Eddy Diffusivity Of Heat Research Articles

Toward a Unified Understanding of Estimating Evapotranspiration: The Linkage Between Three Effective Parsimonious Models

AbstractThe maximum information entropy production model (MaxEnt), the relative humidity at equilibrium approach (ETRHEQ), and the Surface Flux Equilibrium model (SFE) are three recently developed models to estimate evapotranspiration. Although the connection between ETRHEQ and SFE is evident, no attempts have been made to investigate the congruence, distinctions, or potential complementarity between the two models and MaxEnt. Our mathematical analysis demonstrates that minimizing the vertical variance of RH in ETRHEQ is equivalent to minimizing the dissipation function of energy fluxes in MaxEnt, under the assumption of the same eddy diffusivity of heat and water vapor and with a specific expression for the ratio between the thermal inertia terms for H and LE. The connection between ETRHEQ, SFE, and MaxEnt is independent of Monin‐Obukhov similarity theory (MOST)’s extremum solution, and MOST's extreme solution can be viewed as equivalent to introducing a constant correction factor to account for atmospheric stability. While ETRHEQ and MaxEnt can be united within a single hydrometeorological framework, they diverge in their approaches to modeling evapotranspiration, particularly in how they address the roles of vegetation and land surface heterogeneity. More importantly, the unified framework suggests that turbulence fluxes within the atmospheric boundary layer adhere to the principles of maximum information entropy production. The way in which dissipation, along with its associated entropy production, is established using information entropy theory deviates from traditional thermodynamic entropy formulations. Exploring the connection between thermodynamic and information entropy and developing proper formulations of dissipation for energy fluxes presents an appealing avenue for prospective research.

Assessment of the Sensitivity of the Mean Climate Simulation over West Africa to Planetary Boundary Layer Parameterization Using RegCM5 Regional Climate Model

This study evaluates the performance of two planetary boundary parameterizations in simulating the mean climate of West Africa using the Regional Climate Model version 5 (RegCM5). These planetary boundary parameterizations are the Holtslag scheme and the University of Washington scheme. Two sets of three one-year simulations were carried out at 25 km horizontal resolution with three different initial conditions. The first set of simulations used the Holtslag scheme (hereafter referred to as Hol), while the second used the University of Washington (UW) scheme (hereafter referred to as UW). The results displayed in this study are an average of the three simulations. During the JJAS rainy season, with respect to GPCP, both models overestimated total rainfall in the orographic regions. The UW experiment represented total rainfall fairly well compared to its counterpart, Hol. Both models reproduced convective rainfall well, with a relatively weak dry bias over the Guinean coast subregion. Globally, UW performed better than Hol in simulating precipitation. The pattern of near-surface temperature in both models was well reproduced with a higher bias with Hol than with UW. Indeed, the UW scheme led to a cooling effect owing to the reduction in eddy heat diffusivity in the lower troposphere contributing to reduce the bias. As a consequence, the height of the planetary boundary layer (PBL) was best simulated using the UW scheme but was underestimated compared to ERA5, while using the Hol scheme failed to capture the height of the PBL. This is coherent with the distribution of total cloud cover, which was better simulated with the UW scheme compared to the Hol scheme. This study shows that use of both planetary boundary parameterizations leads to a good simulation of most of the climatological characteristics of the West African region. Nevertheless, use of the UW scheme contributes to a better performance than use of the Hol scheme, and the differentiation between the two schemes is significant along the Guinea Coast and in orographic regions. In these topographically complex regions, UW appears to be more appropriate than Hol. This study emphasizes the importance of planetary boundary parameterizations for accurately simulating climate variables and for improving climate forecasts and projections in West Africa.

Numerical investigation on turbulent mixed convective heat transfer of CO2 in a horizontal miniature tube at supercritical pressure

Mixed convective heat transfer behaviors of turbulent supercritical CO2 (SCO2) flowing in a horizontal miniature tube (di = 2 mm) have been investigated using an in-house code. The computational model adopted was verified against experimentally determined data with a number of operating conditions. The numerical simulations were carried out for pressure of 8 MPa, inlet Reynolds number of 42,521, and wall heat fluxes ranging from 50 to 320 kW m−2. A significant influence of natural convection in horizontal forced turbulent SCO2 flow was discerned, despite the small diameter and high turbulence intensity. The mechanism of mixed convection heat transfer was studied by analyzing the cross-sectional distributions of thermal properties, eddy diffusivity of heat, and secondary flow vectors. The effect of wall heat flux on the non-uniformity in heat transfer was further investigated, covering q/G ratios ranging from 41.67 to 266.67 J kg−1. The regime of heat transfer was identified by comparing the numerical results with the reference Nusselt number calculated using the Dittus-Boelter correlation. A transition from enhanced to deteriorated heat transfer regime, as well as subsequently heat transfer recovery was found with increasing bulk fluid temperature. In addition, the applicability of three existing buoyancy parameters (Buc, BuJ, and BuP) was evaluated. The Petukhov buoyancy criteria agreed best with the simulation results. A new threshold of 6.0 for BuP was determined by performing a comparative study with cases without gravity, above which natural convection would have a considerable influence on forced turbulent heat transfer.

Eddy heat exchange at the boundary under white noise turbulence.

We prove the existence of an eddy heat diffusion coefficient coming from an idealized model of turbulent fluid. A difficulty lies in the presence of a boundary, with also turbulent mixing and the eddy diffusion coefficient going to zero at the boundary. Nevertheless, enhanced diffusion takes place. This article is part of the theme issue 'Scaling the turbulence edifice (part 2)'.

Influence of the North Atlantic Oscillation on the Heat Budget of the Mixed Layer in the North Atlantic

The heat budget components that are involved in the formation of the tripole structure of the upper mixed layer (UML) temperature anomalies in the North Atlantic under the influence of the North Atlantic Oscillation (NAO) are analyzed using ORA-S3 oceanic reanalysis data for the winter period in 1959–2011. It is shown that the negative UML temperature anomaly in the western part of the tropical zone during the NAO intensification is mainly due to the anomalies of horizontal heat advection and eddy heat diffusion (i.e., nonlocal factors), as well as due to anomalous heat fluxes on the ocean surface (although with a lower significance level). Antiphase changes in the UML temperature in the eastern part of the tropical zone and in the western part of the subtropical zone are accompanied by the anomalies of the heat budget components of the opposite sign. In the subpolar zone, the anomalies of nonlocal components of heat budget also make significant contribution to the UML temperature variation which is in-phase with the one in the tropics. In the high-latitude areas of deep convection, the anomalous heat fluxes at the UML base are also important, and in the eastern part of the subpolar gyre, the anomalies of the net heat fluxes on the ocean surface are crucial too. The signs of the anomalies of the UML heat budget components forming the UML temperature fields in the North Atlantic during the periods with high and low values of the NAO index are opposite.

Scalar transport in the near field between two coaxial square air jets

The scalar transport in the near field of two square coaxial free air jet flow has been experimentally investigated. In order to study the entrainment and mixing processes taking place between the two jets, heat was used as a scalar. A triple sensor probe was used consisting of an X-wire probe for the point measurement of two velocity components and a single cold wire probe, for the simultaneous recording of instantaneous temperature. From the velocity and temperature signals the momentum and heat flux components were calculated. Eddy diffusivities of heat and momentum were directly evaluated from the experimental data. These diffusivities for all streamwise positions reach a maximum in the interaction region between the two jets; the maximum values increase with the downstream distance in the near field. The quadrant splitting technique applied to turbulent fluxes of momentum and the scalar revealed that the positive contributions to these transport terms are much larger than the negative ones. The quadrant splitting data confirmed that the flow is dominated by large scale coherent structures, which are intermittent in character and permitted the association of the scalar transport with vortical structures occurring in the near field of the coaxial jet flow. A proposed simplified mechanistic flow picture, which shows the passage of a vortex series through the mixing layer in the near field of the jets, is in agreement with the dominant characteristics of the flow.

Numerical prediction of film cooling effectiveness over flat plate using variable turbulent prandtl number closures

Numerical simulations were performed to predict the film cooling effectiveness on the fiat plate with a three- dimensional discrete-hole film cooling arrangement. The effects of basic geometrical characteristics of the holes, i.e. diameter D, length L and pitch S/D were studied. Different turbulent heat transfer models based on constant and variable turbulent Prandtl number approaches were considered. The variability of the turbulent Prandtl number Prt in the energy equation was assumed using an algebraic relation proposed by Kays and Crawford, or employing the Abe, Kondoh and Nagano eddy heat diffusivity closure with two differential transport equations for the temperature variance kθ and its destruction rate eθ. The obtained numerical results were directly compared with the data that came from an experiment based on Transient Liquid Crystal methodology. All implemented models for turbulent heat transfer performed sufficiently well for the considered case. It was confirmed, however, that the two- equation closure can give a detailed look into film cooling problems without using any time-consuming and inherently unsteady models.

A Shear-Based Parameterization of Turbulent Mixing in the Stable Atmospheric Boundary Layer

AbstractIn this study, shear-based parameterizations of turbulent mixing in the stable atmospheric boundary layer (SABL) are proposed. A relevant length-scale estimate for the mixing length of the turbulent momentum field is constructed from the turbulent kinetic energy and the mean shear rate S as . Using observational data from two field campaigns—the Surface Heat Budget of the Arctic Ocean (SHEBA) experiment and the 1999 Cooperative Atmosphere–Surface Exchange Study (CASES-99)— is shown to have a strong correlation with . The relationship between and corresponds to the ratio of the magnitude of the tangential components of the turbulent momentum flux tensor to , known as stress intensity ratio, . The field data clearly show that is linked to stability. The stress intensity ratio also depends on the flow energetics that can be assessed using a shear-production Reynolds number, , where P is shear production of turbulent kinetic energy and is the kinematic viscosity. This analysis shows that high mixing rates can indeed persist at strong stability. On this basis, shear-based parameterizations are proposed for the eddy diffusivity for momentum, , and eddy diffusivity for heat, , showing remarkable agreement with the exact quantities. Furthermore, a broader assessment of the proposed parameterizations is given through an a priori evaluation of large-eddy simulation (LES) data from the first GEWEX Atmospheric Boundary Layer Study (GABLS). The shear-based parameterizations outperform many existing models in predicting turbulent mixing in the SABL. The results of this study provide a framework for improved representation of the SABL in operational models.

Numerical Analysis of Flow Structure Above Dimpled Surfaces with Different Depths in a Channel

Turbulent air flow characteristics in channels of three different dimple depth (δ/D = 0.1, 0.2, and 0.3) placed on the bottom wall are numerically predicted using FLUENT for Reynolds number based on the channel height, Re H = 20,000, and the ratio of channel height to dimple print diameter, H/D = 1.0. The turbulence model employed is a realizable k − ϵ model with no wall function. Steady-state analyses of fluid within and near different dimple depths demonstrate the existence of different vortex pairs. These vortex pairs are investigated at the central position of dimples as well as near the spanwise edge of individual dimples, and become stronger as dimple depth increases. In addition, steady-state results show that the streamwise vorticity distributions, which are associated with the flow recirculation zones positioned within the upstream halves of each dimple, are higher in magnitude and cover larger spatial extents as the dimple depth increases. Magnitudes of eddy diffusivity for momentum and eddy diffusivity for heat are also augmented by the vorticity concentrations within and downstream of individual dimples as the dimple depth increases. Such characteristics are due to the advection of reattaching and recirculating flow within the dimple cavities, as well as to the strong instantaneous secondary flows and mixing within the vortex pairs.

Two phenomenological constants explain similarity laws in stably stratified turbulence.

In stably stratified turbulent flows, the mixing efficiency associated with eddy diffusivity for heat, or equivalently the turbulent Prandtl number (Pr(t)), is fraught with complex dynamics originating from the scalewise interplay between shear generation of turbulence and its dissipation by density gradients. A large corpus of data and numerical simulations agree on a near-universal relation between Pr(t) and the Richardson number (R(i)), which encodes the relative importance of buoyancy dissipation to mechanical production of turbulent kinetic energy. The Pr(t)-R(i) relation is shown to be derivable solely from the cospectral budgets for momentum and heat fluxes if a Rotta-like return to isotropy closure for the pressure-strain effects and Kolmogorov's theory for turbulent cascade are invoked. The ratio of the Kolmogorov to the Kolmogorov-Obukhov-Corrsin phenomenological constants, and a constant associated with isotropization of the production whose value (= 3/5) has been predicted from Rapid Distortion Theory, explain all the macroscopic nonlinearities.

Sensitivity of the regional climate model RegCM4.2 to planetary boundary layer parameterisation

This study investigates the performance of two planetary boundary layer (PBL) parameterisations in the regional climate model RegCM4.2 with specific focus on the recently implemented prognostic turbulent kinetic energy parameterisation scheme: the University of Washington (UW) scheme. When compared with the default Holtslag scheme, the UW scheme, in the 10-year experiments over the European domain, shows a substantial cooling. It reduces winter warm bias over the north-eastern Europe by 2 °C and reduces summer warm bias over central Europe by 3 °C. A part of the detected cooling is ascribed to a general reduction in lower tropospheric eddy heat diffusivity with the UW scheme. While differences in temperature tendency due to PBL schemes are mostly localized to the lower troposphere, the schemes show a much higher diversity in how vertical turbulent mixing of the water vapour mixing ratio is governed. Differences in the water vapour mixing ratio tendency due to the PBL scheme are present almost throughout the troposphere. However, they alone cannot explain the overall water vapour mixing ratio profiles, suggesting strong interaction between the PBL and other model parameterisations. An additional 18-member ensemble with the UW scheme is made, where two formulations of the master turbulent length scale in unstable conditions are tested and unconstrained parameters associated with (a) the evaporative enhancement of the cloud-top entrainment and (b) the formulation of the master turbulent length scale in stable conditions are systematically perturbed. These experiments suggest that the master turbulent length scale in the UW scheme could be further refined in the current implementation in the RegCM model. It was also found that the UW scheme is less sensitive to the variations of the other two selected unconstrained parameters, supporting the choice of these parameters in the default formulation of the UW scheme.

Weak Vertical Diffusion Allows Maintenance of Cold Halocline in the Central Arctic

In spring preceding the record minimum summer ice cover detailed microstructure measurements were made from drifting pack ice in the Arctic Ocean, 110 km from the North Pole. Profiles of hydrography, shear, and temperature microstructure collected in the upper water column covering the core of the Atlantic Water are analyzed to determine the diapycnal eddy diffusivity, the eddy diffusivity for heat, and the turbulent flux of heat. Turbulence in the bulk of the cold halocline layer was not strong enough to generate significant buoyancy flux and mixing. Resulting turbulent heat flux across the upper cold halocline was not significantly different than zero. The results show that the low levels of eddy diffusivity in the upper cold halocline lead to small vertical turbulent transport of heat, thereby allowing the maintenance of the cold halocline in the central Arctic.

Eddy heat diffusion and Subantarctic Mode Water formation

Subantarctic mode waters (SAMW) form in the deep winter mixed layers occuring north of the Subantarctic Front (SAF). The recent increase of hydrographic and surface drifter data in the Southern Ocean allows a better spatial representation of the distinct regions of SAMW formation. This study focuses on the thermodynamical processes acting on the winter mixed layer heat budget. Eddy heat diffusion play a substantial role in the local heat balance, whereas its action vanishes with large‐scale averaging. South of the western boundary currents and north of the SAF, the eddy heating plays an important role in specific regions, counterbalancing the cooling of the mixed layer by Ekman advection and air‐sea fluxes. Specifically, the eddy diffusion term reduces the tendency for mixed layer destabilisation north of the SAF in the Western Indian Ocean downstream of the Agulhas Retroflection and in the Western Pacific downstream of Campbell Plateau. This role for mixed layer eddy fluxes emphasizes a large‐scale control of mixed layer properties by topography and mesoscale processes in the Southern Ocean.

Turbulent carbon exchange in very stable conditions

Turbulent fluxes obtained using the conventional eddy covariance approach result in erratic results with large time fluctuations in extremely stable conditions. This can limit efforts to estimate components of the nocturnal energy budget and respiratory CO2 fluxes. Well-organized fluxes that show a clear dependence on turbulent intensity were obtained when multiresolution decomposition was used to estimate turbulent exchanges. CO2, heat and water vapour fluxes were observed at a site in the eastern Amazon basin that had been cleared for agricultural purposes. Temporal scales of the carbon transfer were determined and shown to be similar to those of latent heat, but as much as three times larger than those of sensible heat. CO2 eddy diffusivities at the temporal scales on which most of the vertical CO2 exchange occurs are shown to be 50 times larger than the eddy diffusivity for heat. A process associated with the vertical scale of the scalar accumulation layer is suggested to explain these different scales and turbulent diffusivities of carbon and sensible heat transfer. For an appreciable range of turbulence intensities, the observed vertical turbulent carbon exchange is insufficient to account for the locally respired CO2 estimated independently. Evidence that shallow drainage currents may account for this is given.

A TWO-EQUATION HEAT TRANSFER MODEL FOR WALL TURBULENT SHEAR FLOWS

A proposal for closing the Reynolds-averaged energy equation is presented at the twoequation level of turbulence modeling. The eddy diffusivity for heat is proposed as a function of the local energy of turbulence, k, and the local temperature time scale, t  , instead of using mixed time scale, m  . The proposed two-equation heat transfer model solves two differential equations, one for the temperature variance, t k , and the other for the temperature time scale, t  . The nearwall limiting behavior of turbulent quantities associated with heat transfer has been captured with the proposed model. Therefore, an additional term is included in the temperature variance equation to improve the prediction of nearwall behavior. Moreover, an exact and noval equation for the temperature time scale, t  , is introduced in this study. The proposed t t k  heat transfer model does not suffer from numerical stiffness problems since natural boundary conditions for the variables t k and t  are used ( t k = t  =0 at y=0). The proposed model is assessed by application to fullydeveloped turbulent channel flows under different wall thermal conditions with different values of Reynolds numbers. The results for all cases examined showed good agreement with those of the direct numerical simulation data.

Formation of subantarctic mode water in the southeastern Indian Ocean

Subantarctic Mode Water (SAMW) is the name given to the relatively deep surface mixed layers found directly north of the Subantarctic Front in the Southern Ocean, and their extension into the thermocline as weakly stratified or low potential vorticity water masses. The objective of this study is to begin an investigation into the mechanisms controlling SAMW formation, through a heat budget calculation. ARGO profiling floats provide estimates of temperature and salinity typically in the upper 2,000 m and the horizontal velocity at various parking depths. These data are used to estimate terms in the mode water heat budget; in addition, mode water circulation is determined with ARGO data and earlier ALACE float data, and climatological hydrography. We find a rapid transition to thicker layers in the central South Indian Ocean, at about 70°S, associated with a reversal of the horizontal eddy heat diffusion in the surface layer and the meridional expansion of the ACC as it rounds the Kerguelen Plateau. These effects are ultimately related to the bathymetry of the region, leading to the seat of formation in the region southwest of Australia. Upstream of this region, the dominant terms in the heat budget are the air–sea flux, eddy diffusion, and Ekman heat transport, all having approximately equal importance. Within the formation area, the Ekman contribution dominates and leads to a downstream evolution of mode water properties.

An alternative two-equation turbulent heat diffusivity closure

The objective of this paper is to present an alternative closure for turbulent heat transport, that has been established on the ground of v 2– f model with so-called elliptic relaxation equation and the two-equation model for turbulent thermal field. New formulae on the eddy heat diffusivity is proposed. Additionally the production term of destruction rate of temperature variance transport equation is reformulated. No damping functions are involved in this model. Results of numerical computation have been compared with the experimental data for fully developed thermal field in the pipe and DNS heat transfer prediction for two-dimensional channel flow. The model predicts reasonably well the near-wall distribution of basic turbulence statistics.

NUMERICAL PREDICTIONS OF HEAT TRANSFER AND FLUID FLOW CHARACTERISTICS FOR SEVEN DIFFERENT DIMPLED SURFACES IN A CHANNEL

Heat transfer and fluid flow characteristics for seven different dimpled surfaces on one surface of a channel are predicted numerically using version 6.1.18 of FLUENT. The turbulent model employed is a realizable κ–ϵ model without a wall function. The different dimples investigated are spherical dimples, tilted cylinder dimples, cylinder dimples, in-line triangular dimples, reverse in-line triangular dimples, staggered triangular dimples, and reverse staggered triangular dimples. Results show the existence of a centrally located vortex pair and vortex pairs near the spanwise edges of each dimple for the three circular dimple types, which augment local magnitudes of eddy diffusivity for momentum and eddy diffusivity for heat. Advection of reattaching and recirculating flows from locations within the spherical-type dimple cavities, as well as strong instantaneous secondary flows and mixing within the vortex pairs, are especially apparent. For the four triangular types of dimples, only one primary flow circulation zone generally is present within individual dimples. In all cases, regions of augmented streamwise vorticity show approximate correspondence to locations where eddy diffusivities for momentum and heat are increased. Overall, the highest heat transfer augmentations, and the most significant local and overall increases to eddy diffusivity for momentum and eddy diffusivity for heat, are produced by the spherical dimples and the tilted cylinder dimples.

NUMERICAL PREDICTIONS OF FLOW STRUCTURE AND LOCAL NUSSELT NUMBER RATIOS ALONG AND ABOVE DIMPLED SURFACES WITH DIFFERENT DIMPLE DEPTHS IN A CHANNEL

Turbulent air flows in channels with dimples placed on the bottom wall are numerically predicted and compared using version 6.0.12 of FLUENT with a realizable k-ε model and no wall function. Three different dimple depths, δ/D = 0.1, 0.2, and 0.3, are considered. Steady-state predictions of fluid within and near different dimples show the presence of different vortex pairs. These include centrally located vortex pairs as well as vortex pairs located near the spanwise edges of individual dimples, which become stronger as dimple depth increases. Magnitudes of eddy diffusivity for momentum and eddy diffusivity for heat are augmented at the same locations, and also increase as dimple depth increases. Such characteristics are due to advection of reattaching and recirculating flow from locations within the dimple cavities, as well as to the strong instantaneous secondary flows and mixing within the vortex pairs. Local Nusselt number ratio data also show the highest augmentations, and the highest local values that increase with dimple depth at surface locations beneath the different vortex pairs, especially within the downstream portions of dimples, as well as near dimple spanwise and downstream edges.

NUMERICAL PREDICTIONS OF FLOW STRUCTURE ABOVE A DIMPLED SURFACE IN A CHANNEL

Turbulent air flow in a channel with deep dimples (δ/D = 0.3) on one wall is numerically predicted using version 6.0.12 of FLUENT with a realizable κ–ϵ model and no wall function. Steady-state results show centrally located vortex pairs, as well as vortex pairs located near the spanwise edges of individual dimples. The fluid within and near these different vortex pairs contains augmented magnitudes of eddy diffusivity for momentum and eddy diffusivity for heat. Such characteristics are due to advection of reattaching and recirculating flow from locations within the dimple cavities, as well as to the strong instantaneous secondary flows and mixing within the vortex pairs.