature variance are analysed. The results indicate that the effect of stability on turbulence is first directly manifested in the vertical velocity variance budget, and results in damping of vertical motions. This then leads to a reduction in the downward transport of horizontal momentum components towards the surface, and consequently to a decrease in the shear production term in the TKE budget: changes in the vertical profile of TKE shear production with increasing Richardson number are significant and have a larger impact on TKE than direct buoyancy destruction. The reduction in vertical velocity variance also results in significant drops in the production terms in the momentum flux, buoyancy flux and temperature variance budgets. Various assumptions and parameters related to low-order turbulence closures are investigated. The results suggest that the vertical velocity variance is a more appropriate parameter than the full TKE on which to base eddy-diffusivity and viscosity models.

Turbulent-Heat-Flux and Temperature-Variance Budgets in a Single-Rib Mounting Channel

Turbulent-Heat-Flux and Temperature-Variance Budgets in a Single-Rib Mounting Channel

Genesis of Indian Ocean Mixed Layer Temperature Anomalies: A Heat Budget Analysis

Abstract The genesis of mixed layer temperature anomalies across the Indian Ocean are analyzed in terms of the underlying heat budget components. Observational data, for which a seasonal budget can be computed, and a climate model output, which provides improved spatial and temporal coverage for longer time scales, are examined. The seasonal climatology of the model heat budget is broadly consistent with the observational reconstruction, thus providing certain confidence in extending the model analysis to interannual time scales. To identify the dominant heat budget components, covariance analysis is applied based on the heat budget equation. In addition, the role of the heat budget terms on the generation and decay of temperature anomalies is revealed via a novel temperature variance budget approach. The seasonal evolution of the mixed layer temperature is found to be largely controlled by air–sea heat fluxes, except in the tropics where advection and entrainment are important. A distinct shift in the importance and role of certain heat budget components is shown to be apparent in moving from seasonal to interannual time scales. On these longer time scales, advection gains importance in generating and sustaining anomalies over extensive regions, including the trade wind and midlatitude wind regimes. On the other hand, air–sea heat fluxes tend to drive the evolution of thermal anomalies over subtropical regions including off northwestern Australia. In the tropics, however, they limit the growth of anomalies. Entrainment plays a role in the generation and maintenance of interannual anomalies over localized regions, particularly off Sumatra and over the Seychelles–Chagos Thermocline Ridge. It is further shown that the spatial distribution of the role and importance of these terms is related to oceanographic features of the Indian Ocean. Mixed layer depth effects and the influence of model biases are discussed.

Direct numerical simulation of turbulent concentric annular pipe flow: Part 2: Heat transfer

A direct numerical simulation is performed for turbulent heat transfer in a concentric annulus at Re D h =8900 and Pr=0.71 for two radius ratios ( R 1/ R 2=0.1 and 0.5) and wall heat flux ratio q ∗=1.0 . Main emphasis is placed on the transverse curvature effect on near-wall turbulent thermal structures. Near-wall turbulent thermal structures close to the inner and outer walls are scrutinized by computing the lower-order statistics. The fluctuating temperature variance and turbulent heat flux budgets are illustrated to confirm the results of the lower-order statistics. Probability density functions of the splat/anti-splat process are investigated to analyze the transverse curvature effect on the strong relationship between sweep and splat events. The present numerical results show that the turbulent thermal structures near the outer wall are more activated than those near the inner wall, which may be attributed to the different vortex regeneration processes between the inner and outer walls.

Investigation of the flow field of a highly heated jet of air

Measurements of mean and fluctuating velocity and temperature and their self- and cross-products to the third-order are presented for a heated axisymmetric air jet. Froude numbers in the range of 3500–13,190, Reynolds numbers in the range of 3470–8500 and non-dimensional streamwise distances, X ∗ , from 0.27 to 1.98 are covered by the data. It was found that turbulence intensity decreases for the heated jet in the region between the inertia dominated and the buoyancy dominated regions which is contrary to findings with helium jets mixing with ambient air to produce density fluctuations. The effects of heating on the turbulent kinetic energy budget and the temperature variance budget show small differences for the inertia dominated region and the intermediate region which help to explain the transition process to the far field plume region. Constants are evaluated for the isotropic eddy diffusivity and generalised gradient hypothesis models as well as the scalar variance model. No significant effect of heating on the dissipation time-scale ratio was found. A novel wire array with an inclined cold wire was used. Measurements obtained with this probe are found to lead to asymmetries in some of the higher-order products. Further investigation suggested that the asymmetries are attributable to an as yet unreported interference effect produced by the leading prong of the inclined temperature wire. The effect may also have implications for inclined velocity wires which contain a temperature component when used in heated flows.

Dissipation methods, Taylor's hypothesis, and stability correction functions in the atmospheric surface layer

The traditional dissipation method and the new approaches suggested by Albertson et al. [1996] and Hsieh et al. [1996] to estimate momentum and heat fluxes were compared using velocity and temperature measurements in the atmospheric surface layer. These measurements were carried out above two different sites (grass and bare soil) over a wide range of atmospheric stability and turbulent intensity conditions. Taylor's hypothesis, flux divergence terms, and stability correction functions which play important roles in the dissipation methods were also evaluated. In highly turbulent intensity flows, deviations from Taylor's hypothesis may cause some errors in estimating dissipation rates and subsequent fluxes. Wyngaard and Clifford [1977] proposed a model to interpret the influence of departures from Taylor's hypothesis. In this study we evaluate this influence in the inertial subrange and discuss the usefulness of Wyngaard and Clifford's model in practice. We also found the flux divergence term in the temperature variance budget equation to be significant, relative to the production term in unstable conditions. Our measurements showed that discarding the flux divergence term resulted in systematic underpredictions of the sensible heat flux by the dissipation methods. The proposed dissipation method by Hsieh et al. [1996] for estimating sensible heat flux was extended to momentum flux, and its implications for stability correction functions were discussed. Good agreement between eddy correlation measured and predicted sensible heat fluxes by the methods of Albertson et al. [1997] and Hsieh et al. [1996] was noted.

Estimation of Momentum and Heat Fluxes Using Dissipation and Flux‐Variance Methods in the Unstable Surface Layer

Dissipation and flux‐variance methods, derived from the turbulent kinetic energy and temperature variance budget equations in conjunction with Monin‐Obukov similarity theory, were used to estimate surface fluxes of momentum and sensible heat. To examine the performance of these two methods, direct eddy correlation measurements were carried out above a nonuniform grass‐covered forest clearing in Durham, North Carolina. The dissipation method sensible heat flux predictions were in good agreement with eddy correlation measurements. Also, the flux‐variance method reproduced the measured sensible heat flux well following an adjustment to the similarity constant. However, the momentum flux (or friction velocity) estimated by the dissipation and flux‐variance methods were both inferior to those for sensible heat flux. The data from this experiment indicated that the above two methods are sensitive to the dimensionless wind shear (ϕm) and temperature standard deviation (ϕθ) functions. On the basis of dimensional analysis and the temperature variance budget equation a new dissipation approach for estimating sensible heat flux was derived. The similarity constant for this new approach was shown to be around 1.6 for uniform surfaces and from the data of this experiment.

Convective scaling of the average dissipation rate of temperature variance in the atmospheric surface layer

The flux of sensible heat from the land surface is related to the average rate of dissipation of temperature fluctuations in the atmospheric surface layer through the temperature variance budget equation. In many cases it is desirable to estimate the heat flux from measurement or inference of the dissipation rate. Here we study how the dissipation rate scales with atmospheric stability, using three inertial range methods to calculate the dissipation rate: power spectra, second order structure functions, and third order structure functions. Experimental data are analyzed from a pair of field experiments, during which turbulent fluctuations of velocity and temperature were measured over a broad range of neutral and unstable atmospheric flows. It is shown that the temperature dissipation rate scales with a single convective power law continuously from near-neutral to strongly unstable stratification. The dissipation scaling is found to nearly match production in the near-neutral region, but to be consistently lower than production in the more convective regimes. The convective scaling is shown to offer a simplified means of computing sensible heat flux from the dissipation rate of temperature variance.