Shape dynamics of melting ice: Experiments, simulations, modeling and analysis

New York University, New York NY

Investigators

Abstract

The Earth's ice reserves are melting with increasing rate. Interpreting what these changes mean for the health of our planet requires models that account for complex processes that act interdependently over immense ranges of length and time scales. The accuracy of global-scale climate models depends on the physics at the most fundamental scales, such as how the melting of ice depends on the shape of its interface with liquid water and the local temperature, salinity, and flow conditions. Applied and computational mathematics and mathematical modeling provide many methods that are well suited to addressing these problems. Applying such techniques and developing new ones specifically for ice melting can provide critical information needed to improve climate models. Better understanding the underlying physics and mathematics can also help to explain the diverse shapes and patterning of natural ice, which could allow local environmental conditions to be inferred from observations of ice. Investigating these important issues also provides opportunities to educate students and train researchers, thereby contributing to a workforce that is well prepared to tackle these and related problems. These projects investigate the melting dynamics of ice through laboratory experiments, numerical simulations, mathematical modeling, and analysis. The general progression of the research program is from idealized settings such as melting of fixed bodies with simple initial forms in fresh water at fixed far-field temperature to increasingly elaborate situations involving changes in geometry, temperature, and salinity. Further extensions address additional couplings such as melting-induced motions of free ice. Experiments will focus on accurate measurement of ice-water interface forms and motions in laboratory settings where the initial geometry, far-field temperature, and salinity profiles can be controlled and systematically varied. Direct numerical computations will employ phase-field methods to simulate the evolution of the temperature, flow, and salt concentration fields that give rise to the interfacial dynamics. Modeling will invoke idealizations based, for example, on boundary layer theory to derive moving-boundary descriptions and stability analyses that relate to pattern formation. All methods will be combined interactively towards targeting significant gaps in the current understanding of how the evolving shape of ice feeds back on the melting process and how the morphology of ice can be used to infer ambient conditions. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.