Stochastic Modeling of Icicle Formation

Abstract

A discrete random walk model has been developed to simulate icicle formation. A three-dimensional icicle is represented by a two-dimensional model with cylindrical symmetry around the vertical axis. The water flux along the icicle is divided into fluid elements which follow a stochastic path downwards towards the tip. During its walk, a fluid element may freeze on the icicle’s lateral surface or at the tip. The fluid elements can also form a pendant drop which may drip from the icicle tip. The freezing probability and the shedding parameter, which are the discrete model’s parameters, are expressed as functions of the heat loss to the airstream and the water supply rate, using simple analytical considerations. The predicted rates of icicle length and diameter growth agree well with experimental data. In addition, the model icicles exhibit the characteristic icicle ribs.