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Access Type

Open Access

Document Type


Degree Program

Mechanical Engineering

Degree Type

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.


First Advisor

Stephen de Bruyn Kops