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- Author or Editor: F. T. M. Nieuwstadt x

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## Abstract

The application of a self-similar profile in the integration of the temperature equation across the stable boundary layer leads to a rate equation for the inversion height. An analytic solution of the resulting equation is derived. Its behavior is determined by two processes; cooling by turbulent mixing and cooling by internal radiation, the latter is parameterized in terms of the surface cooling rate. This parameterization, which attributes the temperature change in the boundary layer close to the surface completely to internal radiation, leads to a monotonic growth of the inversion depth. When the radiation term is neglected and only the turbulent heat flux is taken into account, the solution is governed by a relaxation process.

## Abstract

The application of a self-similar profile in the integration of the temperature equation across the stable boundary layer leads to a rate equation for the inversion height. An analytic solution of the resulting equation is derived. Its behavior is determined by two processes; cooling by turbulent mixing and cooling by internal radiation, the latter is parameterized in terms of the surface cooling rate. This parameterization, which attributes the temperature change in the boundary layer close to the surface completely to internal radiation, leads to a monotonic growth of the inversion depth. When the radiation term is neglected and only the turbulent heat flux is taken into account, the solution is governed by a relaxation process.

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## Abstract

The laboratory experiments of Deardorff and Willis have shown that the dispersion from a low-level source under convective conditions follows mixed-layer similarity. The convective runs of the Prairie Grass dispersion experiment are reanalyzed in this paper. It turns out that mixed-layer similarity scaling also works well for this classic field experiment. The observed cross-wind-integrated concentration closely matches the laboratory results. The observed lateral dispersion coefficients are somewhat larger than those given by Deardorff and Willis.

## Abstract

The laboratory experiments of Deardorff and Willis have shown that the dispersion from a low-level source under convective conditions follows mixed-layer similarity. The convective runs of the Prairie Grass dispersion experiment are reanalyzed in this paper. It turns out that mixed-layer similarity scaling also works well for this classic field experiment. The observed cross-wind-integrated concentration closely matches the laboratory results. The observed lateral dispersion coefficients are somewhat larger than those given by Deardorff and Willis.

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## Abstract

A large number of turbulence observations were made under stable conditions along a meteorological mast at Cabauw, The Netherlands. To present and organize these data we turn to the parameterized equations for the turbulent variances and covariances. In a dimensionless form these equations lead to a local scaling hypothesis. According to this hypothesis, dimensionless combinations of variables which are measured at the same height can be expressed as a function of a single parameter *z*/Î›. Here, Î› is called a local Obukhov length and is defined as Î›=âˆ’Ï„^{3/2}
*T*/(kgwÎ¸) where Ï„ and *w*Î¸) are the kinematic momentum and heat flux, respectively. Note that, in general, Î› may vary across the boundary layer, because Ï„ and *wÎ¸* are still unknown functions of height. The observations support local scaling. In particular, they agree with the limit condition for *z*/Î›â†’âˆž, which predicts that locally scaled variables approach a constant value. The latter result is called *z*-less stratification. An important application of *z*-less stratification is that both the Richardson number and flux Richardson number should become constant in the stable boundary layer. Next we turn to the vertical profiles of Ï„ and *w*Î¸. These profiles can be obtained in principle from a simple boundary-layer model which uses as a closure hypothesis the constant Richardson number and flux Richardson number. The solution for steady-sate conditions loads to *w*Î¸/*w*Î¸_{0};=(1âˆ’z/h)) and Ï„/*u*
_{*}
^{2}=((1âˆ’*z*/*h*)^{3/2}, where ;*w*Î¸_{0} and *u*
_{*}
^{2}, are the surface temperature and momentum fluxes, respectively, and *h* is the boundary-layer height. Observations at Cabauw agree reasonably well with these profiles. However, they should not be considered as generally valid similarity expressions.

## Abstract

A large number of turbulence observations were made under stable conditions along a meteorological mast at Cabauw, The Netherlands. To present and organize these data we turn to the parameterized equations for the turbulent variances and covariances. In a dimensionless form these equations lead to a local scaling hypothesis. According to this hypothesis, dimensionless combinations of variables which are measured at the same height can be expressed as a function of a single parameter *z*/Î›. Here, Î› is called a local Obukhov length and is defined as Î›=âˆ’Ï„^{3/2}
*T*/(kgwÎ¸) where Ï„ and *w*Î¸) are the kinematic momentum and heat flux, respectively. Note that, in general, Î› may vary across the boundary layer, because Ï„ and *wÎ¸* are still unknown functions of height. The observations support local scaling. In particular, they agree with the limit condition for *z*/Î›â†’âˆž, which predicts that locally scaled variables approach a constant value. The latter result is called *z*-less stratification. An important application of *z*-less stratification is that both the Richardson number and flux Richardson number should become constant in the stable boundary layer. Next we turn to the vertical profiles of Ï„ and *w*Î¸. These profiles can be obtained in principle from a simple boundary-layer model which uses as a closure hypothesis the constant Richardson number and flux Richardson number. The solution for steady-sate conditions loads to *w*Î¸/*w*Î¸_{0};=(1âˆ’z/h)) and Ï„/*u*
_{*}
^{2}=((1âˆ’*z*/*h*)^{3/2}, where ;*w*Î¸_{0} and *u*
_{*}
^{2}, are the surface temperature and momentum fluxes, respectively, and *h* is the boundary-layer height. Observations at Cabauw agree reasonably well with these profiles. However, they should not be considered as generally valid similarity expressions.

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## Abstract

A rate equation is derived which describes the development of the boundary-layer height under stable conditions as a function of time.

It takes the form of a linear relaxation equation; its solution is forced toward an equilibrium value. The equilibrium height is connected to the work done by the ageostrophic wind in the boundary layer. The time scale of the relaxation process increases monotonically from a few hours shortly after sunset to a value of the order of 10 h later on. This means that the boundary-layer height evolves very slowly, which may lead to the unwarranted impression that stationary conditions have been reached. The main features of the rate equation are confirmed by comparison with the results of computer simulations and with field observations of the boundary-layer height during clear nights.

## Abstract

A rate equation is derived which describes the development of the boundary-layer height under stable conditions as a function of time.

It takes the form of a linear relaxation equation; its solution is forced toward an equilibrium value. The equilibrium height is connected to the work done by the ageostrophic wind in the boundary layer. The time scale of the relaxation process increases monotonically from a few hours shortly after sunset to a value of the order of 10 h later on. This means that the boundary-layer height evolves very slowly, which may lead to the unwarranted impression that stationary conditions have been reached. The main features of the rate equation are confirmed by comparison with the results of computer simulations and with field observations of the boundary-layer height during clear nights.

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## Abstract

With a large-eddy model the large-scale flow structure of the convective boundary layer is simulated in a box of (5 Ã— 5 Ã— 2) km. The calculation is run till the turbulence has reached a quasi-steady state. At that time we introduce a line-source of contaminants and the calculation is continued with an additional equation for the concentration. We consider both passive and buoyant sources. The latter are simulated by increasing the temperature of the line-source with respect to the ambient temperature. We present data for two dimensionless release heights: *z _{s}
*/

*h*= 0.15 and

*z*/

_{s}*h*= 0.48.

For a passive source our results agree well with the results of Willis and Deardorff and the results of the CONDORS experiments.

With respect to a buoyant source we found that the influence of buoyancy on the plume parameters can be described in terms of the dimensionless buoyancy parameter *F*
_{*}; this conclusion is based on runs for *F*
_{*} = 0.01 and *F*
_{*} = 0.02. The simulations for buoyant plumes are compared with the laboratory experiments of Willis and Deardorff and with the field experiments of Carras and Williams. Only with the latter data did we obtain reasonable agreement. In this comparison we paid special attention to a correction for the initial momentum in the field data and to a correction for the initial dimensions of the line-source in the simulation data.

The large-eddy results allow us to distinguish between plume motion caused by convective turbulence and that caused by the plume buoyancy. We found that the plume motion caused by buoyancy does not obey Briggs' 2/3 law, but is more in agreement with a plume rise formula proposed by Nieuwstadt and de Valk which is based on the assumption that the plume grows due to large scale convective turbulence.

## Abstract

With a large-eddy model the large-scale flow structure of the convective boundary layer is simulated in a box of (5 Ã— 5 Ã— 2) km. The calculation is run till the turbulence has reached a quasi-steady state. At that time we introduce a line-source of contaminants and the calculation is continued with an additional equation for the concentration. We consider both passive and buoyant sources. The latter are simulated by increasing the temperature of the line-source with respect to the ambient temperature. We present data for two dimensionless release heights: *z _{s}
*/

*h*= 0.15 and

*z*/

_{s}*h*= 0.48.

For a passive source our results agree well with the results of Willis and Deardorff and the results of the CONDORS experiments.

With respect to a buoyant source we found that the influence of buoyancy on the plume parameters can be described in terms of the dimensionless buoyancy parameter *F*
_{*}; this conclusion is based on runs for *F*
_{*} = 0.01 and *F*
_{*} = 0.02. The simulations for buoyant plumes are compared with the laboratory experiments of Willis and Deardorff and with the field experiments of Carras and Williams. Only with the latter data did we obtain reasonable agreement. In this comparison we paid special attention to a correction for the initial momentum in the field data and to a correction for the initial dimensions of the line-source in the simulation data.

The large-eddy results allow us to distinguish between plume motion caused by convective turbulence and that caused by the plume buoyancy. We found that the plume motion caused by buoyancy does not obey Briggs' 2/3 law, but is more in agreement with a plume rise formula proposed by Nieuwstadt and de Valk which is based on the assumption that the plume grows due to large scale convective turbulence.

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## Abstract

Using simulations with a large-eddy model we have studied the decay of convective turbulence in the atmospheric boundary layer when the upward surface sensible heat flux is suddenly stopped. The decay of turbulent kinetic energy and temperature variance scales with the dimensionless time *tw*
_{*}/*h*. The temperature fluctuations start to decrease almost immediately after the forcing has been removed, whereas the turbulent kinetic energy stays constant for a time *t* â‰ˆ *h*/*w*
_{*}. Vertical velocity fluctuations decay faster than horizontal fluctuations. Entrainment persists well into the decay process and may explain departures from similarity. Some evidence suggests a decoupling of large and small scales during the decay.

## Abstract

Using simulations with a large-eddy model we have studied the decay of convective turbulence in the atmospheric boundary layer when the upward surface sensible heat flux is suddenly stopped. The decay of turbulent kinetic energy and temperature variance scales with the dimensionless time *tw*
_{*}/*h*. The temperature fluctuations start to decrease almost immediately after the forcing has been removed, whereas the turbulent kinetic energy stays constant for a time *t* â‰ˆ *h*/*w*
_{*}. Vertical velocity fluctuations decay faster than horizontal fluctuations. Entrainment persists well into the decay process and may explain departures from similarity. Some evidence suggests a decoupling of large and small scales during the decay.

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## Abstract

This paper discusses the results of a surface-layer experiment near the Cabauw meteorological mast. We measured momentum, heat and moisture fluxes at two heights, namely, 3.5 and 22.5 m. The measurements also include the mean wind speed and mean temperature profiles. The purpose was to investigate surface-layer similarity laws under nonideal fetch conditions. We found that under such conditions, the shell stress increases with height because of obstacles upstream. As a consequence flux-profile relationships differ from those over uniform terrain. It is shown that these deviations imply a slow relaxation in the exchange coefficient for heat and momentum over a terrain with changing surface roughness. Furthermore, we found that horizontal velocity fluctuations scale on a friction velocity representative of a large area. On the other hand, vertical velocity fluctuations scale on the local friction velocity.

## Abstract

This paper discusses the results of a surface-layer experiment near the Cabauw meteorological mast. We measured momentum, heat and moisture fluxes at two heights, namely, 3.5 and 22.5 m. The measurements also include the mean wind speed and mean temperature profiles. The purpose was to investigate surface-layer similarity laws under nonideal fetch conditions. We found that under such conditions, the shell stress increases with height because of obstacles upstream. As a consequence flux-profile relationships differ from those over uniform terrain. It is shown that these deviations imply a slow relaxation in the exchange coefficient for heat and momentum over a terrain with changing surface roughness. Furthermore, we found that horizontal velocity fluctuations scale on a friction velocity representative of a large area. On the other hand, vertical velocity fluctuations scale on the local friction velocity.

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## Abstract

A case study of nocturnal boundary-layer development is presented. The data include observations of turbulence and of profiles of wind and temperature. The measurements were done along a 200 m high meteorological mast.

The observations are interpreted in terms of the results of a one-dimensional boundary-layer model. The model is derived from the full set of equations governing the evolution of the nocturnal boundary layer by neglecting advection. The validity of this approximation is discussed.

From a comparison of observations and calculated results it follows that the influence of advection is important especially in the upper part of the boundary layer. Nevertheless, we find that important characteristics of the nocturnal boundary layer such as its height can be reasonably well simulated by a one-dimensional model.

## Abstract

A case study of nocturnal boundary-layer development is presented. The data include observations of turbulence and of profiles of wind and temperature. The measurements were done along a 200 m high meteorological mast.

The observations are interpreted in terms of the results of a one-dimensional boundary-layer model. The model is derived from the full set of equations governing the evolution of the nocturnal boundary layer by neglecting advection. The validity of this approximation is discussed.

From a comparison of observations and calculated results it follows that the influence of advection is important especially in the upper part of the boundary layer. Nevertheless, we find that important characteristics of the nocturnal boundary layer such as its height can be reasonably well simulated by a one-dimensional model.

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## Abstract

A model is developed to describe the dispersion of pollutants in a coastal area when stable air masses are transported inland. It is assumed that a convective mixed layer develops over land, the height of which increases with distance from the shoreline. The vertical distribution of pollutants is assumed to be homogeneous within the mixed layer and the distribution in the stable layer aloft is assumed to be Gaussian. Pollutant concentrations in the mixed layer are obtained by analytical integration of the mass conservation equation. It is shown that the earlier and much higher estimates of continuous shoreline fumigation by Lyons and Cole (1973) and Meroney *et al*. (1975) can be derived from our expressions by simplifying substitutions.

## Abstract

A model is developed to describe the dispersion of pollutants in a coastal area when stable air masses are transported inland. It is assumed that a convective mixed layer develops over land, the height of which increases with distance from the shoreline. The vertical distribution of pollutants is assumed to be homogeneous within the mixed layer and the distribution in the stable layer aloft is assumed to be Gaussian. Pollutant concentrations in the mixed layer are obtained by analytical integration of the mass conservation equation. It is shown that the earlier and much higher estimates of continuous shoreline fumigation by Lyons and Cole (1973) and Meroney *et al*. (1975) can be derived from our expressions by simplifying substitutions.

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## Abstract

Modifications of turbulence regime in the sheared convective boundary layer (CBL) by a number of external nonbuoyant forcings are studied experimentally in a thermally stratified wind tunnel and numerically by means of large eddy simulation. This type of CBL is observed in the atmosphere when an originally neutral or stable air mass is advected over a heated underlying surface. Emphasis in the present study is laid on the effects of elevated wind shear and surface roughness on the structure and evolution of the CBL. For the flow cases, for which both numerical and wind tunnel results are available, the numerical predictions of mean flow parameters and turbulence statistics are found to be in good agreement with the experimental results.

In the case of wind shear across the inversion layer, the authors distinguish between positive shear, when the flow above the inversion possesses a higher momentum than mean motion in the mixed layer, and the opposite case of negative shear. For the case of positive shear the growth of the CBL is found to be impeded compared to the shear-free case. Negative shear has an opposite effect on the CBL evolution. In this case, the damping of thermals by stable stratification in the inversion layer is weakened compared to the shear-free case and consequently entrainment is activated. A physical explanation for such a directional effect of elevated shear is suggested. In the case of enhanced bottom roughness, both experiments and numerical simulations provide the evidence of slightly larger CBL growth rate compared to the CBL over a relatively smooth surface with a 10 times smaller roughness length.

## Abstract

Modifications of turbulence regime in the sheared convective boundary layer (CBL) by a number of external nonbuoyant forcings are studied experimentally in a thermally stratified wind tunnel and numerically by means of large eddy simulation. This type of CBL is observed in the atmosphere when an originally neutral or stable air mass is advected over a heated underlying surface. Emphasis in the present study is laid on the effects of elevated wind shear and surface roughness on the structure and evolution of the CBL. For the flow cases, for which both numerical and wind tunnel results are available, the numerical predictions of mean flow parameters and turbulence statistics are found to be in good agreement with the experimental results.

In the case of wind shear across the inversion layer, the authors distinguish between positive shear, when the flow above the inversion possesses a higher momentum than mean motion in the mixed layer, and the opposite case of negative shear. For the case of positive shear the growth of the CBL is found to be impeded compared to the shear-free case. Negative shear has an opposite effect on the CBL evolution. In this case, the damping of thermals by stable stratification in the inversion layer is weakened compared to the shear-free case and consequently entrainment is activated. A physical explanation for such a directional effect of elevated shear is suggested. In the case of enhanced bottom roughness, both experiments and numerical simulations provide the evidence of slightly larger CBL growth rate compared to the CBL over a relatively smooth surface with a 10 times smaller roughness length.