Motivated by the mushy zones of sea ice, volcanoes and icy moons of the outer solar system, we perform a theoretical and numerical study of boundary-layer convection along a vertical heated wall in a bounded ideal mushy region. The mush is comprised of a porous and reactive binary alloy with a mixture of saline liquid in a solid matrix, and is studied in the near-eutectic approximation. Here, we demonstrate the existence of four regions and study their behaviour asymptotically. Starting from the bottom of the wall, the four regions are (i) an isotropic corner region; (ii) a buoyancy dominated vertical boundary layer; (iii) an isotropic connection region; and (iv) a horizontal boundary layer at the top boundary with strong gradients of pressure and buoyancy. Scalings from numerical simulations are consistent with the theoretical predictions. Close to the heated wall, the convection in the mushy layer is similar to a rising buoyant plume abruptly stopped at the top, leading to increased pressure and temperature in the upper region, whose impact is discussed as an efficient melting mechanism.

中文翻译：

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沿垂直受热壁的糊状层中的对流

受外太阳系的海冰、火山和冰卫星的糊状区域的启发，我们在有界的理想糊状区域中对沿垂直加热壁的边界层对流进行了理论和数值研究。糊状物由多孔和反应性二元合金与固体基质中的盐液混合物组成，并在近共晶近似下进行了研究。在这里，我们证明了四个区域的存在并渐近地研究它们的行为。从墙的底部开始，四个区域是 (i) 各向同性角区域；(ii) 以浮力为主的垂直边界层；(iii) 各向同性连接区域；(iv) 顶部边界的水平边界层，具有很强的压力和浮力梯度。数值模拟的比例与理论预测一致。