Search

We survey temperature patterns and heat transport in convective atmospheric boundary layers (CBLs). We use the word “plumes” to describe the emergent temperature patterns, in much the same way that “eddies” describe patterns of motion in turbulent flows. We introduce a two-temperature (2T) toy model to connect the cross-sectional areas of plumes to the scaling properties of temperature gradients, temperature spectra, and heat transport. We find that the half power law (z−1/2, where z is the height above the surface) form of the temperature profile reflects the change in plume cross-sectional area with height and that this is consistent with the mixed length scale required to collapse the peak regions of temperature spectra above the surface friction layer (SFL). We introduce new scaling results for temperature spectra and heat flux cospectra that extend this relationship to most of the SFLs. The spectral properties change in the bottom tenth of the SFL, where the temperature profile becomes logarithmic and temperature fluctuations increasingly display Gaussian statistics. At such small heights, the self-similarity property of the plumes reflects their randomness rather than self-similarity in the order observed above. We conclude with a general discussion, contrasting our interpretation of the role of buoyancy, as being associated with the largest structures in CBL flows, with that of Richardson [Proc. R. Soc. A 87, 354–373 (1920)], who neglected large structures and assumed that it acts locally, on the small eddies. Richardson’s ideas still inform the currently accepted, statistical fluid mechanics model of boundary-layer flows.

We report empirical scaling results of heat and momentum cospectra at heights above the surface friction layer but well within the bottom tenth of the convective boundary layer (CBL), also known as the local free-convection layer. We perform scaling analysis using two field datasets, based on McNaughton et al. (Nonlinear Process Geophys 14:257–271, 2007), and discuss the results using their structural model of CBL turbulence as an untested hypothesis. Using their scaling parameter set, the scaled heat cospectra from the two experiments collapse in small, mid, and large wavenumber ranges as in the reported temperature spectra. The empirical results show: (1) at small wavenumbers, the heat cospectra scale with a length scale $$ \lambda $$ and an amplitude scale $$ H_{0} (z/\lambda )^{1/2} $$ , where $$ \lambda $$ is the peak wavelength of the streamwise velocity spectrum, $$ z $$ is the height above the surface, and $$ H_{0} $$ is the kinematic heat flux at the surface, (2) at mid wavenumbers, the heat-cospectral peak positions and heights scale with a doubly-mixed length scale $$ \lambda^{1/4} z^{3/4} $$ and an amplitude scale $$ H_{0} (z/\lambda )^{1/12} $$ , and (3) at large wavenumbers, the heat cospectra scale with a length scale $$ z $$ and an amplitude scale $$ H_{0} $$ . However, the momentum cospectra resist a similar scaling analysis and display erratic peaks at small wavenumbers. The wavelet analysis of heat and momentum flux time series shows this is related to poor sampling of the momentum flux carried at small wavenumbers.

We survey temperature patterns and heat transport in convective boundary layers (CBLs) from the perspective that these are emergent properties of far-from-equilibrium, complex dynamical systems. We use the term 'plumes' to denote the temperature patterns, in much the same way that the term 'eddies' is used to describe patterns of motion in turbulent flows. We introduce a two-temperature (2T) toy model to connect the scaling properties of temperature gradients, temperature variance and heat transport to the geometric properties of plumes. We then examine temperature (T) probability density functions and w-T joint probability density functions, T spectra and wT cospectra observed both within and above the surface friction layer. Here w is vertical velocity. We interpret these in terms of the properties of the plumes that give rise to them. We focus first on the self-similarity property of the plumes above the SFL, and then introduce new scaling results from within the SFL, which show that T spectra and wT cospectra are not self-similar with height at small heights z/zs

Temperature variance and temperature power spectra in the unstable surface layer have always presented a problem to the standard Monin-Obukhov similarity model. Recently that problem has intensified with the demonstration by Smedman et al. (2007, Q J Roy Meteorol Soc 133: 37–51) that temperature spectra and heat-flux cospectra can have two distinct peaks in slightly unstable conditions, and by McNaughton et al. (2007, Nonlinear Process Geophys 14: 257–271) who showed that the wavenumber of the peak of temperature spectra in a convective boundary layer (CBL), closely above the surface friction layer (SFL), can be sensitive to the CBL depth, z i. Neither the two-peak form at slight instability nor the dependence of peak position on z i at large instability is compatible with the Monin-Obukhov model. Here we examine the properties of temperature spectra and heat-flux cospectra from between these extremes, i.e. from within the unstable SFL, in two experiments. The analysis is based on McNaughton’s model of the turbulence structure in the SFL. According to this model, heat is transported through most of the SFL by sheet plumes, created by the action of impinging outer eddies. The smallest and most effective of these outer eddies have sizes that scale on SFL depth, z s. The z s-scale eddies and plumes are organised within the overall convection pattern in the CBL, and in turn they organise the motion of smaller eddies within the SFL, whose sizes scale on height, z. The main experimental results are: (1) the peak amplitudes of the temperature spectra in the SFL are collapsed with a scaling factor $${(z_{\rm s}z)^{1/3}\varepsilon_{\rm o}^{2/3}}$$ divided by the square of the surface temperature flux, where $${\varepsilon_{\rm o}}$$ is the dissipation rate of turbulent energy in the outer CBL (above the SFL); (2) the peak wavenumbers of the temperature spectra are collapsed with the mixed length scale (z i z s)1/2; (3) the peak wavenumbers of the heat-flux cospectra are collapsed with the doubly-mixed length scale (z i z s)1/4 z 1/2; (4) for z/z s

We present a new account of the kinetic energy budget within an unstable atmospheric surface layer (ASL) beneath a convective outer layer. It is based on the structural model of turbulence introduced by McNaughton (Boundary-Layer Meteorology, 112: 199–221, 2004). In this model the turbulence is described as a self-organizing system with a highly organized structure that resists change by instability. This system is driven from above, with both the mean motion and the large-scale convective motions of the outer layer creating shear across the surface layer. The outer convective motions thus modulate the turbulence processes in the surface layer, causing variable downwards fluxes of momentum and kinetic energy. The variable components of the momentum flux sum to zero, but the associated energy divergence is cumulative, increasing both the average kinetic energy of the turbulence in the surface layer and the rate at which that energy is dissipated. The tendency of buoyancy to preferentially enhance the vertical motions is opposed by pressure reaction forces, so pressure production, which is the work done against these reaction forces, exactly equals buoyant production of kinetic energy. The pressure potential energy that is produced is then redistributed throughout the layer through many conversions, back and forth, between pressure potential and kinetic energy with zero sums. These exchanges generally increase the kinetic energy of the turbulence, the rate at which turbulence transfers momentum and the rate at which it dissipates energy, but does not alter its overall structure. In this model the velocity scale for turbulent transport processes in the surface layer is (kzɛ)1/3 rather than the friction velocity, u*. Here k is the von Karman constant, z is observation height, ɛ is the dissipation rate. The model agrees very well with published experimental results, and provides the foundation for the new similarity model of the unstable ASL, replacing the older Monin–Obukhov similarity theory, whose assumptions are no longer tenable.

We investigate the production components of turbulent spectra within logarithmic layers over flat ground. This assumes that the turbulence giving rise to these spectra consists of active coherent structures (eddies) that are attached to the ground, and whose properties display perfect statistical self-similarity under inner scaling. That is, we take the extreme view that active coherent structures not only contribute to turbulence production spectra but explain the whole of them, so that neither detached eddies nor unstructured motions make any significant contribution. Perfect self-similarityis held to apply only to eddies that are themselves formed totally within the log layer, so the theory applies in the limit of spectra obtained at the hearts of very deep log layers. The model predicts that spectral variance and covariance should become independent of wavenumber at small wavenumbers. This asymptotic behaviour is observed in all neutral spectra from the Kansas experiment. The model also interprets the various positions of the spectral peaks observed at Kansas and in aircraft flights over the sea as consequences of the eddies being aggregated into files aligned with the wind. The observed spectra are therefore consistent with large-scale wedge-like structures being the principal component of active turbulence in the neutral atmospheric surface layer.

This paper reports power spectra and cospectra of windspeed and several scalars measured at two heights nearthe base of an advective inversion. The inversion hadformed over a paddy field downwind of an extensive dryregion. Winds over the paddy field were variable instrength and direction, as a result of convectivemotions in the atmospheric boundary layer passing overfrom the dry region upwind. Fetch over the rice waslarge enough that advective effects on the transportprocesses were small at the upper level and negligibleat the lower level. Results from the lower level areinterpreted in terms of a horizontally homogeneous,but disturbed, surface layer.

We investigate flux underestimates in eddy correlation measurements that are caused by horizontal separation of the sensors. A common eddy correlation setup consists of a sonic anemometer and a humidity sensor which, because of its bulk, must be placed some distance away from the sonic path, leading to a flux loss (of latent heat). Utilizing an additional fast temperature sensor placed near the humidity sensor, we develop a procedure for correcting for this loss. The procedure simultaneously corrects the sensible heat flux for the difference between true temperature and sonic temperature. Our correction procedure, which does not depend on the shape of the cospectrum, is then compared to the widely-used procedure following Moore (1986), which assumes a cospectral model ('Kansas Model’). Both correction methods are applied to data collected within the internal boundary layer over a rice paddy, downwind of arid land. Under conditions of good fetch, they were found to agree well. Under poor fetch conditions, the model-based correction tended to be too small, while the spectrum-independent combined correction was robust. The latter is thus recommended for situations where the cospectral shape can be expected to deviate from the 'Kansas’ shape.

This paper examines the effect of non-stationarity of the wind on similarity of the eddy diffusivities for heat and vapour within a stable layer at the bottom of an internal boundary layer formed downwind of a dry-to-wet transition. First, we present some experimental data taken above a rice crop downwind of very extensive dry range lands at Warrawidgee, NSW, Australia. These data establish that periods of higher wind speed were associated with periods of higher saturation deficit in the canopy of the rice crop, and lower Bowen ratio. It is shown that Bowen ratios calculated for 30-second sub-intervals varied three-fold within a single 20-minute averaging period. Thus periods of higher wind speed corresponded to periods of higher moisture flux and smaller sensible heat flux. An idealized situation is then analysed theoretically. It is assumed that the time scale of the slow variations of the wind is long compared with the surface-layer time scale and that fetch is sufficient that the air near the ground is in continuous equilibrium with the surface. Using a two-scale Reynolds decomposition of the fluctuating wind and scalar variables into active and inactive components, it is shown that unsteadiness can lead to an eddy diffusivity for saturation deficit, calculated as the ratio of average flux to average gradient, that is larger than that for total energy calculated in a similar way. Using this ratio to calculate the ratio of diffusivities for temperature and humidity, KT/Kq, it is found that the latter can be much larger than one if the Bowen ratio is small and negative. Despite this, assuming KT = Kq and using the Bowen ratio method to calculate surface energy fluxes will usually incur only minor errors.

Journal policy on the use of units and notation is presented. A list of preferred symbols is included.

International audience; Townsend's hypothesis states that turbulence near a wall can be divided into an active part that transports momentum, and an inactive part that does not, and that these two kinds of turbulence do not interact. Active turbulence is generated by wind shear and has properties that scale on local parameters of the flow, while inactive turbulence is the product of energetic processes remote from the surface and scales on outer-layer parameters. Both kinds of motion can be observed in the atmospheric surface layer, so Monin-Obukhov similarity theory, which is framed in terms of local parameters only, can apply only to active motions. If Townsend's hypothesis were wrong, so that active and inactive motions do interact in some significant way, then transport processes near the ground would be sensitive to outer-layer parameters such as boundary-layer depth, and Monin-Obukhov theory would fail. Experimental results have shown that heat transport near the ground does depend on processes in the outer layer. We propose a mechanism for this whereby inactive motions initiate active, coherent ejection/sweep structures that carry much of the momentum and heat. We give evidence that the inactive motions take the form of streak patterns of faster and slower air, and argue that these are induced by the pressure effects of large eddies passing overhead. The streak pattern includes regions where faster streams of air overtake and engulf slower-moving streaks. Transverse vortices form across the spines of the streaks at these places and some of them develop into horseshoe vortices. These horseshoe vortices grow rapidly and are rotated forward in the sheared flow so they soon contact the ground, squirting the air confined between the legs of the horseshoe vortex outwards as a forceful ejection. This model is consistent with a wide range of results from the field and laboratory experiments. Heat transport is significantly affected, so undermining the dimensional assumptions of Monin-Obukhov similarity theory.

International audience; We present results from an experiment that was designed to investigate turbulent transport relationships in a nearly homogeneous boundary layer disturbed by unsteady wind swings, as found at the base of an advective inversion with a convective boundary layer overhead. In such a situation we measured vertical gradients and eddy fluxes of temperature and humidity at two heights. From these, the turbulent diffusivities of heat and water vapour are obtained, and compared to the predictions of Monin-Obukhov similarity theory and those of a numerical second-order closure model. It is found that the measured diffusivities exceed both predictions. This is interpreted as a consequence of the unsteady conditions. It is also found that the diffusivity for heat is roughly 10% larger than that for water vapour. This is in agreement with a theoretical treatment of the unsteadiness effects that we developed in an earlier publication. This result is not reproduced by the numerical model because the model has no provision for unsteady conditions. Our result disagrees with that from an earlier, very similar, field experiment, which may be due to a systematic underestimation of sensible heat flux in the older experiment.