一项来自澳大利亚麦考瑞大学、美国犹他大学和达特茅斯学院的研究表明，当海冰内部存在对流流动时，其热导率会显著提高。这一发现可能使气候模型更加准确，因为目前全球模型只考虑了温度和盐度，而没有考虑对流流动。海冰覆盖了约 15% 的海洋表面，它是一层薄薄的层，将大气和海洋隔开，并负责调节地球极地地区这两者之间的热交换。海冰的热导率是气候模型中的一个关键参数。然而，由于海冰结构复杂，由冰、气泡和盐水包裹体组成，这些包裹体是在冰从海洋表面冻结到更深处时形成的，因此很难测量。实际上，海冰可以被认为是一种多孔复合材料，因此对温度和盐度的变化非常敏感。

❄️ 海冰内部的对流流动会显著提高其热导率。 麦考瑞大学的应用数学家 Noa Kraitzman 领导了一项新研究，该研究表明，盐水包裹体内的盐水比淡海水重，这会导致冰内部的对流流动，形成液体流出的通道。研究人员通过将平流-扩散过程与均质化理论相结合，建立了一个新的框架来描述多孔海冰中增强的热传输，该理论将复杂的物理性质简化为有效的整体系数。

❄️ 对流流动会使海冰的有效热导率提高两到三倍。 这项新研究建立在 2001 年的一项研究的基础上，该研究观察到在较高温度下海冰的热导率有所增加。Kraitzman 解释说，在他们的计算中，他们必须推导出有效热导率的新界限，同时还要考虑复杂的二维对流流体流动，并开发一个可以与现场实验测量直接比较的理论模型。他们采用 Padé 近似来获得所需的界限，并专门针对海冰对 Péclet 数进行了参数化，将其视为饱和岩石。

❄️ 研究结果表明，对流流动会使海冰的有效热导率提高两到三倍，尤其是在冰的较低、较温暖的部分，因为温度和冰的渗透性有利于对流。 Kraitzman 告诉《物理世界》杂志，这种增强主要局限于冰冻季节的底部 10 厘米，因为在这些部位海冰内部存在对流流动。将这些界限纳入全球气候模型可以提高模型预测热量通过海冰传输的能力，从而更准确地预测海冰融化速度。

❄️ 研究人员希望获得更多现场测量数据来完善和验证他们的模型。 Kraitzman 和他的同事表示，他们现在希望获得更多现场测量数据来完善和验证他们的模型。他们还想扩展他们的数学框架，以包括更一般的三维流动，并纳入海洋和海冰之间存在的复杂流体交换过程。Kraitzman 说：“通过解决这些不同的领域，我们旨在提高模型的准确性和适用性，特别是在海洋-海冰相互作用模型中，旨在更好地理解极地热交换过程及其全球影响。”

The thermal conductivity of sea ice can significantly increase when convective flow is present within the ice. This new result, from researchers at Macquarie University, Australia, and the University of Utah and Dartmouth College, both in the US, could allow for more accurate climate models – especially since current global models only account for temperature and salinity and not convective flow.

Around 15% of the ocean’s surface will be covered with sea ice at some time in a year. Sea ice is a thin layer that separates the atmosphere and the ocean and it is responsible for regulating heat exchange between the two in the polar regions of our planet. The thermal conductivity of sea ice is a key parameter in climate models. It has proved difficult to measure, however, because of its complex structure, made up of ice, air bubbles and brine inclusions, which form as the ice freezes from the surface of the ocean to deeper down. Indeed, sea ice can be thought of as being a porous composite material and is therefore very sensitive to changes in temperature and salinity.

The salty liquid within the brine inclusions is heavier than fresh ocean water. This results in convective flow within the ice, creating channels through which liquid can flow out, explains applied mathematician Noa Kraitzman at Macquarie, who led this new research effort. “Our new framework characterizes enhanced thermal transport in porous sea ice by combining advection-diffusion processes with homogenization theory, which simplifies complex physical properties into an effective bulk coefficient.”

Thermal conductivity of sea ice can increase by a factor of two to three

The new work builds on a 2001 study in which researchers observed an increase in thermal conductivity in sea ice at warmer temperatures. “In our calculations, we had to derive new bounds on the effective thermal conductivity, while also accounting for complex, two-dimensional convective fluid flow and developing a theoretical model that could be directly compared with experimental measurements in the field,” explains Kraitzman. “We employed Padé approximations to obtain the required bounds and parametrized the Péclet number specifically for sea ice, considering it as a saturated rock.”

Padé approximations are routinely used to approximate a function by a rational analysis of given order and the Péclet number is a dimensionless parameter defined as the ratio between the rate of advection to the rate of diffusion.

The results suggest that the effective thermal conductivity of sea ice can increase by a factor of two to three because of conductive flow, especially in the lower, warmer sections of the ice, where temperature and the ice’s permeability favour convection, Kraitzman tells Physics World. “This enhancement is mainly confined to the bottom 10 cm during the freezing season, when convective flows are present within the sea ice. Incorporating these bounds into global climate models could improve their ability to predict thermal transport through sea ice, resulting in more accurate predictions of sea ice melt rates.”

Looking forward, Kraitzman and colleagues say they now hope to acquire additional field measurements to refine and validate their model. They also want to extend their mathematical framework to include more general 3D flows and incorporate the complex fluid exchange processes that exist between ocean and sea ice. “By addressing these different areas, we aim to improve the accuracy and applicability of our model, particularly in ocean-sea ice interaction models, aiming for a better understanding of polar heat exchange processes and their global impacts,” says Kraitzman.

The present work is detailed in Proceedings of the Royal Society A.

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