Off-campus UMass Amherst users: To download campus access theses, please use the following link to log into our proxy server with your UMass Amherst user name and password.
Non-UMass Amherst users: Please talk to your librarian about requesting this thesis through interlibrary loan.
Theses that have an embargo placed on them will not be available to anyone until the embargo expires.
Master of Science in Mechanical Engineering (M.S.M.E.)
Year Degree Awarded
Month Degree Awarded
boussinesq, approximation, direct, numerical, simulations, potential, energy, stratified, fluids, atmospheric, oceanic, fluid, dynamics
In flows with stable density stratification, a portion of the gravitational potential energy is available for conversion to kinetic energy. The remainder is not and is called “background potential energy”. The partition of potential energy is analogous to the classical division of energy due to motion into its kinetic and internal components. Computing background and available potential energies is important for understanding stratified flows. In many numerical simulations, though, the Boussinesq approximations to the Navier-Stokes equations are employed. These approximations are not consistent with conservation of energy. In this thesis we re-derive the governing equations for a buoyancy driven fluid using Boussinesq approximations. Analytical and stochastic approaches to partitioning potential energy are developed and analyzed in simplified 1-D cases. Finally, ambient and deviatoric potential energies, quantities analogous to background and available potential energy are introduced. Direct Numerical Simulations are used to formulate an energy budget. The actual and surrogate potential energies are compared based on the simulation results.
Stephen de Bruyn Kops