The present study investigates the non-Oberbeck-Boussinesq (NOB) effects which arise due to the temperature dependence of material properties in cryogenic helium experiments of turbulent Rayleigh-Bénard convection. Here we quantify these effects solely by the difference of the measured mean temperature at the center of the closed cell, $T_c$, from the arithmetic mean temperature obtained from the prescribed fixed and uniform temperatures at the top and bottom copper plates of the apparatus, $T_m=(T_{\mathrm{bot}}+T_{\mathrm{top}})/2$. To this end, the material properties such as specific heat at constant pressure, dynamic viscosity, thermal conductivity, the isobaric expansivity, and the mass density are expanded into power series with respect to temperature up to the quadratic order with coefficients obtained from the software package HEPAK. A subsequent nonlinear regression that uses deep convolutional networks delivers a dependence of the strength of non-Oberbeck-Boussinesq effects in the pressure-temperature parameter plane. Strength of the NOB effects is evaluated via the deviation of the mean temperature profile ${\xi }_{\mathrm{NOB}}\equiv T_m-T_c$ from the top-bottom-symmetric Oberbeck-Boussinesq case ${\xi }_{\mathrm{NOB}}=0$. Training data for the regression task are obtained from 236 individual long-term laboratory measurements at different Rayleigh numbers which span eight orders of magnitude.

• Received 24 May 2023
• Accepted 24 August 2023

DOI:https://doi.org/10.1103/PhysRevFluids.8.094606

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society