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, , among key parameters in a DHVC including the gravitational acceleration , thermal expansion coefficient , channel half width , friction temperature , and the maximum magnitude of Reynolds shear stress . Direct numerical simulation (DNS) data indicate that at sufficiently high Grashof numbers, , supporting the validity of the analysis. Based on analysis of the DNS data, a mixed scale is found to be a proper scale for the Reynolds shear stress in a DHVC. Here, is the maximum mean velocity in the direction, and is the friction velocity. This mixed scale also captures the scaling of the Reynolds normal stresses better than previously used scales.
- Received 7 December 2018
DOI:https://doi.org/10.1103/PhysRevFluids.4.051501
©2019 American Physical Society