The transient growth in thermocapillary liquid layers is examined by nonmodal stability theory. Two kinds of thermocapillary liquid layers including linear flow and return flow are considered. The transient growth is measured by a growth function, which depends on both the velocity and temperature. It was found that rather large transient growth occurs in subcritical flows at small Prandtl numbers (Pr), while the temperature field on the surface has a negative effect on the transient growth. In particular, the transient growth function increases significantly with the Reynolds number, but decreases with Pr. The most amplified perturbation is characterized by counter-rotating vortices and streaks, which are both nearly streamwise. Energy analysis shows that the energy of transient growth mainly comes from the basic flow, while the work done by Marangoni forces on the surface is negligible.

中文翻译：

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热毛细管液体层的瞬态生长

通过非模态稳定性理论研究了热毛细管液层中的瞬态生长。考虑了两种热毛细管液体层，包括线性流和回流。瞬态增长通过增长函数来衡量，该函数取决于速度和温度。发现在亚临界流体中，在较小的Prandtl数（Pr）下会发生相当大的瞬态增长，而表面的温度场对瞬态增长有负面影响。特别是，瞬时增长函数随雷诺数显着增加，而随Pr减小。放大幅度最大的扰动的特征是反向旋转的涡流和条纹，它们几乎都沿流向流动。能量分析表明，瞬态增长的能量主要来自基本流量，