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Applied Mathematics and Mechanics

, Volume 37, Issue 9, pp 1203–1218 | Cite as

Transient growth in Poiseuille-Rayleigh-Bénard flows of binary fluids with Soret effect

  • Jun HuEmail author
  • D. Henry
  • H. Benhadid
  • Xieyuan Yin
Article

Abstract

The transient growth due to non-normality is investigated for the Poiseuille-Rayleigh-Bénard problem of binary fluids with the Soret effect. For negative separation factors such as ψ = −0.1, it is found that a large transient growth can be obtained by the non-normal interaction of the two least-stable-modes, i.e., the upstream and downstream modes, which determine the linear critical boundary curves for small Reynolds numbers. The transient growth is so strong that the optimal energy amplification factor G(t) is up to 102 ~ 103. While for positive separation factors such as ψ = 0.1, the transient growth is weak with the order O(1) of the amplification factor, which can even be computed by the least-stable-mode. However, for both cases, the least-stable-mode can govern the long-term behavior of the amplification factor for large time. The results also show that large Reynolds numbers have stabilization effects for the maximum amplification within moderate wave number regions. Meanwhile, much small negative or large positive separation factors and large Rayleigh numbers can enlarge the maximum transient growth of the pure streamwise disturbance with the wavenumber α = 3.14. Moreover, the initial and evolutionary two-dimensional spatial patterns of the large transient growth for the pure streamwise disturbance are exhibited with a plot of the velocity vector, spanwise vorticity, temperature, and concentration field. The initial three-layer cell vorticity structure is revealed. When the amplification factor reaches the maximum G max, it develops into one cell structure with large amplification for the vorticity strength.

Key words

binary fluid Soret effect transient growth Poiseuille-Rayleigh-Bénard flow 

Chinese Library Classification

O35 

2010 Mathematics Subject Classification

76E06 76R05 

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Copyright information

© Shanghai University and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Institute of Applied Physics and Computational MathematicsBeijingChina
  2. 2.Laboratoire de Mécanique des Fluides et d’AcoustiqueCNRS/Université de Lyon, Ecole Centrale de Lyon/Université Lyon 1/INSA de Lyon, ECLEcully CedexFrance
  3. 3.Department of Modern MechanicsUniversity of Science and Technology of ChinaHefeiChina

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