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- Author or Editor: R. C. Srivastava x
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Abstract
The effect of discrete sampling on the measurement of the root mean square frequency f rms of the Doppler spectrum by the bipolar video zero-crossing rate method is discussed. It is shown that discrete sampling results in an underestimate of f rms. A method of correcting for the underestimate is suggested. Conditional positive and negative axis-crossing rates, or the rates at which the signal vector crosses a phase angle in the counterclockwise and clockwise directions, are defined and shown to be equal to (f rms + f̄)/2 and (f rms − f̄)/2, respectively, where f̄ is the mean of the Doppler spectrum of the signal. This result suggests that the conditional axis-crossing rates may be used for the measurement of spectrum mean and variance. The effect of discrete sampling on the conditional axis-crossing rates is also discussed.
Abstract
The effect of discrete sampling on the measurement of the root mean square frequency f rms of the Doppler spectrum by the bipolar video zero-crossing rate method is discussed. It is shown that discrete sampling results in an underestimate of f rms. A method of correcting for the underestimate is suggested. Conditional positive and negative axis-crossing rates, or the rates at which the signal vector crosses a phase angle in the counterclockwise and clockwise directions, are defined and shown to be equal to (f rms + f̄)/2 and (f rms − f̄)/2, respectively, where f̄ is the mean of the Doppler spectrum of the signal. This result suggests that the conditional axis-crossing rates may be used for the measurement of spectrum mean and variance. The effect of discrete sampling on the conditional axis-crossing rates is also discussed.
Abstract
Some computations of the evolution of raindrop-size distributions under the operation of the processes of drop breakup and coalescence are presented. It is found that the size distribution approaches a stationary state. The stationary size distributions for different rainfall rates are roughly parallel to each other when logf(r) is plotted against r, f(r) being the concentration density of drops of radius r. A comparison with observations shows that the computed distributions are flatter than the observed ones. It is suggested that other processes besides the breakup and coalescence of raindrops shape their distribution with size.
Abstract
Some computations of the evolution of raindrop-size distributions under the operation of the processes of drop breakup and coalescence are presented. It is found that the size distribution approaches a stationary state. The stationary size distributions for different rainfall rates are roughly parallel to each other when logf(r) is plotted against r, f(r) being the concentration density of drops of radius r. A comparison with observations shows that the computed distributions are flatter than the observed ones. It is suggested that other processes besides the breakup and coalescence of raindrops shape their distribution with size.
Abstract
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Abstract
A ono-dimensioral time-dependent model of a downdraft driven by the melting and evaporation of precipitation and precipitation loading is formulated. Equations for particle melting, particle evaporation, particle concentration, precipitation content, thermodynamic energy, and vertical air velocity are formulated and solved numerically. In the environment, the lapse rate of temperature and the relative humidity are prescribed. At the top of the downdraft column, the temperature, relative humidity, vertical air velocity, and the phase and size distribution of the precipitation particles are prescribed. Two types of particle size distribution are considered: a distribution consisting of a single exponential function of the negative of the particle diameter, and a distribution consisting of two exponential functions of different slopes joining continuously at a melted diameter of 3 mm. The effects of lapse rate of environmental temperature, precipitation content, its phase and size distribution on the intensity of the downdraft are examined. With lapse rate of temperature approaching the dry-adiabatic value, even very light precipitation can drive intense downdraft. As the stability of the thermal stratification is increased, progressively higher precipitation contents and eventually high precipitation contents in the form of ice are needed to drive intense downdraft. A size distribution of precipitation particles having a relative abundance of smaller particles also favors intense downdrafts. The downdraft can be driven solely below cloud base provided the cloud delivers the necessary precipitation at its base. A comparison with available meager observations of wet downbursts lends support to these results. Observations of the lapse rate of temperature and precipitation content, including its phase and size distribution, in situations of wet downbursts are recommended.
Abstract
A ono-dimensioral time-dependent model of a downdraft driven by the melting and evaporation of precipitation and precipitation loading is formulated. Equations for particle melting, particle evaporation, particle concentration, precipitation content, thermodynamic energy, and vertical air velocity are formulated and solved numerically. In the environment, the lapse rate of temperature and the relative humidity are prescribed. At the top of the downdraft column, the temperature, relative humidity, vertical air velocity, and the phase and size distribution of the precipitation particles are prescribed. Two types of particle size distribution are considered: a distribution consisting of a single exponential function of the negative of the particle diameter, and a distribution consisting of two exponential functions of different slopes joining continuously at a melted diameter of 3 mm. The effects of lapse rate of environmental temperature, precipitation content, its phase and size distribution on the intensity of the downdraft are examined. With lapse rate of temperature approaching the dry-adiabatic value, even very light precipitation can drive intense downdraft. As the stability of the thermal stratification is increased, progressively higher precipitation contents and eventually high precipitation contents in the form of ice are needed to drive intense downdraft. A size distribution of precipitation particles having a relative abundance of smaller particles also favors intense downdrafts. The downdraft can be driven solely below cloud base provided the cloud delivers the necessary precipitation at its base. A comparison with available meager observations of wet downbursts lends support to these results. Observations of the lapse rate of temperature and precipitation content, including its phase and size distribution, in situations of wet downbursts are recommended.
Abstract
A simple one-dimensional, time-dependent model of an evaporatively driven downdraft is presented. The model is described by equations for raindrop evaporation, raindrop concentration, water substance, thermodynamic energy and vertical air velocity. At the top of the downdraft, the pressure, temperature, relative humidity, vertical air velocity and the raindrop size distribution are specified; Marshall–Palmer and monodisperse drop size distributions are considered. The environment of the downdrafts is assumed to be still and steady and is specified by the height distributions of temperature and water vapor. The bottom of the downdraft is considered to be open. Calculations are presented for downdrafts developing in the subcloud layer of high-based cumulus. It is found that the intensity of the downdraft at the bottom of the column, increases with 1) increasing lapse rate of temperature in the environment, 2) increasing rainwater mixing ratio at the top of the downdraft 3) increasing relative humidity of the environment and 4) decreasing raindrop size; it decreases with increasing mixing of environmental air into the downdraft. At the bottom, the downdraft is usually very dry, and its temperature does not differ from that of the environment by more than a few degrees; a cooling is observed only at high rainwater mixing ratio and lapse rate of temperature close to the dry adiabatic. In relatively stable lapse rates, weak oscillatory motion and transient formation of “scud” cloud are found to occur. A comparison with microburst observations during the Joint Airport Weather Study (JAWS) Project suggests that a majority of those microbursts was evaporatively driven, and originated near the cloud base.
Abstract
A simple one-dimensional, time-dependent model of an evaporatively driven downdraft is presented. The model is described by equations for raindrop evaporation, raindrop concentration, water substance, thermodynamic energy and vertical air velocity. At the top of the downdraft, the pressure, temperature, relative humidity, vertical air velocity and the raindrop size distribution are specified; Marshall–Palmer and monodisperse drop size distributions are considered. The environment of the downdrafts is assumed to be still and steady and is specified by the height distributions of temperature and water vapor. The bottom of the downdraft is considered to be open. Calculations are presented for downdrafts developing in the subcloud layer of high-based cumulus. It is found that the intensity of the downdraft at the bottom of the column, increases with 1) increasing lapse rate of temperature in the environment, 2) increasing rainwater mixing ratio at the top of the downdraft 3) increasing relative humidity of the environment and 4) decreasing raindrop size; it decreases with increasing mixing of environmental air into the downdraft. At the bottom, the downdraft is usually very dry, and its temperature does not differ from that of the environment by more than a few degrees; a cooling is observed only at high rainwater mixing ratio and lapse rate of temperature close to the dry adiabatic. In relatively stable lapse rates, weak oscillatory motion and transient formation of “scud” cloud are found to occur. A comparison with microburst observations during the Joint Airport Weather Study (JAWS) Project suggests that a majority of those microbursts was evaporatively driven, and originated near the cloud base.
Abstract
No abstract available.
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Abstract
The currently accepted theory of the growth of cloud drops by condensation employs an equation for the rate of increase of drop mass and an equation for the supersaturation. The latter equation gives the average supersaturation over a large volume, or the macroscopic supersaturation. Use of this supersaturation in the equation for the growth of cloud drops is criticized. In a first approach at a microscopic theory, the average supersaturation over the volume occupied by a drop, called the microscopic supersaturation, is used to calculate the growth of the drop. The microscopic supersaturation can differ from drop to drop due to randomness in their spatial distribution and is affected differently by fluctuations of vertical air velocity than the macroscopic supersaturation. In a second approach at a microscopic theory, the diffusion equations for water vapor and heat, together with appropriate boundary conditions, are solved for an assemblage of drops. It is shown again that a microscopic supersaturation may be defined for calculating drop growth and that this supersaturation can also differ from drop to drop and responds differently to vertical air velocity fluctuations than the macroscopic supersaturation. In the microscopic approaches both the random distribution of drops and vertical air velocity fluctuations can affect the growth of cloud drops by condensation; this is in contrast to conclusions drawn from the currently accepted theory. Estimates of the variance of the microscopic supersaturation are given. It is shown that diffusive interactions between drops in a population can be neglected if the dimensionless parameter [(l */r 0) (Dτ)] where l * is the volume fraction of the drops, r 0 is a typical drop radius, D is the diffusivity, and τ is the age of the diffusion process, is very small compared to unity.
Abstract
The currently accepted theory of the growth of cloud drops by condensation employs an equation for the rate of increase of drop mass and an equation for the supersaturation. The latter equation gives the average supersaturation over a large volume, or the macroscopic supersaturation. Use of this supersaturation in the equation for the growth of cloud drops is criticized. In a first approach at a microscopic theory, the average supersaturation over the volume occupied by a drop, called the microscopic supersaturation, is used to calculate the growth of the drop. The microscopic supersaturation can differ from drop to drop due to randomness in their spatial distribution and is affected differently by fluctuations of vertical air velocity than the macroscopic supersaturation. In a second approach at a microscopic theory, the diffusion equations for water vapor and heat, together with appropriate boundary conditions, are solved for an assemblage of drops. It is shown again that a microscopic supersaturation may be defined for calculating drop growth and that this supersaturation can also differ from drop to drop and responds differently to vertical air velocity fluctuations than the macroscopic supersaturation. In the microscopic approaches both the random distribution of drops and vertical air velocity fluctuations can affect the growth of cloud drops by condensation; this is in contrast to conclusions drawn from the currently accepted theory. Estimates of the variance of the microscopic supersaturation are given. It is shown that diffusive interactions between drops in a population can be neglected if the dimensionless parameter [(l */r 0) (Dτ)] where l * is the volume fraction of the drops, r 0 is a typical drop radius, D is the diffusivity, and τ is the age of the diffusion process, is very small compared to unity.
Abstract
A simple model of the evolution of particle size distributions by coalescence and spontaneous and binary disintegrations is formulated. Spontaneous disintegration involves single particles, while coalescence and binary disintegrations involve pairs of particles. Analytical solutions for the mean mass of the distribution and the equilibrium size distribution are obtained for the case of constant collection kernel and disintegration parameters. At equilibrium, the forms of the size distributions are identical under the action of coalescence and either or both disintegration processes; the particle concentration is proportional to the total mass concentration (M) and the mean mass of the distribution is independent of M when only coalescence and binary disintegrations are operative. At small values of M, the effects of spontaneous disintegrations dominate over those of binary disintegrations while the reverse is the case at large values of M. Some of the findings of the present simple model are in qualitative agreement with the results of numerical calculations of the evolution of raindrop size spectra with realistic formulations of drop coalescence and breakup.
Abstract
A simple model of the evolution of particle size distributions by coalescence and spontaneous and binary disintegrations is formulated. Spontaneous disintegration involves single particles, while coalescence and binary disintegrations involve pairs of particles. Analytical solutions for the mean mass of the distribution and the equilibrium size distribution are obtained for the case of constant collection kernel and disintegration parameters. At equilibrium, the forms of the size distributions are identical under the action of coalescence and either or both disintegration processes; the particle concentration is proportional to the total mass concentration (M) and the mean mass of the distribution is independent of M when only coalescence and binary disintegrations are operative. At small values of M, the effects of spontaneous disintegrations dominate over those of binary disintegrations while the reverse is the case at large values of M. Some of the findings of the present simple model are in qualitative agreement with the results of numerical calculations of the evolution of raindrop size spectra with realistic formulations of drop coalescence and breakup.
Abstract
The processes of condensation, coalescence and drop breakup tend to produce exponential raindrop size spectra. The intercept n 0 and slope λ of the exponential distribution are given by differential equations expressing the conservation of raindrop concentration and rainwater content M. The differential equations are solved numerically using published experimental data on coalescence efficiency and spontaneous breakup. The number of fragments resulting from a collisional breakup S 0 is taken as a variable parameter. Calculations show that 1) the effects of collisional breakup usually predominate over those of spontaneous breakup, 2) for dM/dt=0, a stationary λ results which is a function of S 0, and 3) for dM/dt>0, λ tends to a quasi-static value which depends upon S 0 and (1/M 2) (dM/dt) but is close to the stationary value for the same S 0. In each case n 0 is determined by the values of λ and M. Binary interactions, i.e., drop coalescence and collisional breakup, tend to produce raindrop size spectra which have approximately constant λ and an n 0 approximately proportional to M. A method of parameterization for cumulus dynamics models is suggested in which both n 0 and λ are calculated.
Abstract
The processes of condensation, coalescence and drop breakup tend to produce exponential raindrop size spectra. The intercept n 0 and slope λ of the exponential distribution are given by differential equations expressing the conservation of raindrop concentration and rainwater content M. The differential equations are solved numerically using published experimental data on coalescence efficiency and spontaneous breakup. The number of fragments resulting from a collisional breakup S 0 is taken as a variable parameter. Calculations show that 1) the effects of collisional breakup usually predominate over those of spontaneous breakup, 2) for dM/dt=0, a stationary λ results which is a function of S 0, and 3) for dM/dt>0, λ tends to a quasi-static value which depends upon S 0 and (1/M 2) (dM/dt) but is close to the stationary value for the same S 0. In each case n 0 is determined by the values of λ and M. Binary interactions, i.e., drop coalescence and collisional breakup, tend to produce raindrop size spectra which have approximately constant λ and an n 0 approximately proportional to M. A method of parameterization for cumulus dynamics models is suggested in which both n 0 and λ are calculated.
