• Rapid Communication

Scaling of Reynolds stresses in a differentially heated vertical channel

Tie Wei
Phys. Rev. Fluids 4, 051501(R) – Published 28 May 2019

Abstract

This Rapid Communication investigates the scaling of the Reynolds shear and normal stresses in a differentially heated vertical channel (DHVC). Analysis of the mean momentum balance equation, with an approximation of the mean temperature in the outer layer via a logarithmic function, reveals a relationship, gαθτδ|Rwu|ctr=O(1), among key parameters in a DHVC including the gravitational acceleration g, thermal expansion coefficient α, channel half width δ, friction temperature θτ, and the maximum magnitude of Reynolds shear stress |Rwu|ctr. Direct numerical simulation (DNS) data indicate that at sufficiently high Grashof numbers, gαθτδ|Rwu|ctr0.951, supporting the validity of the analysis. Based on analysis of the DNS data, a mixed scale uτUmax is found to be a proper scale for the Reynolds shear stress in a DHVC. Here, Umax is the maximum mean velocity in the x direction, and uτ is the friction velocity. This mixed scale also captures the scaling of the Reynolds normal stresses better than previously used scales.

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  • Received 7 December 2018

DOI:https://doi.org/10.1103/PhysRevFluids.4.051501

©2019 American Physical Society

Physics Subject Headings (PhySH)

Fluid Dynamics

Authors & Affiliations

Tie Wei*

  • Department of Mechanical Engineering, New Mexico Institute of Mining and Technology, Socorro, New Mexico 87801, USA

  • *tie.wei@nmt.edu

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Issue

Vol. 4, Iss. 5 — May 2019

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