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Mathematical Modeling of Coastal Dune Dynamics

Project Full Title:

Modeling the growth and migration of vegetated sand dunes along the eastern shore of Lake Michigan

Project Mentor(s):

Yurk,Brian

Project Mentor(s) EMail:

yurk@hope.edu

Project Start Date:

5/31/2021

Project End Date:

8/28/2021

Project Description:

The eastern shore of Lake Michigan is home to the largest complex of freshwater coastal dunes in the world. Researchers have observed and modeled dune dynamics for several decades. However, until recently, mathematical models have focused almost exclusively on desert dunes, which lack significant vegetation. Vegetation plays a critical role in building and shaping coastal dunes by modifying local wind flow, hindering sand erosion, and facilitating sand accretion. Reciprocally, sand deposition and erosion impact vegetation growth and population dynamics. This summer we (mathematicians Brian Yurk and Tim Pennings in collaboration with several geologists) will begin a long-term project of measuring and modeling coastal dune dynamics with particular focus on the interaction between vegetation and physical dune processes. The close tie between field experiments and model development, parametrization, and validation for both the physical and biological models will be one unique aspect of this research. The summer research will include 1) reading pertinent scholarly articles; 2) conducting experiments to collect wind flow, vegetation density, and sand transport data requiring substantial fieldwork climbing and hiking local dunes; 3) studying necessary background topics in applied mathematics, including differential equations, partial differential equations, dynamical systems, and numerical analysis; and 4) developing mathematical models of dune and vegetation dynamics. As with all projects, students will write a paper and develop and give a presentation on the results. A background in calculus and basic differential equations is required. Any background in numerical analysis, computer programing, biology, or geology would also be helpful.

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