Transition from classical to ultimate melting

TL;DR

This paper investigates the transition in melting dynamics from classical to ultimate turbulence, revealing a scale-dependent change in boundary layer behavior that improves large-scale melt rate predictions.

Contribution

It demonstrates the existence of a melting transition from laminar to turbulent boundary layers through experiments and simulations across four orders of magnitude in scale.

Findings

Identified a transition from slow to fast melting at larger scales.

Linked the transition to a change from classical to ultimate turbulence.

Provided a framework for better extrapolation of melt rates in geophysical contexts.

Abstract

Melting is omnipresent in nature and technology, with applications ranging from metallurgy, biology, food science, and latent thermal energy storage to oceanography, geophysics, and climate science, and occurring on all scales from sub-millimeter to global scales. The key objective is to understand the rate at which an object melts as a function of its size and of the ambient conditions. To achieve this it is important to be able to extrapolate from small scale experiments and observations to large or even global scales. This is done by scaling laws. However, these are only meaningful if there is no transition from one scaling relation to another one. Here we show, however, that for both fixed and freely-advected melting objects immersed in a turbulent flow a melting transition does exist, namely from slow melting at the small scales to fast melting at the large scales. We do so by controlled melting experiments and corresponding direct numerical simulations, covering four orders of magnitude in scale. The transition corresponds to the transition from a laminar-type boundary layer around the melting object to a turbulent-type boundary layer, i.e., from so-called classical turbulence to ultimate turbulence, with its enhanced transport properties. Our results thus provide a quantitative understanding of the flow physics of the melting process and thereby enable a better extrapolation and prediction of melt rates on large scales such as relevant in geophysics, oceanography, and climate science.