Waves on Icicles

TL;DR

This paper introduces a new instability theory based on thermal diffusion in thin water layers to explain the uniform 1 cm wave patterns observed on icicles, linking atmospheric heat diffusion and water flow dynamics.

Contribution

It presents a novel formula and instability theory that explains the formation of uniform wave patterns on icicles through thermal diffusion and fluid flow effects.

Findings

Wave intervals are approximately 1 cm.

Thermal diffusion in thin water layers controls wave formation.

Laplace instability explains the specific wavelength.

Abstract

Icicles with wave patterns on their surfaces can sometimes be seen hanging from roofs of buildings. Surprisingly, most of these wave patterns are at intervals of about 1 cm. The reason for this uniformity of interval has not been clarified. Here we show a formula to explain this remarkable phenomenon by introducing a new instability theory. This theory is given by thermal diffusion in thin water layer streams flowing along the icicles. The streams change the temperature distribution and control waves of short wavelengths. The specific wavelength (about 1 cm) can be determined by Laplace instability of the heat field in the atmosphere and by the thermal diffusion effect in thin-layer streams.