Characteristics of the wavelength of ripples on icicles

TL;DR

This paper presents a theoretical analysis of the ripple wavelength on icicles, deriving a simpler formula and examining how various parameters influence ripple formation, with findings indicating insensitivity to water supply rates, icicle diameter, and air temperature.

Contribution

It introduces a new, simplified formula for ripple wavelength on icicles and explores the effects of environmental parameters on ripple formation.

Findings

Wavelength is insensitive to water supply rates.

Wavelength is unaffected by icicle diameter.

Wavelength shows minimal dependence on air temperature.

Abstract

It is known that the wavelength of the ripples on icicles in nature is of centimeter-scale. Such study on morphological instability of ice-water interface during ice growth from flowing supercooled water film with one side being a free surface has recently been made [K. Ueno, Phys. Rev. E 68, 021603 (2003)]. This is a first theoretical study taking into account the influence of the shape of the water-air surface on the growth condition of infinitesimal disturbances of the ice-water interface. A simpler formula to determine the wavelength of the ripples than that in the previous paper is derived. It seems that the wavelength of ripples is insensitive to the water supply rates, diameters of the icicles and surrounding air temperatures. The details of dependence of the wavelengh of ripples on these parameters are investigated.