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- Author or Editor: J. W. Telford x
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Abstract
In this paper the equations for a field of convective plumes are non-dimensionalized. These were derived in an earlier paper by formulating a model which included turbulence as an independent property with a specific kinetic energy. The numerical solutions previously discussed are extended so as to cover all conditions. It is shown that two non-dimensional parameters fully determine the solutions obtained.
The field consists of plumes rising up to a level where the stability of the overlying air forces the air to turn about and descend again between the plumes to the surface. The model uses the beat flux, the layer depth, and the surface turbulence intensity (rms turbulent velocity) as parameters and does not include the wind specifically. The previous cases of the field solutions showed properties similar to those observed in atmospheric convection, as then discussed, and this paper extends the number of solutions so the general behavior becomes clear. These results show how there is likely to be a limit to the maximum depth of the layer and suggest that a different form of convection may be expected when heating continues after this depth is reached. The variation of this depth is discussed in terms of changing surface turbulence and heat flux or rate of temperature increase.
Abstract
In this paper the equations for a field of convective plumes are non-dimensionalized. These were derived in an earlier paper by formulating a model which included turbulence as an independent property with a specific kinetic energy. The numerical solutions previously discussed are extended so as to cover all conditions. It is shown that two non-dimensional parameters fully determine the solutions obtained.
The field consists of plumes rising up to a level where the stability of the overlying air forces the air to turn about and descend again between the plumes to the surface. The model uses the beat flux, the layer depth, and the surface turbulence intensity (rms turbulent velocity) as parameters and does not include the wind specifically. The previous cases of the field solutions showed properties similar to those observed in atmospheric convection, as then discussed, and this paper extends the number of solutions so the general behavior becomes clear. These results show how there is likely to be a limit to the maximum depth of the layer and suggest that a different form of convection may be expected when heating continues after this depth is reached. The variation of this depth is discussed in terms of changing surface turbulence and heat flux or rate of temperature increase.
Abstract
This paper examines in detail some of the assumptions previously used by the author in modeling the convective boundary layer. It has been customary to mathematically model atmospheric convection with plumes and blobs in which the air is taken to be incompressible in analogy with the fluid in water tank models used in the past to justify much of this work. It is not always clear in formulating such equations what exactly are the approximations thus introduced as the physical foundation of the model, and this is a point of confusion detracting from the main work. This paper shows that the modification needed to accurately account for the compressibility of the air is simple and the changes resulting in the final variables negligible. The effect that turbulence and its decay to heat have on the density used in the model is discussed and its omission is shown to be justified.
Abstract
This paper examines in detail some of the assumptions previously used by the author in modeling the convective boundary layer. It has been customary to mathematically model atmospheric convection with plumes and blobs in which the air is taken to be incompressible in analogy with the fluid in water tank models used in the past to justify much of this work. It is not always clear in formulating such equations what exactly are the approximations thus introduced as the physical foundation of the model, and this is a point of confusion detracting from the main work. This paper shows that the modification needed to accurately account for the compressibility of the air is simple and the changes resulting in the final variables negligible. The effect that turbulence and its decay to heat have on the density used in the model is discussed and its omission is shown to be justified.
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The process of growth by coalescence is examined from the viewpoint of a discrete rather than a continuous accretion process. It is concluded that, for drops beginning growth at twice the volume of their neighbors, random fluctuations in the times taken for different drops to effect captures can lead to the formation of a complete raindrop spectrum in times shorter than that required for growth to raindrop size by the continuous growth process.
Under typical conditions, drops of 23-microns radius can form in the order of 5 minutes in a cloud of droplets of 10 microns, while smaller numbers of much larger drops can be expected in reasonable times. The latter are likely to be important in chain-reaction theories.
Abstract
The process of growth by coalescence is examined from the viewpoint of a discrete rather than a continuous accretion process. It is concluded that, for drops beginning growth at twice the volume of their neighbors, random fluctuations in the times taken for different drops to effect captures can lead to the formation of a complete raindrop spectrum in times shorter than that required for growth to raindrop size by the continuous growth process.
Under typical conditions, drops of 23-microns radius can form in the order of 5 minutes in a cloud of droplets of 10 microns, while smaller numbers of much larger drops can be expected in reasonable times. The latter are likely to be important in chain-reaction theories.
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This is a theoretical study of an isolated plume in still air. Previous work, based on similarity concepts to give the mixing rates, is shown to be inadequate, and a new hypothesis is proposed which appears to lead to better agreement with present measurements made in the atmosphere. In particular, the similarity theory does not allow realistic initial conditions to be taken at the bottom of the plume. When the new theory is adjusted to these conditions a substantial change (in the direction needed to fit the observations) is seen in the shape of the new plume as compared to the previous similarity model.
Abstract
This is a theoretical study of an isolated plume in still air. Previous work, based on similarity concepts to give the mixing rates, is shown to be inadequate, and a new hypothesis is proposed which appears to lead to better agreement with present measurements made in the atmosphere. In particular, the similarity theory does not allow realistic initial conditions to be taken at the bottom of the plume. When the new theory is adjusted to these conditions a substantial change (in the direction needed to fit the observations) is seen in the shape of the new plume as compared to the previous similarity model.
Abstract
From observations made from the ground and from aircraft it is considered that clear air thermals are continuing plumes. They form above the forced convection region near the surface; initially their temperature excess is about 1C, their size 200 m, and upward velocity about 1 m sec−1. The thermals rise through a neutral to slightly stable environment of thermally quiet, slowly descending air; however, the air both inside and outside the thermal is strongly turbulent. The thermal initially accelerates upwards and probably decreases in size. Air is continually mixing into and out of the thermal, and at levels above about 100 m the size remains sensibly constant. The whole field increases in temperature, partly as a result of the detrainment of warm air from the thermals and partly from downward motion of their stable environment.
Abstract
From observations made from the ground and from aircraft it is considered that clear air thermals are continuing plumes. They form above the forced convection region near the surface; initially their temperature excess is about 1C, their size 200 m, and upward velocity about 1 m sec−1. The thermals rise through a neutral to slightly stable environment of thermally quiet, slowly descending air; however, the air both inside and outside the thermal is strongly turbulent. The thermal initially accelerates upwards and probably decreases in size. Air is continually mixing into and out of the thermal, and at levels above about 100 m the size remains sensibly constant. The whole field increases in temperature, partly as a result of the detrainment of warm air from the thermals and partly from downward motion of their stable environment.
