Search Results

You are looking at 1 - 5 of 5 items for

  • Author or Editor: Fausto Carlos de Almeida x
  • Refine by Access: All Content x
Clear All Modify Search
Fausto Carlos de Almeida

Abstract

The effects of small-scale cloud turbulent motions on the growth of a droplet spectrum are investigated by numerically solving the stochastic collection growth equation. Four different initial distributions of cloud droplets characterized by different mean mass radii R 0 are analyzed. The growth of these initial droplet distributions using the turbulent collision efficiency function of Almeida and the non-turbulent (still-air) collision efficiency functions of Davis and Sartor and of Almeida are compared. Increased growth rates are obtained for the turbulent collision efficiency functions presented by Almeida.

For initial droplet distributions with R 0 ≤ 8 µm, light to moderate growth rates are observed for the turbulent case, while no growth is observed for the non-turbulent cases. For a droplet distribution of R 0 = 10 µm (typical of a condensation grown cloud droplet distribution), the still-air collection cases still do not product any growth, but the turbulent collection case does produce precipitation-size drops in less than 20 min. For larger mean mass radius distributions, R 0 ≥ 12 µm, both growth cases produce precipitation-size drops, although for the same time interval turbulent growth produces larger concentrations.

The results of these droplet growth calculations are analyzed in connection with understanding warm rain initiation and its consequences in cloud modification experiments.

Full access
Fausto Carlos de Almeida

Abstract

The collision efficiencies for small cloud drops moving under the influence of gravity in a viscous, incompressible, turbulent medium are obtained for drop radii of 10 µm < R 1 < 50 µm and droplet/drop ratios of 0 < R 2/R 1 < 1. For the scales of motion considered, the 2/3 Kolmogorov law defines the cloud's turbulent flow structure, which is assumed to be locally homogeneous and isotropic. Two levels of the rate of energy dissipation per unit mass, e = 1 and c = 10 cm2 s−3, representing typical values for the initial stages of cloud development, are considered. The turbulent collision efficiencies are calculated numerically as outlined in Part I of this study (Almeida, 1976). When compared to the nonturbulent (still-air) collision efficiency values, these turbulent collision efficiencies show remarkable differences. For drop radii of R 1 > 40 µm the differences are negligible. However, for smaller drop radii the turbulent collision efficiencies are much larger than the still-air efficiencies.

Implications of these increased collision efficiencies in the theoretical condensation/still-air collection growth problem are discussed. It is shown, for example, that a drop with a radius of R 1 = 15 µm in a turbulent environment collides more efficiently than does a drop with a radius of R 1 = 25 µm in still air.

Tables are presented with the numerical values of both turbulent and nonturbulent linear collision efficiency functions.

Full access
Fausto Carlos De Almeida

Abstract

Numerical solutions of the collisional problem for small cloud droplets in a nonturbulent, zero-electrical-field condition are obtained by use of the Oseen flow approximation and then compared with other calculations under the same conditions using both the Stokes and Oseen flow approximations. Possible causes for the differences in the gravitational collision efficiency results for unequal size drops are analyzed. It is concluded that calculations using the Stokes or the Oseen flow assumptions should not yield very different results, i.e., the causes of the differences should be numerical rather than physical. It is suggested that some of these numerical differences can be attributed to numerical instabilities appearing in the solution of the equations of motion, errors caused by trial-and-error schemes, and the use of different initial vertical separations for this initial value problem. The possibility that the results of the collisional problem may also be altitude-dependent (within the variations found in real clouds) is also raised. A table of the calculated collision efficiency function is presented. Results for the collision angle and impact velocities are also given.

The effects that the different efficiency results might have on the growth behavior of a cloud droplet population are tested in a stochastic collection growth model. Growth rates up to 4 min faster are found.

Full access
Fausto Carlos De Almeida

Abstract

In the theoretical study of the evolution of a cloud droplet spectrum, the collision kernel function in the stochastic collection growth equation plays an important role in defining its characteristics. To evaluate this kernel function the collisional behavior of isolated pain of cloud droplets is investigated. This constitutes the collisional problem. This problem has been solved in the literature for the case of droplets moving under the action of deterministic forcing fields, such as gravity and electrical forces. Here, we will introduce a new approach to incorporate the case of droplets moving under the action of probabilistic forcing fields, such as turbulence. This has resulted in a more general definition of the collision kernel function. This new collision kernel is shown to be capable of representing not only the turbulent case, but to reduce to the deterministic definition of the kernel function given in the literature. The method of solution includes the numerical solution of the equations of motion for droplet pairs moving in a viscous turbulent environment and the sampling procedure to determine the probability curves of the kernel function as defined in this study. Errors committed in the evaluation of the probability curves, or for that matter, of the kernel function for both deterministic and probabilistic problems are analyzed. The general solutions are outlined.

Full access
Fausto Carlos De Almeida
and
Roger D. Dennett

Abstract

Two schemes for the numerical solution of the stochastic collection growth equation for cloud drops are compared. Their numerical approaches are different. One (the Berry/Reinhardt method) emphasizes accuracy; the other (the Bleck method) emphasizes speed. Our analysis shows that for applications where the number of solutions (time steps) does not exceed 104 the accuracy-oriented scheme is faster. For larger, repetitive applications, such as a comprehensive cloud model, an objective analysis can be made on the merits of exchanging accuracy for computational time.

Full access