The dispersion of marked fluid in turbulent shear flow

TLDR

The analysis by Taylor (1954) based on the Reynolds analogy has been extended to describe the diffusion of marked fluid in turbulent open‑channel flow. The same analysis can be applied to longitudinal dispersion of discrete particles, both neutrally buoyant and buoyant, and compared with observations by Batchelor, Binnie & Phillips (1955, 1958). The study finds that the longitudinal diffusion coefficient is 5.9 uτh, agreeing with experiments, while the lateral diffusion coefficient is 0.23 uτh—three times larger than isotropic predictions—and that the analysis also describes particle dispersion consistent with earlier observations.

Abstract

The analysis used by Taylor (1954) and based on the Reynolds analogy has been extended to describe the diffusion of marked fluid in the turbulent flow in an open channel. The coefficient of longitudinal diffusion arising from the combined action of turbulent lateral diffusion and convection by the mean flow is computed to be 5·9uτh, where h is the depth of fluid and uτ the friction velocity. This is in agreement with experiments described herein. The laterla diffusion coefficient is found by experiment to be 0·23uτh, which is three times larger than the value obtained by the assumption of isotropy. The same analysis can be used to describe the longitudinal dispersion of discrete particles, both of zero buoyancy and of finite buoyancy, and comparison is made with observations by Batchelor, Binnie & Phillips (1955) and Binnie & Phillips (1958).