Date of Award

Spring 1-1-2013

Document Type


Degree Name

Doctor of Philosophy (PhD)


Applied Mathematics

First Advisor

Baylor Fox-Kemper

Second Advisor

Keith Julien

Third Advisor

Mark Ablowitz

Fourth Advisor

Natasha Flyer

Fifth Advisor

Bengt Fornberg


This dissertation is loosely organized around efforts to improve vertical ocean mixing in global climate models and includes an in-depth analysis of Stokes drift, optimization of a new global climate model wave component, and development of a meshless spectral wave model. Stokes drift (hereafter SD) is an important vector component that appears often in wave-averaged dynamics. Mathematically, SD is the mean difference between Eulerian and Lagrangian velocities and intuitively can be thought of as the near-surface ocean current induced from wave motion. Increasingly, spectral wave models are being used to calculate SD globally. These models solve a 5D wave action balance equation and typically require large computational resources to make short to medium-range forecasts of the sea state.

In the first part, a hierarchy of SD approximations are investigated and new approximations that remove systematic biases are derived. A new 1D spectral approximation is used to study the effects of multidirectional waves and directional wave spreading on SD. It is shown that these effects are largely uncorrelated and affect both the magnitude and direction of SD in a nonlinear fashion that is sensitive with depth.

In the second part, efforts to add a wave model component to the NCAR Community Earth System Model are discussed. This coupled component will serve as the backbone to a new Langmuir mixing parameterization and uses a modified version of NOAA WAVEWATCH III (a third-generation spectral wave model). In addition, the governing wave action balance equation is reviewed and several variations are derived and formulated.

In the third part, construction of a monochromatic spectral wave model using RBF-generated finite differences is described. Several numerical test cases are conducted to measure performance and guide further development. In kinematic comparisons with WAVEWATCH III, the meshless prototype is approximately 70–210 times more accurate and uses a factor of 12 to 17 less unknowns.