Joint probabilities and mixing of isolated scalars emitted from parallel jets

Abstract

Mixing and reaction between two scalars initially separated by scalar-free ambient fluid is important in problems ranging from ecology to engineering. Using a two-channel planar laser-induced fluorescence (PLIF) system the instantaneous spatial structure of two independent scalars emitted from parallel jets into a slow coflow is quantified. Of particular interest is the scalar covariance used to define the correlation coefficient. Joint probability distribution functions (JPDFs) and instantaneous images of the scalar fields demonstrate that initially the flow mainly consists of incursions of fluid from one jet into the other, and vice versa, before scalars have time to assemble in attracting regions of the flow and coalesce due to diffusive flux. Decomposing the joint probability distribution exhibits the effect these events have on scaler overlap and scalar covariance. Along the centreline near where the mean profiles of the jets meet, the scalar covariance is negative; however, the covariance becomes positive as the scalars converge in shared structure and diffusive flux bridges a reduced barrier of ambient fluid. The mixing path between scalar filaments can be probabilistically observed through the conditional diffusion of the two scalars at various points in the flow.