Potential Temperature Flux Research Articles

Two-dimensional calculation of spatial distribution of neutral atoms for a planar inductively coupled oxygen discharge

Two-dimensional self-consistent fluid simulation of inductively coupled oxygen plasma is presented. The model equations include continuity equations for charged species and neutral oxygen atom, the Poisson equation, and the electron energy balance equation. The drift–diffusion approximation is employed. From the Maxwell equations, the induced electric field and absorbed power are calculated. The two-dimensional spatial distributions of charged species densities, charged species flux, density and flux of atomic oxygen, electric potential, and electron temperature are calculated. The effect of the gas pressure on the plasma uniformity is investigated. As the pressure increases, the spatial distributions of charged species and neutral atom have their peak values in the toroidal region where a large amount of the input power is absorbed by the plasma.

Isentropic zonal average formalism and the near‐surface circulation

AbstractThe isentropic zonal average formalism is extended to include a rigorous treatment of the bottom boundary of the atmosphere. We define a ‘surface zone’, where isentropes in the latitudinal plane are interrupted by the earth's surface. The zonal average equations of motion and their time average in isentropic coordinates are rederived in the presence of the surface zone. Applying the extended formalism to a baroclinic wave model, we show that near‐surface equatorward mean flow is driven by eastward surface form drag in isentropic coordinates, which in turn is related to poleward geostrophic potential temperature flux at the surface. A potential vorticity–potential temperature picture of extratropical general circulation dynamics above and within the surface zone is presented. We highlight the importance of poleward mean flow in the upper region of the surface zone and investigate the antisymmetric distribution of mean meridional mass flow about the median potential temperature of surface air. Copyright © 2004 Royal Meteorological Society.

Large-Eddy Simulation: How Large is Large Enough?

The length scale evolution of various quantities in a clear convective boundary layer (CBL), a stratocumulus-topped boundary layer, and three radiatively cooled (“smoke cloud”) convective boundary layers are studied by means of large-eddy simulations on a large horizontal domain (25.6 × 25.6 km2). In the CBL the virtual potential temperature and the vertical velocity fields are dominated by horizontal scales on the order of the boundary layer depth. In contrast, the potential temperature and the specific humidity fields become gradually dominated by mesoscale fluctuations. However, at the mesoscales their effects on the virtual potential temperature fluctuations nearly compensate. It is found that mesoscale fluctuations are negligibly small only for conserved variables that have an entrainment to surface flux ratio close to −0.25, which is about the flux ratio for the buoyancy. In the CBL the moisture and potential temperature flux ratios can have values that significantly deviate from this number. The geometry of the buoyancy flux was manipulated by cooling the clear convective boundary layer from the top, in addition to a positive buoyancy flux at the surface. For these radiatively cooled cases it is found that both the vertical velocity as well as the virtual potential temperature spectra tend to broaden. The role of the buoyancy flux in their respective prognostic variance equations is discussed. It is argued that in the upper part of the clear CBL, where the mean vertical stratification is stable, vertical velocity variance and virtual potential temperature variance cannot be produced simultaneously. For the stratocumulus case, in which latent heat release effects in the cloud layer play an important role in its dynamics, the field of any quantity, except for the vertical velocity, becomes dominated by mesoscale fluctuations. In general, the location of the spectral peak of any quantity becoming constrained by the domain size should be avoided. The answer to the question of how large the LES horizontal domain size should be in order to include mesoscale fluctuations will, on the one hand, depend on the type of convection to be simulated and the kind of physical question one aims to address, and, on the other hand, the time duration of the simulation. Only if one aims to study the dynamics of a dry CBL that excludes moisture, a rather small domain size suffices. In case one aims to examine either the spatial evolution of the fields of any arbitrary conserved scalar in the CBL, or any quantity in stratocumulus clouds except for the vertical velocity, a larger domain size that allows the development of mesoscale fluctuations will be necessary.

Potential Enthalpy: A Conservative Oceanic Variable for Evaluating Heat Content and Heat Fluxes

Abstract Potential temperature is used in oceanography as though it is a conservative variable like salinity; however, turbulent mixing processes conserve enthalpy and usually destroy potential temperature. This negative production of potential temperature is similar in magnitude to the well-known production of entropy that always occurs during mixing processes. Here it is shown that potential enthalpy—the enthalpy that a water parcel would have if raised adiabatically and without exchange of salt to the sea surface—is more conservative than potential temperature by two orders of magnitude. Furthermore, it is shown that a flux of potential enthalpy can be called “the heat flux” even though potential enthalpy is undefined up to a linear function of salinity. The exchange of heat across the sea surface is identically the flux of potential enthalpy. This same flux is not proportional to the flux of potential temperature because of variations in heat capacity of up to 5%. The geothermal heat flux across the o...

Long-Term Observations of the Dynamics of the Continental Planetary Boundary Layer

Time series of mixed layer depth, zi, and stable boundary layer height from March through October of 1998 are derived from a 915-MHz boundary layer profiling radar and CO 2 mixing ratio measured from a 447-m tower in northern Wisconsin. Mixed layer depths from the profiler are in good agreement with radiosonde measurements. Maximum zi occurs in May, coincident with the maximum daytime surface sensible heat flux. Incoming radiation is higher in June and July, but a greater proportion is converted to latent heat by photosynthesizing vegetation. An empirical relationship between zi and the square root of the cumulative surface virtual potential temperature flux is obtained ( r 2 5 0.98) allowing estimates of zi from measurements of virtual potential temperature flux under certain conditions. In fair-weather conditions the residual mixed layer top was observed by the profiler on several nights each month. The synoptic mean vertical velocity (subsidence rate) is estimated from the temporal evolution of the residual mixed layer height during the night. The influence of subsidence on the evolution of the mixed, stable, and residual layers is discussed. The CO 2 jump across the inversion at night is also estimated from the tower measurements.

Pressure‐potential‐temperature covariance in convection with rotation

AbstractThe pressure‐potential‐temperature covariance in free and rotating turbulent convection with no mean velocity shear is analysed, using a dataset generated with a large‐eddy simulation (LES) model. The pressure field is resolved into turbulence‐turbulence, buoyancy and Coriolis components, and the contributions from these components to the pressure‐gradient‐potential‐temperature covariance in the budget equation for the potential‐temperature flux are examined.In non‐rotating convection, the buoyancy contribution compensates for about one half of the buoyant production term in the flux budget equation, and the turbulence‐turbulence contribution is well approximated by the Rotta‐type return‐to‐isotropy model with the relaxation time‐scale set proportional to the turbulence energy dissipation time‐scale.In convection with rotation, neither the simplest Rotta‐type model with the relaxation time‐scale proportional to the energy dissipation time‐scale nor the more sophisticated two‐component‐limit (TCL) nonlinear model are able to accurately describe the LES data. A somewhat better agreement is found when a limitation is imposed on the relaxation time‐scale due to the background rotation. The simplest model for the buoyancy contribution, where it is set proportional to the buoyant production term in the flux budget equation, fares poorly. The TCL model shows better agreement with LES data although some uncertainties remain. However, the relative importance of the buoyancy contribution to the pressure‐gradient‐potential‐temperature covariance decreases with increasing rotation rate.In contrast, the Coriolis contribution becomes more important as the rotation rate increases. Neither the simplest linear model for the Coriolis contribution nor the much more complex nonlinear TCL model are found to be adequate. Neither model appropriately accounts for the component of the angular velocity of rotation that is parallel to the component of the pressure gradient in question. In the seemingly simplest case considered in the present paper, when the rotation vector is aligned with the vector of gravity, no Coriolis contribution to the vertical‐pressure‐gradient‐potential‐temperature covariance is predicted by these models. This results in a strong underestimation of the pressure term in the flux budget equation and may lead to an erroneous prediction of the vertical potential‐temperature flux in convection with rotation. In an attempt to remedy the situation, an extension of the TCL model that contains only one extra empirical coefficient is developed and checked against LES data.

Atmospheric and surface variations during westerly wind bursts in the tropical western pacific

AbstractAn analysis is made of variations in both the surface energy balance and the regional atmospheric dynamic and thermal structure during 44 westerly wind bursts (WWBs) in the western equatorial Pacific Ocean from 1979 to 1995. The study assesses winds, convective available potential energy, cloud properties, precipitation, surface temperature, and surface heat flux while distinguishing between brief (5–25 day periodicity) and sustained (30–90 day) WWBs. Datasets used in the study include fields from the NCEP/NCAR and ECMWF re‐analyses, and satellite retrievals of clouds (ISCPP), precipitation (MSU), moisture (TOVS), and surface solar flux.Both brief and sustained WWBs, by definition, experience strong low‐level westerly winds that typically induce an increased surface latent‐heat flux of approximately 30 W m−2. Enhanced cloud thickness, precipitation, and upper tropospheric easterly wind anomalies accompany surface westerly winds, though maxima in winds lag those in clouds and precipitation by about one day for brief WWBs and four days for sustained events. WWBs of both types experience strong seasonality, occurring frequently in all seasons except boreal summer.Important distinctions between brief and sustained WWBs can also be made. Westerly anomalies typically extend above 200 hPa during brief WWBs but are generally confined to the lower troposphere (below 400 hPa) for sustained events. Sustained WWBs are also preceded by a quiescent period of reduced cloud thickness and surface winds that is accompanied by strong incident solar flux. Convective instability, as judged by a variety of techniques, increases by approximately 30% during this quiescent period. Brief WWBs do not include the precursory surface warming or convective destabilization of sustained WWBs. Notwithstanding the warming episodes before the events, sustained WWBs are associated with a net surface cooling approximately 40% larger than brief WWBs.The relationship between brief and sustained WWBs and the phase of the Madden‐Julian Oscillation (MJO) (as judged from outgoing long‐wave radiation) is also examined. Results support the classification of events as ‘brief’ and ‘sustained’ as used in this study, with brief WWBs occurring frequently during both wet and dry phases of the MJO, while sustained WWBs occur uniquely during the MJO wet phase. The association of brief and sustained WWBs with the MJO is shown to be independent of the El Niiio Southern Oscillation phase. It is therefore proposed that some, but not all, WWBs may be viewed as the surface signature of the MJO and that the mechanisms responsible for the MJO play an integral role in the formation and sustenance of sustained WWBs.

Third-Order Transport and Nonlocal Turbulence Closures for Convective Boundary Layers*

The turbulence closure problem for convective boundary layers is considered with the chief aim to advance the understanding and modeling of nonlocal transport due to large-scale semiorganized structures. The key role here is played by third-order moments (fluxes of fluxes). The problem is treated by the example of the vertical turbulent flux of potential temperature. An overview is given of various schemes ranging from comparatively simple countergradient-transport formulations to sophisticated turbulence closures based on budget equations for the second-order moments. As an alternative to conventional “turbulent diffusion parameterization” for the flux of flux of potential temperature, a “turbulent advection plus diffusion parameterization” is developed and diagnostically tested against data from a large eddy simulation. Employing this parameterization, the budget equation for the potential temperature flux provides a nonlocal turbulence closure formulation for the flux in question. The solution to this equation in terms of the Green function is nothing but an integral turbulence closure. In particular cases it reduces to closure schemes proposed earlier, for example, the Deardorff countergradient correction closure, the Wyngaard and Weil transport-asymmetry closure employing the second derivative of transported scalar, and the Berkowicz and Prahm integral closure for passive scalars. Moreover, the proposed Green-function solution provides a mathematically rigorous procedure for the Wyngaard decomposition of turbulence statistics into the bottom-up and top-down components. The Green-function decomposition exhibits nonlinear vertical profiles of the bottom-up and top-down components of the potential temperature flux in sharp contrast to universally adopted linear profiles. For modeling applications, the proposed closure should be equipped with recommendations as to how to specify the temperature and vertical velocity variances and the vertical velocity skewness.

On the structure, paths, and fluxes associated with Agulhas rings

In January 1993, two Agulhas rings were sampled in the eastern South Atlantic during the World Ocean Circulation Experiment one‐time hydrographic section A11. The first of these, Ring 1, was sampled at 36°S, 4°E in the Subtropical Frontal Zone and was smaller and less energetic than other, more typical Agulhas rings, owing partly to its interactions with the North Subtropical Front. The other, Ring 2, was sampled at 33°S, 10°E in the subtropics. This ring was average in size and reasonably representative of the rings observed in the southeast Atlantic during the early 1990s. The path of the rings is found to be dominated by advection in the mean flow rather than self‐induced velocities of eddies under the β effect. We observe significant differences in reduced gravity and available heat and salt anomalies in the rings; from these we infer temporal variability in the stratification of rings upon their formation at the Agulhas Retroflection. This temporal variability in the structure of rings will affect the fluxes associated with them. Data collected within Ring 2 show that neglecting consideration of the water beneath the 10°C isotherm underestimates the volume flux by half and the potential temperature and salinity flux by in excess of one third and one half, respectively. Using a base of the 3.5°C isotherm and including the high‐salinity intermediate water from the Indian Ocean is found to be more appropriate. With these conditions, six Agulhas rings per year entering the subtropical South Atlantic would equate to a volume flux of 9 Sv and an absolute potential temperature and salinity flux of 84 Sv°C and 322 Sv psu (1 Sv psu ≈ 106 kg s−1). The significant flux of intermediate water from the Indian Ocean may be as important in the return path of the thermohaline circulation as the intermediate water that enters the South Atlantic through Drake Passage. Further, the water associated with Agulhas rings and cooler than 10°C potentially contributes a larger volume flux to the warm water return path than the corresponding surface and upper thermocline water.

Observed Lagrangian Transition of Stratocumulus into Cumulus during ASTEX: Mean State and Turbulence Structure

Aircraft measurements made during the ‘‘First Lagrangian’’ of the Atlantic Stratocumulus Transition Experiment (ASTEX) between 12 and 14 June 1992 are presented. During this Lagrangian experiment an air mass was followed that was advected southward by the mean wind. Five aircraft flights were undertaken to observe the transition of a stratocumulus cloud deck to thin and broken stratocumulus clouds penetrated by cumulus from below. From the horizontal aircraft legs the boundary layer mean structure, microphysics, turbulence structure, and entrainment were analyzed. The vertical profiles of the vertical velocity skewness are shown to illustrate the transition of a cloudy boundary layer predominantly driven by longwave radiative cooling at the cloud top to one driven mainly by convection due to an unstable surface stratification and cumulus clouds. During the last flight before the stratocumulus deck was observed to be broken and replaced by cumuli, the total water flux, the virtual potential temperature flux, and the vertical velocity variance in the stratocumulus cloud layer were found significantly larger compared with the previous flights. To analyze the cloud-top stability the mean jumps of conserved variables across the inversion were determined from porpoising runs through the cloud top. These jumps were compared with cloud-top entrainment instability criteria discussed in the literature. It is suggested that enhanced entrainment of dry air is a key mechanism in the stratocumulus‐cumulus transition.

Numerical study of the structure and evolution of a heated planetary boundary layer with a jet

The structure and evolution of a heated, sheared planetary boundary layer (PBL) similar to the one developed on July 11, 1987, during the First International Satellite Land Surface Climatology Project (ISLSCP) Field Experiment (FIFE) are investigated by a two‐ and a three‐dimensional large eddy simulation (LES) model. The simulated results are utilized to compare with the single Doppler lidar data whose validity, however, has never been thoroughly verified due to insufficient independent observations. In contrast to the traditional research on a buoyancy‐driven, windless convective boundary layer (CBL), the horizontal and vertical domains of this study are designed to be sufficiently large so that the principal physical processes involved in the development of this boundary layer can be successfully simulated. They include (1) large eddies generated by the surface sensible heat flux, (2) internal gravity waves excited in the stable layer due to the lifting mechanism exerted by the rising large eddies, (3) interaction between the waves and the background wind shear, and (4) wave breakdown caused by the convective instability when the flow speed exceeds the phase speed. The mean and statistical properties of this boundary layer turn out to be quite different from those of a CBL. Among them, the most unique feature is that in the stable layer the direction of the momentum flux ( ), which is transported by the gravity waves, is countergradient. The occurrence of this phenomenon, derived by lidar and confirmed by the simulation, is associated with the existence of a critical layer where the Doppler‐shifted frequency vanishes. Under this critical layer the vertical profile of horizontal velocity variance ( ) is found to exhibit a second maximum. The simulated results of potential temperature flux ( ) as well as the potential temperature variance ( ) also imply a second local absolute value maximum in the stable layer. The former is believed to be closely related to the formation of convective instability. Despite the model's ability in simulating the physical processes involved in the FIFE PBL, the large quantitative discrepancy discovered between the model‐generated and the lidar‐extracted statistical properties lead to a consistency check for the latter. It is shown that in the stable layer the magnitudes of the lidar‐observed momentum flux ( ) and the vertical velocity variance ( ) appear to be too strong. Several possible error sources which can contaminate the lidar observations are discussed.

Uncertainty of Boundary Layer Heat Budgets Computed from Wind Profiler—RASS Networks

Uncertainties in the evaluation of the atmospheric heat budget, in which the turbulent heat flux divergence term is calculated as a residual, are investigated for a triangular array of 915-MHz wind profilers—radio acoustic sounding systems (RASS) using a surface-integral method. A scaling analysis of the residual error heat budget equation reveals the basic characteristics and magnitudes of the uncertainties. These values are verified with a Monte Carlo simulation technique for synthetic datasets in which the triangle size is of the order of 30 km (meso-γ scale). The uncertainties depend on measurement errors, atmospheric stability, mean wind speed, triangle size, and averaging time. In addition, we estimate the effects of baroclinity and mean wind divergence on the accuracy of the calculation of the heat budget. Idealized, barotropic, and divergence-free conditions are studied to investigate the influence of various instrument accuracies on profiles of the turbulent virtual potential temperature flux divergence term. Results show that this term can be computed as a residual of the other terms with an uncertainty that varies from approximately 0.4 to 1.6 K h−1 for typical ranges of mean wind speed and stability, given current accuracies for 1-h averages of wind profiler—RASS. Uncertainties of the remaining terms in the equation are smaller. Although the uncertainties found are of about the same magnitude as typical maximum daytime boundary layer turbulent sensible heat flux divergences, 1.2 K h−1, it is found that under favorable conditions meaningful turbulent heat flux divergences can be obtained. The computations, however, become very uncertain under conditions of strong baroclinity or wind divergence.

A generalized scaling for convective shear flows

During the last two decades, different scalings for convective boundary layer (CBL) turbulence have been proposed. For the shear-free regime, Deardorff (1970) introduced convective velocity and temperature scales based on the surface potential temperature flux,Q s , the buoyancy parameter, β, and the time-dependent boundary-layer depth,h. Wyngaard (1983) has proposed decomposition of turbulence into two components, bottom-up (b) and top-down (t), the former characterized byQ s , the latter, by the potential temperature flux due to entrainment,Q h . Sorbjan (1988) has devised height-dependent velocity and temperature scales for both b- and t-components of turbulence. Incorporating velocity shear, the well known similarity theory of Monin and Obukhov (1954) has been developed for the atmospheric surface layer. Zilitinkevich (1971, 1973) and Betchov and Yaglom (1971) have elaborated this theory with the aid of directional dimensional analysis for a particular case when different statistical moments of turbulence can be alternatively attributed as being of either convective or mechanical origin. In the present paper, we attempt to create a bridge between the two approaches pointed out above. A new scaling is proposed on the basis of, first, decomposition of statistical moments of turbulence into convective (c), mechanical (m) and covariance (c&m) contributions using directional dimensional analysis and, second, decomposition of these contributions into bottom-up and top-down components using height-dependent velocity and temperature scales. In addition to the statistical problem, the scaling suggests a new approach of determination of mean temperature and velocity profiles with the aid of the budget equations for the mean square fluctuations.

Sampling errors in the vertical fluxes of potential temperature and moisture measured by aircraft during FIFE

The First International Satellite Land Surface Climatology Project (ISLSCP) Field Experiment (FIFE) was carried out over a 15 × 15 km area in central Kansas [Sellers et al., this issue]. The site size was constrained by land use characteristics, topography, and, importantly, the ability to field a reasonable network of surface observations of plant physiology, soil moisture, and radiative characteristics as well as surface observations of meteorological observations, including vertical fluxes of sensible heat and moisture. As described by Kelly [this issue], aircraft flying within the atmospheric boundary layer over the FIFE site played an important role: they provided direct measurements of the vertical fluxes of sensible heat and moisture above the FIFE site. Potential temperature flux and sensible heat flux differ by the constant ρdcp, where ρd is the dry air density (which is nearly constant in the atmospheric boundary layer) and cp is the specific heat of dry air at constant pressure.

Gravity Wave 1-leat Fluxes: A Lagrangian Approach

Abstract The effect of a vertically propagating, internal gravity wave on the vertical flux of potential temperature (heat) is considered by averaging the local heat flux vector over a potential temperature surface. This approach gives the wave heat flux a simple physical picture which is not readily apparent from the more common Eulerian formulation. This method also allows the eddy diffusion coefficient to be a function of the phase of the wave. Such a phase dependent eddy diffusion has been previously considered from an Eulerian viewpoint as a model of a convectively unstable gravity wave. Here, the Lagrangian method confirms and corrects the Eulerian results. Earlier work is extended by modeling a constant amplitude “breaking” wave, as well as by considering eddy diffusion coefficients that are asymmetric with respect to the wave breaking region. In all cases studied, 1ocalizing the eddy diffusion to the region of wayebreaking decreases the average heat flux.

Effects of Shear, Stability and Valley Characteristics on the Destruction of Temperature Inversions

Abstract A dry two-dimensional version of the Colorado State Cloud/Mesoscale Model was used to study the morning, inversion destruction cycle in a variety of deep mountain valley configurations. Eleven simulations were run to examine the effects of valley width, surface heating rate, wind shear above the valley, valley orientation, sidewall slope, initial stability and variable surface albedo on the evolution of the daytime boundary layer in the valley. Each was initiated with a stable layer filling the valley to ridgetop with a neutral layer above the ridge. The model was driven at the lower surface by a sinusoidally varying potential temperature flux which approximates the diurnal heating cycle. All simulations show that the initial inversion layer is destroyed by a combination of three processes; a growing surface based neutral layer over the valley floor, the destabilization of the stable air mass by the recirculation of air warmed over the slopes and the descent of the inversion top by the transport ...

Dynamical Model Simulation of the Morning Boundary Layer Development in Deep Mountain Valleys

Abstract A dry, two-dimensional version of the Colorado State University Multi-dimensional Cloud/Mesoscale Model was used to study the cross-valley evolution of the wind and temperature structures in an idealized east-west oriented mountain valley. Two simulations were performed, one in which the valley was heated symmetrically and a second in which a mid-latitude heating distribution was imposed. Both runs were initiated identically with a stable layer filling the valley to ridgetop and a neutral layer above the ridge. A specified sinusoidal surface potential temperature flux function approximating the diurnal cycle forced the model at the lower boundary. The results of the two simulations were remarkably similar. The model realistically reproduced the gross features found in actual valleys in both structure and timing. The simulated inversions were destroyed three and one-half hours after sunrise as a result of a neutral layer growing up from the surface meeting a descending inversion top. Slope winds w...

An Observational Test of the Quasi-Geostrophic Relation between Eddy Momentum Flux Convergence and Eddy Fluxes of Potential Vorticity and Potential Temperature

The quasi-geostrophic relation between the fluxes of momentum, potential vorticity and potential temperature is tested with atmospheric data by computing the convergence of momentum flux as a residual of of the potential temperature and potential vorticity flux and comparing it to the momentum flux convergence computed directly. It is shown that in the troposphere between 18 and 74°N the observed momentum flux convergence differs from the quasi-geostrophic convergence by 25–60% depending on tropospheric level and season.