Collision Rate of Small Graupel and Water Drops

A. Khain Institute of the Earth Science, The Hebrew University of Jerusalem, Jerusalem, Israel

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M. Pinsky Institute of the Earth Science, The Hebrew University of Jerusalem, Jerusalem, Israel

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M. Shapiro Faculty of Mechanical Engineering, Technion—Israel Institute of Technology, Haifa, Israel

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A. Pokrovsky Institute of the Earth Science, The Hebrew University of Jerusalem, Jerusalem, Israel

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Abstract

An approach permitting one to calculate the collision efficiency and the collision kernel of spherical particles of different densities for Reynolds numbers up to 100 (300-μm-radius drops, or 700-μm-radius graupel) is presented. It is used for the calculation of graupel–drop collision efficiencies and collision kernels in calm air for low-, medium-, and high-density graupel at 750- and 500-mb pressure levels.

Low-density graupel interacts with water droplets in a way similar to ice crystals: there exists a cutoff size, below which graupel cannot collect water droplets. The authors have shown that the cutoff size decreases with the growth of graupel density, so that medium- and high-density graupel is able to collect droplets with the radii exceeding a certain minimum size. The graupel–drop collision efficiency increases with the drop size up to a maximum value and then sharply decreases to zero, when the drops' terminal velocity approaches the terminal velocity of graupel. As soon as the terminal velocity of drops exceeds that of graupel (so that graupel is captured by drops), the collision efficiency experiences a jump to values significantly exceeding 1, and then decreases rapidly to about 1 with the increase of the drop size.

It is shown by means of detailed hydrodynamic calculations that low- and medium-density graupel particles have significantly lower collision efficiencies with cloud droplets as compared to those of drop collectors of both the same size or mass as graupel. This result contradicts the widely used intuitive assumption that graupel–drop collision efficiencies are equal to the drop–drop collision efficiencies.

Calculations show that the graupel–drop collision kernel increases with height, especially when droplets with the radii under 10 μm are collected. The graupel–drop collision efficiencies and kernels for low-, medium-, and high-density graupel are presented in tables.

Corresponding author address: Alexander P. Khain, The Ring Family Dept. Atmos. Sciences, The Institute of Earth Sciences, Givat Ram Campus, The Hebrew University of Jerusalem, Givat Ram, Jerusalem 91904, Israel. Email: Khain@vms.huji.ac.il

Abstract

An approach permitting one to calculate the collision efficiency and the collision kernel of spherical particles of different densities for Reynolds numbers up to 100 (300-μm-radius drops, or 700-μm-radius graupel) is presented. It is used for the calculation of graupel–drop collision efficiencies and collision kernels in calm air for low-, medium-, and high-density graupel at 750- and 500-mb pressure levels.

Low-density graupel interacts with water droplets in a way similar to ice crystals: there exists a cutoff size, below which graupel cannot collect water droplets. The authors have shown that the cutoff size decreases with the growth of graupel density, so that medium- and high-density graupel is able to collect droplets with the radii exceeding a certain minimum size. The graupel–drop collision efficiency increases with the drop size up to a maximum value and then sharply decreases to zero, when the drops' terminal velocity approaches the terminal velocity of graupel. As soon as the terminal velocity of drops exceeds that of graupel (so that graupel is captured by drops), the collision efficiency experiences a jump to values significantly exceeding 1, and then decreases rapidly to about 1 with the increase of the drop size.

It is shown by means of detailed hydrodynamic calculations that low- and medium-density graupel particles have significantly lower collision efficiencies with cloud droplets as compared to those of drop collectors of both the same size or mass as graupel. This result contradicts the widely used intuitive assumption that graupel–drop collision efficiencies are equal to the drop–drop collision efficiencies.

Calculations show that the graupel–drop collision kernel increases with height, especially when droplets with the radii under 10 μm are collected. The graupel–drop collision efficiencies and kernels for low-, medium-, and high-density graupel are presented in tables.

Corresponding author address: Alexander P. Khain, The Ring Family Dept. Atmos. Sciences, The Institute of Earth Sciences, Givat Ram Campus, The Hebrew University of Jerusalem, Givat Ram, Jerusalem 91904, Israel. Email: Khain@vms.huji.ac.il

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