Abstract
This paper investigates the scaling of turbulent kinetic energy (TKE) and temperature variance production in a differentially heated vertical channel (DHVC). In a DHVC, TKE is produced by two distinctively different mechanisms: buoyancy production and shear production. In the present work, identity equations are derived for the global integrals of shear-produced TKE and temperature variance production. The derived identity equations agree well direct numerical simulation (DNS) data. At sufficiently high Rayleigh number the global integral of the shear-produced TKE is found, based on the DNS data, to scale as . Here is the wall-normal direction, is the channel half-width, is the mean streamwise velocity in the direction, is the maximum mean streamwise velocity, and is the friction velocity. is the Reynolds shear stress, where is the velocity fluctuation in the direction, is the velocity fluctuation in the direction, and angle brackets denote averaging operation. The global integral of the buoyancy-produced TKE at sufficiently high Grashof number is found to scale as where is the gravitational acceleration, is the thermal expansion coefficient, and is the covariance of the streamwise velocity fluctuation and the temperature fluctuation . The global integrals of temperature variance production and temperature dissipation are found to grow with the Grashof number in a logarithmic-like fashion as where is the mean transformed temperature, is the wall-normal turbulent transport of heat, is the friction temperature, and is the Grashof number. Based on the characteristics of the flux Richardson number, a four-layer structure is proposed for the TKE budget equation in a DHVC.
- Received 21 February 2019
DOI:https://doi.org/10.1103/PhysRevFluids.4.081501
©2019 American Physical Society