scholarly journals Characteristics of the Heat Flux in the Unstable Atmospheric Surface Layer

2016 ◽  
Vol 73 (11) ◽  
pp. 4519-4529 ◽  
Author(s):  
Maithili Sharan ◽  
Piyush Srivastava
Keyword(s):  
Heat Flux ◽  
Surface Layer ◽  
Temperature Gradient ◽  
Power Law ◽  
Atmospheric Surface Layer ◽  
Potential Temperature ◽  
Stability Parameter ◽  
Layer Potential ◽  
Power Law Function ◽  
The Stability

Abstract The behavior of the heat flux H with respect to the stability parameter (=z/L, where z is the height above the ground, and L is the Obukhov length) in the unstable atmospheric surface layer is analyzed within the framework of Monin–Obukhov similarity (MOS) theory. Using MOS equations, H is expressed as a function of and vertical surface-layer potential temperature gradient . A mathematical analysis is carried out to analyze the theoretical nature of heat flux with the stability parameter by considering the vertical potential temperature gradient as (i) a constant and (ii) a power-law function of heat flux. For a given value of H, two values of associated with different stability regimes are found to occur in both the conditions, suggesting the nonuniqueness of MOS equations. Turbulent data over three different sites—(i) Ranchi, India; (ii) the Met Office’s Cardington, United Kingdom, monitoring facility; and (iii) 1999 Cooperative Atmosphere–Surface Exchange Study (CASES-99; United States—are analyzed to compare the observed nature of H with that predicted by MOS. The analysis of observational data over these three sites reveals that the observed variation of H with is consistent with that obtained theoretically from MOS equations when considering the vertical temperature gradient as a power-law function of heat flux having the exponent larger than 2/3. The existence of two different values of the stability parameter for a given value of heat flux suggests that the application of heat flux as a boundary condition involves some intricacies, and it should be applied with caution in convective conditions.

scholarly journals Effects of Atmospheric Surface Layer Stability on Turbulent Fluxes of Heat and Water Vapor across the Water–Atmosphere Interface

2016 ◽  
Vol 17 (11) ◽  
pp. 2835-2851 ◽  
Author(s):  
Yusri Yusup ◽  
Heping Liu
Keyword(s):  
Heat Flux ◽  
Surface Layer ◽  
Wind Speed ◽  
Temperature Gradient ◽  
Atmospheric Surface Layer ◽  
Numerical Models ◽  
Atmospheric Stability ◽  
Stable Conditions ◽  
Vapor Pressure Gradient ◽  
Stability Ranges

Abstract Widely used numerical models to estimate turbulent exchange of latent heat flux (LE) and sensible heat flux H across the water–atmosphere interface are based on the bulk transfer relations linked indirectly to atmospheric stability, even though the accurate prediction of the influence of stability on fluxes is uncertain. Here eddy covariance data collected over the water surface of Ross Barnett Reservoir, Mississippi, was analyzed to study how atmospheric stability and other variables (wind speed, vapor pressure gradient, and temperature gradient) in the atmospheric surface layer (ASL) modulated LE and H variations in different stability ranges. LE and H showed right-skewed, bell-shaped distributions as the ASL stability shifted from very unstable to near neutral and then stable conditions. The results demonstrate that the maximum (minimum) LE and H did not necessarily occur under the most unstable (stable) conditions, but rather in the intermediate stability ranges. No individual variables were able to explain the dependence of LE and H variations on stability. The coupling effects of stability, wind speed, and vapor pressure gradient (temperature gradient) on LE (H) primarily caused the observed variations in LE and H in different stability ranges. These results have important implications for improving parameterization schemes to estimate fluxes over water surfaces in numerical models.

Phase Field Modeling of Solidification in Single Component Systems

2017 ◽  
Author(s):  
Sepideh Kavousi ◽  
Dorel Moldovan
Keyword(s):  
Heat Flux ◽  
Temperature Gradient ◽  
Power Law ◽  
Phase Field ◽  
Thermal Gradient ◽  
Solidification Rate ◽  
Single Component ◽  
Effect Of Temperature ◽  
Phase Field Modeling ◽  
Field Modeling

Using phase field modeling simulation approach we investigate the effect of various parameters on the primary and secondary dendrite arm spacing during directional solidification in a single component system. In previous studies the effect of temperature gradient was assumed to be negligible in the transversal directions with a temperature rate equal to the product of thermal gradient and solidification rate. In our study the temperature field is obtained from energy conservation equation by considering the balance of latent heat released in the regions where solidification occurs and energy dissipation due to directional temperature gradient as boundary condition. In our simulations, we implemented a numerical method that enables the investigation of solidification in larger domains. Specifically, the temperature and the order parameter equations are solved only in the domains close to the solidification front; approach that reduces the computational costs significantly. We investigate the interplay and the effect of thermal gradient, solidification rate, undercooling temperature, and the cooling heat flux on arm spacing. By using a well-established power law relation the primary and secondary arm spacing are calculated for various solidification parameters. We also show that, for large heat fluxes, the secondary arm spacing is almost constant for different undercooling temperatures; behavior that demonstrates the need for correction of the power law relation by including the effect of heat flux.

scholarly journals Countergradient heat flux observations during the evening transition period

2014 ◽  
Vol 14 (17) ◽  
pp. 9077-9085 ◽  
Author(s):  
E. Blay-Carreras ◽  
E. R. Pardyjak ◽  
D. Pino ◽  
D. C. Alexander ◽  
F. Lohou ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Heat Flux ◽  
Surface Layer ◽  
Transition Period ◽  
Potential Temperature ◽  
Sensible Heat Flux ◽  
Buoyancy Flux ◽  
Horizontal Shear ◽  
Evening Transition ◽  
Virtual Potential Temperature

Abstract. Gradient-based turbulence models generally assume that the buoyancy flux ceases to introduce heat into the surface layer of the atmospheric boundary layer in temporal consonance with the gradient of the local virtual potential temperature. Here, we hypothesize that during the evening transition a delay exists between the instant when the buoyancy flux goes to zero and the time when the local gradient of the virtual potential temperature indicates a sign change. This phenomenon is studied using a range of data collected over several intensive observational periods (IOPs) during the Boundary Layer Late Afternoon and Sunset Turbulence field campaign conducted in Lannemezan, France. The focus is mainly on the lower part of the surface layer using a tower instrumented with high-speed temperature and velocity sensors. The results from this work confirm and quantify a flux-gradient delay. Specifically, the observed values of the delay are ~ 30–80 min. The existence of the delay and its duration can be explained by considering the convective timescale and the competition of forces associated with the classical Rayleigh–Bénard problem. This combined theory predicts that the last eddy formed while the sensible heat flux changes sign during the evening transition should produce a delay. It appears that this last eddy is decelerated through the action of turbulent momentum and thermal diffusivities, and that the delay is related to the convective turnover timescale. Observations indicate that as horizontal shear becomes more important, the delay time apparently increases to values greater than the convective turnover timescale.

Evaluating turbulent length scales from local MOST extension with different stability functions in first order closures for stably stratified boundary layer

2021 ◽  
Author(s):  
Andrey Debolskiy ◽  
Evgeny Mortikov ◽  
Andrey Glazunov ◽  
Christof Lüpkes
Keyword(s):  
Boundary Layer ◽  
Asymptotic Behavior ◽  
Surface Layer ◽  
Similarity Theory ◽  
Functional Dependence ◽  
Stability Parameter ◽  
Turbulent Length Scale ◽  
First Order ◽  
Stability Functions ◽  
The Stability

<p>According to the Monin-Obukhov similarity theory (MOST), in the stratified surface layer of the atmosphere, the mean vertical velocity and scalars gradients are related to the turbulent fluxes of these quantities and to the distance z from the surface in a universal manner. The stability parameter ζ=z/L, where L is the Obukhov turbulent length scale, is the only dimensionless parameter that determines the flux-gradient relationships. This imposes a dependency of the dimensionless velocity and buoyancy gradients on ζ in form of universal nondimensional stability functions for  the surface layer. Over the decades a number of them were proposed and derived mostly from extensive field campaigns of measurements in the ABL. The stability functions differ from each other by both open coefficients and functional dependence on  ζ.  They have a limited range of applicability, which is often extended by incorporating the assumption about their asymptotic behavior.</p><p>           A generalization of MOST by considering the dependence of the dimensionless gradients on the local stability parameter z/Λ  in the framework of first order closures allows the extension of  the universal stability functions from the surface layer to most of the ABL. However, because of applicability constraints, differences in the asymptotic behavior and in other implied assumptions, it is not immediately obvious, which set of stability functions will perform best. In this study we analyze a set of stability functions which are implemented in a uniform manner into a one-dimensional first-order closure.  The latter applies a turbulent mixing length with generalized local MOST scaling which fits to a surface schemes employing corresponding functions for consistency. We use two numerical experiment setups accompanied with LES data for validation which correspond to the weakly stable GABLES1 case and to LES simulations of the very stable ABL based on measurements at the Antarctic station DOME-C (van der Linden et al. 2019). We also focus on the sensitivity of the 1D model results to coarser grids with respect to both the used  surface flux schemes and  the ABL turbulence closures since their are meant to be used in climate models because of numerical efficiency.</p><p>Authors want to aknowledge partial funding by Russian Foundation for Basic Research (RFBR project N 20-05-00776), sensitivity analysis and closure development were performed with support  of Russian Science Foundation (RSF No 20-17-00190). Steven van der Linden for providing LES data of DOME-C based experiments.</p><p>References:</p><p>van der Linden S.J. et al. Large-Eddy Simulations of the Steady Wintertime Antarctic Boundary Layer // Boundary Layer Meteorology 173.2 (2019): 165-192.</p>

Exploring Self-Correlation in Flux–Gradient Relationships for Stably Stratified Conditions

2006 ◽  
Vol 63 (11) ◽  
pp. 3045-3054 ◽  
Author(s):  
P. Baas ◽  
G. J. Steeneveld ◽  
B. J. H. van de Wiel ◽  
A. A. M. Holtslag
Keyword(s):  
Heat Flux ◽  
Stability Parameter ◽  
Lapse Rate ◽  
Physical Processes ◽  
Obukhov Length ◽  
Flux Gradient ◽  
Stable Conditions ◽  
Measurement Uncertainties ◽  
Relative Errors ◽  
The Stability

Abstract In this paper, the degree of scatter in flux–gradient relationships for stably stratified conditions is analyzed. It is generally found that scatter in the dimensionless lapse rate ϕh is larger than in the dimensionless shear ϕm when plotted versus the stability parameter z/Λ (where Λ is the local Obukhov length). Here, this phenomenon is explained to be a result of self-correlation due to the occurrence of the momentum and the heat flux on both axes, measurement uncertainties, and other possibly relevant physical processes left aside. It is shown that the ratio between relative errors in the turbulent fluxes influences the orientation of self-correlation in the flux–gradient relationships. In stable conditions, the scatter in ϕm is largely suppressed by self-correlation while for ϕh this is not the case (vice versa for unstable stratification). An alternative way of plotting is discussed for determining the slope of the linear ϕm function.

scholarly journals Vertical refraction angle derived from the variance of the angle-of-arrival fluctuations

1979 ◽  
Vol 89 ◽  
pp. 227-238 ◽  
Author(s):  
F. K. Brunner
Keyword(s):  
Thermal Stability ◽  
Surface Layer ◽  
Temperature Gradient ◽  
Stability Parameter ◽  
Temperature Structure ◽  
Refraction Angle ◽  
Vertical Temperature Gradient ◽  
Angle Of Arrival ◽  
Vertical Temperature ◽  
Temperature Structure Parameter

A theory is developed for evaluating the vertical refraction angle from the variance of the angle-of-arrival fluctuations, assuming a horizontally homogeneous turbulent atmospheric surface layer. The vertical refraction angle is mainly a function of the vertical temperature gradient, and the variance of the angle-of-arrival is related to the temperature structure parameter CT2. However, surface layer similarity theory states that both the mean vertical temperature gradient and CT2 are functions of the same scaling temperature T* and a thermal stability parameter. This therefore provides an indirect method of determining the vertical refraction angle from a measurement of the variance of the angle-of-arrival and an estimate of the thermal stability parameter. Advantages of this method over other techniques of evaluating vertical refraction are discussed.

scholarly journals Countergradient heat flux observations during the evening transition period

2014 ◽  
Vol 14 (6) ◽  
pp. 7711-7737 ◽  
Author(s):  
E. Blay-Carreras ◽  
E. R. Pardyjak ◽  
D. Pino ◽  
D. C. Alexander ◽  
F. Lohou ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Heat Flux ◽  
Surface Layer ◽  
Time Scale ◽  
Transition Period ◽  
Potential Temperature ◽  
Buoyancy Flux ◽  
Horizontal Shear ◽  
Evening Transition ◽  
Virtual Potential Temperature

Abstract. Gradient-based turbulence models generally assume that the buoyancy flux ceases to introduce heat into the surface layer of the atmospheric boundary layer in temporal consonance with the gradient of the local virtual potential temperature. Here, we hypothesize that during the evening transition a delay exists between the instant when the buoyancy flux goes to zero and the time when the local gradient of the virtual potential temperature indicates a sign change. This phenomenon is studied using a range of data collected over several Intensive Observational Periods (IOPs) during the Boundary Layer Late Afternoon and Sunset Turbulence field campaign conducted in Lannemezan, France. The focus is mainly on the lower part of the surface layer using a tower instrumented with high-speed temperature and velocity sensors. The results from this work confirm and quantify a flux-gradient delay. Specifically, the observed values of the delay are ~30–80 min. The existence of the delay and its duration can be explained by considering the convective time scale and the competition of forces associated with the classical Rayleigh–Bénard problem. This combined theory predicts that the last eddy formed while the sensible heat flux changes sign during the evening transition should produce a delay. It appears that this last eddy is decelerated through the action of turbulent momentum and thermal diffusivities, and that the delay is related to the convective turn – over time – scale. Observations indicate that as horizontal shear becomes more important, the delay time apparently increases to values greater than the convective turnover time-scale.

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