Thermal boundary-layer structure in laminar horizontal convection

We present experimentally obtained time-averaged vertical temperature profiles theta(z) in horizontal convection (HC) in water (Prandtl number Pr similar or equal to 6), which were measured near the heating and cooling plates that are embedded in the bottom of HC samples. Three HC rectangular samples of different sizes but the same aspect ratio Gamma L : W : H = 10 : 1 : 1 (L, W and H are the length, width and height of the sample, respectively) were used in the experiments, which allowed us to study HC in a Rayleigh-number range 2 x 10(10) less than or similar to Ra less than or similar to 9 x 10(12). The measurements revealed that above the cooling plate, the mean temperature profiles have a universal scaling form theta(z/lambda(c)) with lambda(c) being a Ra-dependent thickness of the cold thermal boundary layer (BL). The theta(z/lambda(c))-profiles agree well with solutions to a laminar BL equation in HC, which is derived under assumption that the large-scale horizontal velocity achieves its maximum near the plate and vanishes in the bulk. Above the heating plate, the mean temperature field has a double-layer structure: in the lower layer, the theta profiles scale with the hot thermal BL thickness lambda(h), while in the upper layer, they again scale with lambda(c). Both scaling forms are in good agreement with the solutions to the BL equation with a proper parameter choice.