Turbulent Prandtl number and characteristic length scales in stably stratified flows: steady-state analytical solutions

Sukanta Basu*, Albert A.M. Holtslag

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

In this study, the stability dependence of turbulent Prandtl number (Prt) is quantified via a novel and simple analytical approach. Based on the variance and flux budget equations, a hybrid length scale formulation is first proposed and its functional relationships to well-known length scales are established. Next, the ratios of these length scales are utilized to derive an explicit relationship between Prt and gradient Richardson number. In addition, theoretical predictions are made for several key turbulence variables (e.g., dissipation rates, normalized fluxes). The results from our proposed approach are compared against other competing formulations as well as published datasets. Overall, the agreement between the different approaches is rather good despite their different theoretical foundations and assumptions.

Original languageEnglish
Pages (from-to)1273-1302
JournalEnvironmental Fluid Mechanics
Volume21
Issue number6
Early online date29 Oct 2021
DOIs
Publication statusPublished - 2021

Keywords

  • Anisotropy
  • Buoyancy length scale
  • Gradient Richardson number
  • Shear length scale
  • Stable boundary layer

Fingerprint

Dive into the research topics of 'Turbulent Prandtl number and characteristic length scales in stably stratified flows: steady-state analytical solutions'. Together they form a unique fingerprint.

Cite this