Convective Turbulence in Superfluid Solutions 3He–4He

In present work, we continue our experimental investigations of heat instability in superfluid 3He–4He solutions heated from below. We research two solutions with 3He concentrations 5.0% and 9.5% for temperature of 270 mK. It is found that for 5% solution the dependence \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\nabla T(\dot{Q})$\end{document} is linear in temperature range studied whereas for the solution of 9.5% we observed the deviation from linear dependence above some critical value  \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\dot{Q}_{c}$\end{document} . This effect manifests the thermal instability which appears under start of phase separation in 9.5% solution if heat flow is switched on. For 5.0% solution where one does not observe the phase separation at the values of  \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\dot{Q}$\end{document}  applied, the instability was not observed. To identify the possible mechanism of a thermal instability in stratified solution, we estimated the dependence of the Nusselt number on relative Raileigh number Ra/Rac. One observes that the dependence can be fitted as Nu=(Ra/Rac)b where b=0.31±0.04. Note that the dependence obtained agrees rather good with the empiric expression of (Busse in Rep. Prog. Phys. 41:1929, 1978) and connecting the numbers Nu and Ra for turbulent convection. This gives grounds to conclude the heat transfer in a stratified solution is realized by transition to the regime of turbulent convection.