Collision Efficiency, Collision Angle and Impact Velocity of Hydrodynamically Interacting Cloud Drops: A Numerical Study

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  • 1 National Center of Atmospheric Research, Boulder, Colo. 80307
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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.

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.

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