Vertical transport of turbulent kinetic energy in the surface layer over a paddy field

Turbulent kinetic energy and its vertical flux were measured at two heights over a paddy field. The vertical transport of turbulent kinetic energy was always downward right above the paddy field and was frequently downward at higher levels within a few metres above the crop. Contributions to the downward transport arise mainly from the turbulent kinetic energy of horizontal wind velocity components. It is shown from the analysis of probability distributions that appreciable transport takes place intermittently in a few large downward bursts and that these downdrafts are efficient for downward energy transport.In the budget of turbulent kinetic energy, the flux divergence term and the energy dissipation term are the main loss terms under unstable conditions. These terms increase in magnitude with increasing instability. Buoyant production is insufficient to balance these losses. The imbalance term involving the pressure-work term is probably one of the main energy sources in unstable conditions.     

A Surface-Layer Study of the Transport and Dissipation of Turbulent Kinetic Energy and the Variances of Temperature,Humidity and CO$$_$$

We discuss scalar similarities and dissimilarities based on analysis of the dissipation terms in the variance budget equations, considering the turbulent kinetic energy and the variances of temperature, specific humidity and specific CO\(_2\) content. For this purpose, 124 high-frequency sampled segments are selected from the Boundary Layer Late Afternoon and Sunset Turbulence experiment. The consequences of dissipation similarity in the variance transport are also discussed and quantified. The results show that, for the convective atmospheric surface layer, the non-dimensional dissipation terms can be expressed in the framework of Monin–Obukhov similarity theory and are independent of whether the variable is temperature or moisture. The scalar similarity in the dissipation term implies that the characteristic scales of the atmospheric surface layer can be estimated from the respective rate of variance dissipation, the characteristic scale of temperature, and the dissipation rate of temperature variance.     

Streamwise heat flux budget in the atmospheric surface layer

Atmospheric surface-layer measurements of terms in the equation for the streamwise heat flux confirm previous results in both laboratory and atmosphere that the temperature-pressure gradient correlation acts as a sink, approximately equal in magnitude to the production term. The measured viscous dissipation term is independent of stability and represents less than 10% of the production term over the range of experimental stability conditions. Models for the temperature-pressure gradient correlation are compared with the measurements.     

Conditional Analysis of an Internal Boundary Layer

Data from a convective internal boundary layer (IBL) are analyzed by focusing on the instantaneousstructure of the top of the IBL instead of the time-average structure.A conditional averaging technique is developed todiscriminate between air from above the IBL and air from below the IBL , which alternately invade some instrument levels due tosubstantial variation of the top of the convective IBL.Sensitivity to the conditional sampling criteria is examined.Inside the IBL , buoyant and mechanicalproduction and dissipation dominate the turbulent kinetic energy budget.The horizontal advection and turbulent transport terms are smaller, but not negligible. The inferred pressure correlation term is negligible.Above the IBL , buoyant production and dissipation, although weak,dominate the turbulent kinetic energy budget. Shear generation andturbulent transport are smaller but significant.     

The Temperature–Humidity Covariance in the Marine Surface Layer: A One-dimensional Analytical Model

An analytical model that predicts how much of the temperature–humidity covariance within the marine atmospheric surface layer (ASL) originates just above the ASL and just near the surface is proposed and tested using observations from the Risø Air Sea Experiment (RASEX). The model is based on a simplified budget for the two-scalar covariance that retains three basic terms: production, dissipation, and vertical transport. Standard second-order closure formulations are employed for the triple moments and the dissipation terms, and the canonical mixing length for the closure model is assumed linear with height (z) from the surface. Despite the poor performance of the gradient–diffusion closure in reproducing the measured triple moment, the overall covariance model was shown to be sufficiently robust to these assumptions. One of the main findings from the analytical treatment is the origin of the asymmetry in how the top and bottom boundary conditions affect the two-scalar covariance in the ASL. The analytical model reveals that ‘bottom-up’ boundary-condition variations scale with \(z^{-\sqrt{a}}\) , while ‘top-down’ variations scale with \(z^{\sqrt{a}}\) , where a is a constant that can be derived from similarity and closure constants. The genesis of this asymmetry stems from the flux-transport term but is modulated by the dissipation, and persists even in the absence of any inhomogeneity in the local production function. It is shown that the local production function acts to adjust the relative proportions of these two boundary conditions with weights that vary with the Obukhov length. The findings here do not provide ‘finality’ to the discussions on the covariance between humidity and temperature or the role of entrainment in modulating the turbulence within the ASL. Rather, they are intended to guide new hypotheses about interpretations of existing field data and identify needs for future field and numerical experiments.     

Turbulent kinetic energy budgets from a large-eddy simulation of airflow above and within a forest canopy

The output of a large-eddy simulation was used to study the terms ofthe turbulent kinetic energy (TKE) budget for the air layers above andwithin a forest. The computation created a three-dimensional,time-dependent simulation of the airflow, in which the lowest third ofthe domain was occupied by drag elements and heat sources to representthe forest. Shear production was a principal source of TKE in theupper canopy, diminishing gradually above tree-top height and moresharply with depth in the canopy. The transfer of energy to subgridscales (dissipation) was the main sink in the upper part of the domainbut diminished rapidly with depth in the canopy. Removal ofresolved-scale TKE due to canopy drag was extremely important,occurring primarily in the upper half of the forest where the foliagedensity was large. Turbulent transport showed a loss at the canopytop and a gain within the canopy. These general features have beenfound elsewhere but uncertainty remains concerning the effects ofpressure transport. In the present work, pressure was calculateddirectly, allowing us to compute the pressure diffusion term. Wellabove the canopy, pressure transport was smaller than, and opposite insign to, the turbulent transport term. Near the canopy top andbelow, pressure transport acted in concert with turbulent transport toexport TKE from the region immediately above and within the uppercrown, and to provide turbulent energy for the lower parts of theforest. In combination, the transport terms accounted for over half ofthe TKE loss near the canopy top, and in the lowest two-thirds of thecanopy the transport terms were the dominant source terms in thebudget. Moreover, the pressure transport was the largest source ofturbulent kinetic energy in the lowest levels of the canopy, beingparticularly strong under convective conditions. These resultsindicate that pressure transport is important in the plant canopyturbulent kinetic energy budget, especially in the lowest portion ofthe stand, where it acts as the major driving force for turbulentmotions.     

Scaling Properties of Biologically Active Scalar Concentration Fluctuations in the Atmospheric Surface Layer over a Managed Peatland

The higher-order scalar concentration fluctuation properties are examined in the context of Monin–Obukhov similarity theory for a variety of greenhouse gases that have distinct and separate source/sink locations along an otherwise ideal micrometeorological field site. Air temperature and concentrations of water vapour, carbon dioxide and methane were measured at high frequency (10 Hz) above a flat and extensive peat-land soil in the San Joaquin–Sacramento Delta (California, USA) area, subjected to year-round grazing by beef cattle. Because of the heterogeneous distribution of the sources and sinks of CO₂ and especially CH₄ emitted by cattle, the scaling behaviour of the higher-order statistical properties diverged from predictions based on a balance between their production and dissipation rate terms, which can obtained for temperature and H₂O during stationary conditions. We identify and label these departures as ‘exogenous’ because they depend on heterogeneities and non-stationarities induced by boundary conditions on the flow. Spectral analysis revealed that the exogenous effects show their signatures in regions with frequencies lower than those associated with scalar vertical transport by turbulence, though the two regions may partially overlap in some cases. Cospectra of vertical fluxes appear less influenced by these exogenous effects because of the modulating role of the vertical velocity at low frequencies. Finally, under certain conditions, the presence of such exogenous factors in higher-order scalar fluctuation statistics may be ‘fingerprinted’ by a large storage term in the mean scalar budget.     

Second-Order Modelling of Turbulence in Katabatic Flows

A complete one-dimensional second-order closure model is used to simulate katabatic flows observed on glaciers and ice caps. The model is tested with two different closure assumptions for the viscous dissipation, one based on a prognostic equation for and the other on a diagnostic buoyant length scale. Both formulations give quite similar results. Model simulations are compared to observations made over sloping ice surfaces during periods dominated by katabatic flow. In general, good agreement is found for both mean wind and temperature profiles as well as eddy correlation measurements. It is also found that the turbulent transport terms play an important role in katabatic flows as opposed to the classical stable boundary layer where these terms are usually ignored. Even the turbulent transport of temperature variance, which leads to the well-known countergradient term in unstable boundary layers, is relatively important for modelling the observed temperature profiles. The effect of these terms on the flux-profile relationships, using observed and simulated profiles, is also discussed.     

The Characteristics of Turbulence Structure and Transfer over the Middle Area of the Tibetan Plateau

In this paper, turbulent data obtained from the Damxung site during the Secondary Tibetan Plateau Science Experiment (TIPEX) in 1998 are used to study the characteristics of the turbulent spectra, turbulence transport, and the dissipation rates of turbulent kinetic energy, temperature variance, and humidity variance in the middle area of the Tibetan Plateau. The turbulent spectra of wind velocity, potential temperature, and humidity satisfy the-2/3 power law in the high frequency range. Horizontal transportation of heat and water vapor is negligible compared with vertical transportation under strong unstable conditions, and as the stability parameter z/L increases (where z is the observational height, and L is the Monin Obukhov length), horizontal transportation becomes dominant under near-neutral, neutral, and stable conditions. The non-dimensional temperature and humidity variances are 20% less than the temperature and humidity gradient variances. These deficits appear to increase as the absolute stability parameter increases. Moreover, the effects of turbulence transportation and pressure variance exist throughout the entire stability region.     

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.Also at Johns Hopkins University, Baltimore, MarylandAlso at Los Alamos National Laboratory, Los Alamos, New Mexico.     

Some Basic Properties of the Surrogate Subgrid-Scale Heat Flux in the Atmospheric Boundary Layer

The development of improved subgrid-scale (SGS) models for large-eddy simulation of scalar transport in the atmospheric boundary layer requires an improved understanding of basic properties of the SGS fluxes. High frequency atmospheric wind speed and temperature data sampled at a height of 1.7 m are used to measure SGS heat fluxes and dissipation of temperature variance, by means of one-dimensional filtering and invoking Taylor's hypothesis. Conditional averaging is used to isolate interesting features of the SGS signals, and to relate them to the large-scale characteristics of the flow, such as the presence of coherent structures. Both mean and conditionally averaged SGS quantities are compared with those obtained using a standard eddy-diffusivity model. Within the limitations imposed by the one-dimensional data analysis, we observe that the model appears unable to reproduce important features of the real signals, such as the negative dissipation of temperature variance associated with strong negative resolved temperature gradients due to the ejection of warm air under unstable atmospheric stability conditions.     

Note on the viscous heating term in the temperature variance equation

Experimental results in the atmospheric surface layer indicate that the viscous heating term in the equation for the mean-square value of the turbulent temperature fluctuation is small, but the correlation between temperature and turbulent energy dissipation fluctuations is significant.     

Turbulent Kinetic Energy Dissipation in the Surface Layer

We estimated the turbulent kinetic energy (TKE) dissipation rate for thirty-two 1-h intervals of unstable stratification covering the stability range 0.12 ≤ −z/L ≤ 43 (z/L is the ratio of instrument height to the Obukhov length), by fitting Kolmogorov’s inertial subrange spectrum to streamwise spectra observed over a desert flat. Estimated values are compatible with the existence of local equilibrium, in that the TKE dissipation rate approximately equalled the sum of shear and buoyant production rates. Only in the neutral limit was the turbulent transport term in the TKE budget measured to be small.     

The budget of carbon dioxide variance in the surface layer over vegetated fields

The budget equation for carbon dioxide variance can be represented by production, dissipation and flux divergence terms. Each term is measured under near neutral to moderately unstable conditions over vegetated fields. The flux divergence term is about an order of magnitude smaller than production and dissipation terms, though it shows a loss for 0.006 < _v < 1 and a gain for 1 < - _v < 10. Here, _v is the Monin-Obukhov stability parameter including humidity effect. As expected from a closure of the budget, the nondimensional production and dissipation terms are basically identical and represented by the same functional form: (1–16 _v )^–1/2.     

Analysis of the turbulence structure of a marine low-level jet

Four aircraft measurement sets made in late May 1989 within low level jets over the Baltic Sea have been analyzed to estimate the turbulence energy budget. It is concluded that the jets had the same origin as found in an earlier study from the same general area: inertial oscillation caused by frictional decoupling when relatively warm air flows out over much colder water.In order to combine budget estimates from the four flights to form a representative average, self-preservation similarity was assumed. When the terms were made nondimensional with the proper scale combination, the largest terms in all four runs were of order one, indicating that the scaling is physically sound.Three terms were found to dominate the turbulence energy budget: shear production, dissipation and pressure transport. The latter was obtained as remainder term, since local time rate of change and advection terms were found to be of negligible magnitude. Shear production was found in a narrow layer above the jet core and in a much deeper layer below it. The pressure transport term was a gain in this layer as well, helping to keep the layer below the jet well mixed. This is in agreement with results from aircraft measurements in the low level jet and monsoon boundary layer over the Arabian Sea.It is concluded that development of the inertial jet downwind of a coastline is of fundamental importance for exchange of momentum at the sea surface in conditions when relatively warm air is advected over cold water. The jet produces turbulence that promotes mixing in the lower layers, which sharpens the shear below the jet core, so that mixing becomes even more effective. Turbulence brought down to the surface by the pressure transport term is likely to be of the inactive type, which does not produce shear stress. Through the above-mentioned process it is, however, instrumental in promoting the mechanism that eventually produces active turbulence, the carrier of momentum.     

Generation and dissipation of microwave refractive-index fluctuations in the boundary layer

The index of refraction and its short-term variations have been measured on a 152-m meteorological tower at three fixed levels and on a moveable platform. Analysis of the data reveals that the time rates of production and dissipation of refractivity fluctuations are approximately in balance under a variety of meteorological conditions, and that changes in the rate of dissipation usually coincide with comparable changes in the rate of production. Under reasonably stationary conditions, terms corresponding to the rate of change and vertical diffusion of refractivity variance are found to be negligible. Power spectral densities of the variations increase when the rate of generation (and dissipation) increase, and conversely. Comparison of the results with simultaneous acoustic sounder returns provides a valuable insight into the mechanisms responsible for changes in the rates of production and dissipation.     

On the flow structure and turbulence during sweep and ejection events in a wind-tunnel model canopy

Particle image velocimetry (PIV) data obtained in a wind-tunnel model of a canopy boundary layer is used to examine the characteristics of mean flow and turbulence. The vector spacing varies between 1.7 and 2.5 times the Kolmogorov scales. Conditional sampling based on quadrants, i.e. based on the signs of velocity fluctuations, reveals fundamental differences in flow structure, especially between sweep and ejection events, which dominate the flow. During sweeps, the downward flow generates a narrow, highly turbulent, shear layer containing multiple small-scale vortices just below canopy height. During ejections, the upward flow expands this shear layer and the associated small-scale flow structures to a broad region located above the canopy. Consequently, during sweeps the turbulent kinetic energy (TKE), Reynolds stresses, as well as production and dissipation rates, have distinct narrow peaks just below canopy height, whereas during ejections these variables have broad maxima well above the canopy. Three methods to estimate the dissipation rate are compared, including spectral fits, measured subgrid-scale (SGS) energy fluxes at different scales, and direct measurements of slightly underresolved instantaneous velocity gradients. The SGS energy flux is 40–60% of the gradient-based (direct) estimates for filter sizes inside the inertial range, while decreasing with scale, as expected, within the dissipation range. The spectral fits are within 5–30% of the direct estimates. The spectral fits exceed the direct estimates near canopy height, but are lower well above and below canopy height. The dissipation rate below canopy height increases with velocity magnitude, i.e. it has the highest values during sweep and quadrant 1 events, and is significantly lower during ejection and quadrant 3 events. Well above the canopy, ejections are the most dissipative. Turbulent transport during sweep events acts as a source below the narrow shear layer within the canopy and as a sink above it. Transport during ejection events is a source only well above the canopy. The residual term in the TKE transport equation, representing mostly the effect of pressure–velocity correlations, is substantial only within the canopy, and is dominated by sweeps.     

Molecular dissipation of turbulent fluctuations in the convective mixed layer part II: Height variations of characteristic time scales and experimental test of molecular dissipation models

Extensive turbulence measurements from the Limagne and Beauce experiments were used to compute a characteristic time scale of the turbulence field (Τ = second moment/dissipation rate) for turbulent kinetic energy, temperature and humidity variances, and temperature-humidity covariance. The height variations of these time scales were analysed. The characteristic half-time scale Τ/2 of the turbulent velocity field was found, as expected, to be of the same order of magnitude as the large-eddy time scale Τ _L = Z_i/w*, showing that the turbulence structure is controlled by large eddies in the bulk of the mixed layer. The increase of Τ/2 above z/Z _i ～- 0.7 implies, however, that this time scale is no longer relevant to destruction of turbulent kinetic energy in the statically stable region with negative heat fluxes. An effective time scale Τ_eff, introduced by Zeman (1975), has been computed and its behaviour discussed. The scales for θ′ ², q′², and θ′q′ were found to be much shorter than Τ. Furthermore, a significant difference in behaviour was also revealed between the characteristic time scales of temperature and humidity fields in the stable layer. By using these experimental estimates, we tested some of the models for molecular dissipations, which are currently in use in higher order closure atmospheric boundary-layer models. The parameterized dissipation rates for θ′ ², and q′ ² agree well qualitatively with experimental estimates in the bulk of the mixed layer. In the stable layer, however, the parameterized dissipation rate ε _θ tends to become larger than the experimental ones although the parameterized dissipation rate ε _q still agrees with the experimental ones. For the molecular dissipation of θ′q′, this current model becomes physically inconsistent in the middle part of the mixed layer, because this term may become a production term for temperature-humidity covariance.     

Further results from a laboratory model of the convective planetary boundary layer

The turbulence in a laboratory convective mixed layer is probed more extensively than in the preliminary study of Willis and Deardorff (1974), and results presented. Turbulence intensities, spectra and probability distributions using mixed-layer scaling compare favorably with similarly scaled field measurements not available or plentiful in 1974. However, the velocity spectra in the convection tank exhibit only a short inertial subrange due to the close proximity of the dissipation subrange to the energy-containing range.The turbulence budget suggests that the convergence of the vertical transport of pressure fluctuations is a rather important term.Results on the entrainment rate are also presented, using both mixed-layer scaling and local interfacial scaling.     

Some dynamical consequences of Greenhouse gas warming

Abstract

The change in December‐February climate simulated by the CCC GCM for a doubling of CO₂ is viewed from a Northern Hemisphere middle‐latitude persepctive. The simulated change in temperature is such as to reduce equator‐to‐pole and ocean‐to‐land temperature gradients in the body of the troposphere and this is expected to result in less baroclinicity and baroclinic instability, weaker eddies and transports and generally to a decrease in synoptic activity or, in other words, to more “summer‐like” conditions.

The overall “rate of working” of the atmosphere, as measured by the generation of available potential energy, its conversion to kinetic energy and subsequent dissipation, decreases by some 12%. However, while the amount of available potential energy in the atmosphere decreases by about the same amount, the amount of kinetic energy is unchanged. Differences to the mean zonal, standing and transient eddy components of available potential and kinetic energies and to their rates of generation and conversion show that the energy cycle has changed in ways that might not be immediately expected.

Despite the general decrease in activity, the net poleward transport of energy by the atmosphere is remarkably unchanged. This is accomplished with the expected decrease in the transport of dry static energy being off‐set by an increase in latent energy transport. This is true both for mean zonal and eddy transports. That the same amount of energy is transported by a generally less active atmosphere shows that, in a sense, the flow structures are more “efficient” in the warmer climate and calculations are made to quantify this. The transport of energy in latent form is much more efficient due to the strong increase in moisture content that accompanies the temperature increase.