Penetrative Rayleigh-Bénard convection in water near its maximum density point

Abstract

The presence of a density maximum in water near 4 °C significantly modifies the nature and onset conditions of convective flows due to imposed temperature differences. In the present study, vertical temperature gradients are imposed upon a horizontal, rectangular layer of water, with the top and bottom surfaces maintained above and below the maximum density temperature, respectively. In such an arrangement, convection beginning in the lower, unstable portion of the layer (as small as 1/3 of the layer height) may penetrate into the upper, stable region. The resulting convection patterns are visualized using schlieren or shadowgraph techniques along multiple visual axes. The measured onset conditions and observed patterns are discussed in the context of preceding predictions and experimental observations in similar penetrative systems. As expected from the non-Boussinesq nature of water in this temperature range, convection sets in at temperature differences below those predicted by linear stability theory when the unstable portion of the layer is sufficiently small. The conduction-convection transition is also hysteretic in nature. At onset, the convection pattern consists of parallel, transverse rolls due to the boundary conditions of the fluid chamber. When the unstable portion of the layer is significantly less than half of the fluid layer height, the convective motion is found to penetrate only partway into the upper stable region, within which weakly counter-rotating motions are driven. At higher Rayleigh numbers, the fluid undergoes secondary transitions to either hexagonal cellular or longitudinal roll states which are visualized for the first time. Pattern heights and wavenumbers were measured in some instances, establishing qualitative (in general) and quantitative (over some parameter ranges) agreement with linear theory.