Derivative Statistics of Axial Velocity and Passive Scalar in the Jet Diffusion Field of High-Schmidt-Number Matter

Abstract

In this study, a water solution of dye (whose Schmidt number Sc is about 3,800) was issued into the quiescent water as an axisymmetric turbulent jet and the simultaneous measurements of axial velocity and concentration have been performed using the combined probe of I-type hot-film and fiber-optic concentration sensor based on the Lambert-Beer's law. Then we calculated the PDF (Probability Density Function) for the streamwise velocity derivative ∂u/∂x and streamwise concentration derivative ∂c/∂x. It was confirmed that the PDFs for ∂u/∂x skew negatively, and the values of skewness (S ∂u/∂x ) and flatness factor (F ∂u/∂x ) are consistent with the other researcher's data (see Sreenivasan and Antonia, Annual Review of Fluid Mechanics, Vol.29, 1997, where the extensive past data of turbulent velocity and temperature (whose Prandtl number is Pr = 0.7) fields are summarized). However, with regard to the PDFs for ∂c/∂x, the skewness (S ∂c/∂x ) show the values very close to zero, unlikely the past other data of the temperature fields which show the magnitude of 0.5 ∼ 1.0. On the other hand, the flatness factor (F ∂c/∂x ) show the values of 7.0 ∼ 8.0 which are consistent with the temperature fields. This result suggests that the fine-scale structure of a highSchmidt-number diffusion field is almost isotropic although it is intermittent.