Dissertation Defense: Accuracy and Simplicity in One Equation Turbulence Models 

The complex structure and dynamics of turbulence combined with computational limitations create a fundamental barrier. Turbulence is both rich in scale and chaotic in time, thus time accurate predictions of turbulent flows are out of reach for many important applications. If direct numerical simulations are not feasible, we turn to turbulence modeling. Unfortunately, many inexpensive popular models lack a strong theoretical backbone. We seek models that efficiently and accurately capture important flow characteristics. Eddy viscosity models, which model the effect of unresolved scales with enhanced dissipation, are the most commonly used today.

The scaling of the time averaged energy dissipation rate as U^3/L is fundamental, and has been proved mathematically and supported experimentally. Nonetheless, this law is violated in numerical tests of popular models. Numerical dissipation introduced by commonly used multistep methods is a potential cause or contributing factor. We explore the effects of numerical dissipation in multistep methods applied to the Navier-Stokes equations on this scaling. Additionally, any eddy viscosity models themselves may overdissipate, particularly in the presence of boundary layers. We look to create models that fit the true behavior of the underlying equations. By enforcing correct near wall behavior of the turbulent viscosity through a new turbulence length scale, we prevent overdissipation in the long time average while minimizing computational complexity. Motivated by enforcing model accuracy in the near wall area, the inclusion or exclusion of viscous diffusion in the k-equation is debated. By examining the derivation of the k-equation, we show that inclusion leads to incorrect near wall asymptotics.

Advisor:  Dr. William J Layton