Date of Award


Document Type


Degree Name

Master of Science (MS)


School of Mathematical and Statistical Sciences

Committee Chair/Advisor

Qingshan Chen

Committee Member

Lea Jenkins

Committee Member

Vince Ervin


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 of interest for the multilayer case.

Author ORCID Identifier



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