Partial Differential Equation Models for Sea Ice Processes
Abstract
PROJECT SUMMARY Partial Differential Equation Models for Sea Ice ProcessesWith the opening of the Arct ic Ocean comes expanding navigational, economic and scientificopportunities, along with more complex competitive and national securi ty environments, andincreasing demands on the U.S. Navy and U.S. Coast Guard. The sea ice pack and its future trajectorydominate any considerations of the Arctic marine environment. Significantly advancing ourability to understand, model and predict the behavior o f sea ice is a central challenge to improvingclimate and ocean models and to meeting the demands on the U.S. military in the Arctic Region.In modeling the basic dynamic and thermodynamic behavior of sea ice, a sustained effort overmany years has been put into deve loping large scale, coarse grained numerical models with gridspacings on the order of tens of kilometers. These models serve as key components in globalclimate models that produce long term projections of Earths climate system. On the other hand,and on much finer t properties of sea ice, treated as a compositematerial with polycrystalline and porous brine microstructures on the millimeter to c entimeterscale. Theories of homogenization for composites have been used quite successfully to modeland predict the effective behavi or on centimeter to meter scales of fluid flow, heat flux, and thepropagation of electromagnetic waves through sea ice as a material with complex microstructure.Here we propose to develop novel, effective partial differential equation models for key processesin la rge scale ice pack dynamics, bringing the types of homogenization methods above toa much broader range of issues. The ice cover is t reated as a composite of ice floes and sea water,and ice concentration is the area fraction of the ocean surface covered by ice. A m ain goal is todevelop a model for predicting the location, width and geometry of the marginal ice zone (MIZ),a transitional region w ith strong wave-ice interactions, and sea ice concentrations ranging from80% near the dense inner core of the pack to 15% in the spa rse outer fringes. We will develophomogenization models for the interaction of ocean surface waves with the composite ice coverin th e MIZ, based on a Stieltjes integral representation for the effective propagation characteristicsinvolving a spectral measure which depends on the geometry of ice floe configurations. We willalso develop advection diffusion equations to model the evolution of the sea ice concentration fieldin the MIZ under dynamic and thermodynamic forcing. Specific objectives include:* MIZ as a moving phase t ransition region. Develop a PDE model for simulating phase changefronts to predict MIZ seasonal behavior, such as widening of the Be ring-Chukchi MIZ by afactor of four while migrating 1,600 km poleward during the melt season, and long term trends.* Waves in the MI Z. Develop a spectral analysis, based on random matrix theory, that providesa framework to address questions such as a possible Ande rson transition in wave localizationand attenuation characteristics depending on ice floe geometry and crowding.* Advection diffusio n model for sea ice concentration. Develop PDE models for the sea iceconcentration field that can help predict response to forcing o ver a range of scales; use modelof diffusive behavior of floe dynamics to study how advective fields affect ice concentrationevoluti on; further develop our PDE method for filling the polar data gap in ice concent new insights into the physics of key sea ice processes,and fundamentally advance the mathematical modeling of sea ice.Approved for P ublic Release.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Oct 22, 2021
- Source ID
- N000142112909
Entities
People
- Kenneth M. Golden
Organizations
- Office of Naval Research
- United States Navy
- University of Utah