Edward E. O'Brien's Seminal Contributions to Turbulence Theory

A brief overview will be presented of the influential contributions of Edward E. (Ted) O'Brien to the theory of turbulence, with an emphasis on scalar mixing and reaction.~While perhaps best known for his work on the transported PDF methods, Ted's contributions are very diverse and consider a broad range of theoretical and computational approaches.~~In the 1960s, he made some very fundamental contributions to the spectral theory of reactive scalars, analyzed the consequences of passive scalar tagging using Corsin's ``backward Lagrangian diffusion'' concept, and contributed to the interpretation of Kraichnan's ``direct interaction approximation'' (DIA) for turbulent mixing.~~~In the 1970s-1980s, he focused on scalar PD Functional and Function methods. In fact, he is widely recognized for introducing and popularizing single- and multi-point PDF closures, as well as the scalar-gradient PDF within the reactive turbulent flow community.~In the 1990s, he focused on applying the EDQNM and the ``amplitude mapping closure'' (AMC) models, respectively~to reactive turbulent scalars and mixing.~~With wider availability of supercomputers in the late 1990's-2000's, Ted utilized DNS for the development and appraisal of modern turbulence closures.~~He is also credited with introducing the ``filtered density function'' (FDF) transport equation for LES of turbulent reactive flows.~~In fact, he is the first to develop a transported scalar-FDF equation for multi-species turbulent reactive flows.~~Professor O'Brien's publications continue to be highly cited within the turbulence research community.