Edward E. O'Brien contributions to reactive-flow turbulence

Professor Edward Ephraim O'Brien (“Ted”) has made lasting contributions to the theory and modeling of scalar mixing and reaction in turbulent flows. With a doctoral dissertation at The Johns Hopkins University in 1960, entitled “On the Statistical Behavior of a Dilute Reactant in Isotropic Turbulence,” supervised by the legend Stanley Corrsin, and in the company of notable pioneer of turbulence, John Leask Lumley, Ted's academic training propelled him through a prolific career. In the opening article of this Special Issue, we provide a review of some of Ted's contributions. First, a summary is presented of his work on the examination of the failure of the cumulant discard approximation for the scalar mixing. This is followed by a highlight of his impacts on other spectral theories of turbulence including Kraichnan's direct interaction approximation. His contributions to more modern theoretical/computational description of reactive turbulence are discussed next, including the transported probability density function (pdf) formulation, scalar-gradient pdf transport equation, scalar interfaces, and the filtered density function. Finally, some of his research on Direct Numerical Simulation of compressible turbulence is reviewed.