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

2021/04/29 by Sukanta Basu, Basu, Sukanta, A.A.M. Holtslag +1 · 2 citations
Earth and Planetary Sciences · Engineering · Environmental Science · #Atmospheric and Oceanic Physics (physics.ao-ph) #Climate variability and models #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Turbulent Flows #Meteorological Phenomena and Simulations

paper · pdf · doi:10.48550/arxiv.2104.14378

openalex publication_date 2021/04/29 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

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

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• Model of incompressible turbulent flows via a kinetic theory
• Extreme vertical drafts as drivers of Lagrangian dispersion in stably stratified turbulent flows

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