Date of Award


Document type


Access Type

Open Access Dissertation

Degree Name

Doctor of Philosophy (PhD)

Degree Program

Mechanical Engineering

First Advisor

Stephen M. de Bruyn Kops

Second Advisor

J. Blair Perot

Third Advisor

Bruce E. Turkington

Subject Categories

Mechanical Engineering


Theory of turbulence at small scales plays a fundamental role in modeling turbulence and in retrieving information from physical measurements of turbulent flows. A systematic methodology based on direct numerical simulations of turbulent flows is developed to investigate universality of small scale turbulence. Understanding characteristics of the small scale intermittency in turbulent flows and the accuracy of the models, measurements, and theories in predicting it are the main objectives. The research is designed to address two central questions; 1) possible effects of large scale anisotropies on the small scale turbulence and 2) potential biases in characterizing small scale turbulence due to the nature of the quantities used to extract the information, known as surrogates. Direct numerical simulations of forced, isotropic homogeneous turbulence with extraordinarily fine spatial resolution on a periodic box up to 4096 × 4096 × 4096 grid points are analyzed first, to provide a clear insight to the small scale turbulence in the absence of large scale anisotropy. Direct numerical simulations of forced, homogeneous and axisymmetric density stratified flows on a periodic box up to 4096 × 4096 × 2048 grid points with the buoyancy Reynolds number ranging from 10 to 220 are considered next. Different levels of density stratification in the vertical direction cause different levels of large scale anisotropy in the flows. These unique simulations provide a clear picture of turbulent structures over an extensive range of scales. The dissipation rate of turbulent kinetic energy is chosen as the main descriptor of small scale structures. A comprehensive study on surrogates of energy dissipation rate is conducted to identify the best descriptor of the small scale turbulence based on easily measured quantities in physical experiments. In particular, the one-dimensional longitudinal and transverse surrogates, as well as a surrogate based on the asymmetric part of the strain rate tensor, are considered.The statistical analysis of local and locally averaged energy dissipation rate indicates that the small scale intermittency manifested in the energy dissipation rate is universal with intermittency exponent of μ = 0.25 ± 0.05, independent of flow conditions and measurement methods. In contrary, the general shape of the probability density functions of energy dissipation rate is strongly skewed to reflect all the existing dynamics in the flow. The surrogates are fundamentally different than the energy dissipation rate. The longitudinal and transverse surrogates overestimate the intermittency exponent by factors of 1.5 and 2.2, respectively. The scale dependency of the moments of locally averaged energy dissipation rate is proposed as a powerful technique to identify the dominant dynamics of the complex flows for a specific range of scales in physical space. Specifically, for the stratified turbulence, this method suggests a superposition of patches of three-dimensional turbulence superimposed on the background semi two-dimensional stratified flow.