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Full-Text Articles in Physical Sciences and Mathematics
Quantifying Heterogeneity Along A Hillslope Using Seismic Refraction, Structure From Motion, And X-Ray Fluorescence In The Piedmont, South Carolina, Leah Topping
All Theses
The critical zone (CZ) is the life sustaining outer layer of the earth that spans from the top of unweathered bedrock to the tops of the trees. This dynamic zone is always evolving because a variety of chemical, physical, and biological processes transform bedrock into regolith, creating a spatially heterogeneous CZ architecture. This study aims to investigate the relationships between regolith thickness, seismic velocities, and chemical profiles as a function of slope position and it is hypothesized bedrock composition, fracture density, and foliation are the key factors controlling the physical heterogeneity in the top 1-2 meters of the CZ. To …
A Conservative Numerical Scheme For The Multilayer Shallow Water Equations, Evan Butterworth
A Conservative Numerical Scheme For The Multilayer Shallow Water Equations, Evan Butterworth
All Theses
An energy-conserving numerical scheme is developed for the multilayer shallow water equations (SWE’s). The scheme is derived through the Hamiltonian formulation of the inviscid shallow water flows related to the vorticity-divergence variables. Through the employment of the skew-symmetric Poisson bracket, the continuous system for the multilayer SWE’s is shown to preserve an infinite number of quantities, most notably the energy and enstrophy. An energy-preserving numerical scheme is then developed through the careful discretization of the Hamiltonian and the Poisson bracket, ensuring the skew-symmetry of the latter. This serves as the groundwork for developing additional schemes that preserve other conservation properties …