浮冰圆柱体在淡水与盐水环境中的融化
Melting of floating ice cylinders in fresh and saline environments
AI总结：
本文实验研究浮冰圆柱体在淡水与盐水中的融化行为，揭示其倾覆条件、振荡动力学及羽流与传热的标度规律，并将结果与真实冰山现象定性关联。
摘要：
我们通过实验研究了浮冰圆柱体的融化过程。实验在水箱中进行，冰圆柱体半径在5 cm至12 cm之间，水平漂浮且其轴线垂直于重力方向。水箱中的水处于室温，盐度范围为0 g/L至35 g/L。这些条件对应的瑞利数范围为$10^5 \lesssim \mathrm{Ra} \lesssim 10^9$。通过使用由H$_2$O-D$_2$O混合物制成的冰，改变了相对密度，从而改变了漂浮行为。此外，我们还探索了两层稳定分层的情况。我们研究了圆柱体横截面的形态演化，并结合其与对流流动的相互作用来解释观测结果。圆柱体仅在淡水中会发生倾覆，而在盐水环境中则不会。这种行为可以通过浮力与阻力所施加的力矩之间的平衡来解释，这些力矩随着圆柱体的融化和旋转而变化。我们将圆柱体倾覆后的振荡运动建模为阻尼非线性振子。冰圆柱体的向下羽流遵循线源羽流的预期标度关系。羽流的雷诺数随瑞利数在两个区域中呈现标度关系，即对于$\mathrm{Ra} < O(10^7)$有$\mathrm{Re} \propto \mathrm{Ra}^{1/2}$，对于$\mathrm{Ra} > O(10^7)$有$\mathrm{Re} \propto \mathrm{Ra}^{1/3}$，而传热（以努塞尔数无量纲化）遵循$\mathrm{Nu} \propto \mathrm{Ra}^{1/3}$。尽管盐的加入显著改变了溶质、热和动量边界层，但这些标度关系与初始尺寸或水体盐度无关地成立。虽然我们的实验与真实冰山之间存在重要差异，但我们的结果可以在定性上与峡湾及孤立冰山周围发生的自然现象联系起来。
英文摘要：
We experimentally investigated the melting of floating ice cylinders. Experiments were carried out in a tank, with ice cylinders with radii between 5 cm and 12 cm, floating horizontally with their axis perpendicular to gravity. The water in the tank was at room temperature, with salinities ranging from 0 g/L to 35 g/L. These conditions correspond to Rayleigh numbers in the range $10^5 \lesssim \mathrm{Ra} \lesssim 10^9$. The relative density and thus the floating behaviour was varied by employing ice made of H$_2$O-D$_2$O mixtures. In addition, we explored a two-layer stable stratification. We studied the morphological evolution of the cross-section of the cylinders and interpreted our observations in the context of their interaction with the convective flow. The cylinders only capsize in fresh water but not when the ambient is saline. This behaviour can be explained by the balance between the torques exerted by buoyancy and drag, which change as the cylinder melts and rotates. We modelled the oscillatory motion of the cylinders after a capsize as a damped non-linear oscillator. The downward plume of the ice cylinders follows the expected scalings for a line-source plume. The plume's Reynolds number scales with Rayleigh number in two regimes, namely $\mathrm{Re} \propto \mathrm{Ra}^{1/2}$ for $\mathrm{Ra} < O(10^7)$ and $\mathrm{Re} \propto \mathrm{Ra}^{1/3}$ for $\mathrm{Ra} > O(10^7)$, and the heat transfer (nondimensional as Nusselt number) scales as $\mathrm{Nu} \propto \mathrm{Ra}^{1/3}$. Although the addition of salt substantially alters the solutal, thermal and momentum boundary layers, these scaling relations hold irrespectively of the initial size or the water salinity. While important differences exist between our experiments and real icebergs, our results can qualitatively be connected to natural phenomena occurring in fjords and around isolated icebergs.
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