Transitional fluctuations of thermal boundary layer in horizontal convection

Abstract

Fluctuations of thermal boundary layer (BL) in horizontal convection (HC) strongly affect the global heat transport through the HC sample and predominately determine the flow state. Here, we present a systematic experimental study of vertical profiles of mean temperature and temperature variance in the thermal BL of a HC flow that are heated and cooled from the bottom. Three rectangular HC samples filled with de-ionised water are used in the experiment. They have the same aspect ratios Γ≡L:W:H=10:1:1 but with different L (L, W and H are, respectively the length, width and height of the sample). The Rayleigh number Ra varies in the range 2×1010≲Ra≲1.3×1013, and the Prandtl number Pr is in the range 3.9≲Pr≲6.5. For all Ra in the studied range, we find that the cold thermal BL above the cooling plate remains laminar and the vertical profiles of measured mean temperature follow a universal scaling form predicted for laminar BL by Yan, Shishkina and He (J. Fluid Mech., vol. 915, 2021, R5). Above the heated plate, on the contrary, temperature fluctuations in the hot thermal BL undergo several transitional changes as Ra increases. For Ra≲6×1010, the thermal BL has a stable double-layer structure agreeing with the predicted scaling form for laminar BL and the temperature fluctuations are nearly zero. In the range 6×1010≲Ra≲1.1×1011, temperature fluctuations inside the BL have intermittent decayed oscillations, which results in deviations of the measured mean temperature profiles from the predicted scaling form. For 1.1×1011≲Ra≲1012, the temperature oscillations inside the BL become continuous and stable. Correspondingly, an intermediate layer emerges in the thermal BL, where the mean temperature profile has a sinusoidal variation on the distance z above the heated plate. For 1012≲Ra≲1.3×1013, the temperature fluctuations in the intermediate layer become irregular and intermittent, indicating a growing mixing intensity as Ra increases. When Ra exceeds 7×1012, the vertical distribution of mean temperature in the intermediate layer is uniform because of strong mixing. The temperature-variance vertical profiles follow a power-law function σT2(z)∼z−γ with the exponent γ=0.66, which agrees with the Priestley prediction for thermal convection over a heated horizontal surface. Our results thus reveal a series of transitional changes of temperature fluctuations, from laminar to chaotic states, in the hot thermal BL. They predominately account for the enhancement of global heat transport in the HC flow observed by Reiter and Shishkina (J. Fluid Mech., vol. 892, 2020, R1).