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Collision, Coalescence and Breakup of Raindrops. Part II: Parameterization of Fragment Size Distributions

T. B. LowDepartment of Physics, University of Toronto, Toronto, Ontario M5S 1A7, Canada

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Roland ListDepartment of Physics, University of Toronto, Toronto, Ontario M5S 1A7, Canada

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Abstract

The experimental drop collision/breakup results of Low (1977) and Low and List (1982) and McTaggart-Cowan and List (1975b), taken at laboratory pressure and terminal drop speeds, were parameterized for future use in cloud and precipitation modeling. The primary analyses of the 10 representative raindrop pairs were based on the three main geometric shapes generally assumed by the drop pairs after their initial contact and before breakup (or coalescence): filaments, sheets and disks. Relationships for the average total fragment number for each category are given. The fragment number distributions resulting from the collisions in each classification were fitted as sums of normal and log-normal distributions with the parameters of each distribution being related to the drop sizes and physical quantities derived from them (like the collision kinetic energy, CKE).

Each collision was then weighted according to the individual contribution and summed to give the probability of occurrence of each breakup type. The weighting functions were based on the CKE of each pair as determined in the center of drop mass frame. With the newly established coalescence efficiencies for raindrop pairs by Low and List (1982) the collision breakup equations were expanded into general overall equations for all drop pairs as expected in natural rain.

Abstract

The experimental drop collision/breakup results of Low (1977) and Low and List (1982) and McTaggart-Cowan and List (1975b), taken at laboratory pressure and terminal drop speeds, were parameterized for future use in cloud and precipitation modeling. The primary analyses of the 10 representative raindrop pairs were based on the three main geometric shapes generally assumed by the drop pairs after their initial contact and before breakup (or coalescence): filaments, sheets and disks. Relationships for the average total fragment number for each category are given. The fragment number distributions resulting from the collisions in each classification were fitted as sums of normal and log-normal distributions with the parameters of each distribution being related to the drop sizes and physical quantities derived from them (like the collision kinetic energy, CKE).

Each collision was then weighted according to the individual contribution and summed to give the probability of occurrence of each breakup type. The weighting functions were based on the CKE of each pair as determined in the center of drop mass frame. With the newly established coalescence efficiencies for raindrop pairs by Low and List (1982) the collision breakup equations were expanded into general overall equations for all drop pairs as expected in natural rain.

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