Lower bound for transient growth of inclined buoyancy layer

doi:10.1007/s10483-017-2202-8

Applied Mathematics and Mechanics (English Edition) ›› 2017, Vol. 38 ›› Issue (6): 779-796.doi: https://doi.org/10.1007/s10483-017-2202-8

Lower bound for transient growth of inclined buoyancy layer

Xiangming XIONG, Jianjun TAO

Center for Applied Physics and Technology (CAPT)-MOE Key Laboratory of High Energy Density Physics Simulation (HEDPS), State Key Laboratory for Turbulence and Complex System (SKLTCS), Department of Mechanics and Engineering Science, College of Engineering, Peking University, Beijing 100871, China

收稿日期:2016-04-15 修回日期:2016-09-27 出版日期:2017-06-01 发布日期:2017-06-01
通讯作者: Xiangming XIONG E-mail:xiongxmw@pku.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Nos. 11225209, 11490553, and 11521091)

Lower bound for transient growth of inclined buoyancy layer

Xiangming XIONG, Jianjun TAO

Center for Applied Physics and Technology (CAPT)-MOE Key Laboratory of High Energy Density Physics Simulation (HEDPS), State Key Laboratory for Turbulence and Complex System (SKLTCS), Department of Mechanics and Engineering Science, College of Engineering, Peking University, Beijing 100871, China

Received:2016-04-15 Revised:2016-09-27 Online:2017-06-01 Published:2017-06-01
Contact: Xiangming XIONG E-mail:xiongxmw@pku.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Nos. 11225209, 11490553, and 11521091)

摘要/Abstract

摘要：

The relationship between stabilities of the buoyancy boundary layers along an inclined plate and a vertical plate immersed in a stratified medium is studied theoretically and numerically. The eigenvalue problem of energy stability is solved with the method of descending exponentials. The disturbance energy is found to be able to grow to 11.62 times as large as the initial disturbance energy for Pr = 0.72 when the Grashof number is between the critical Grashof numbers of the energy stability and the linear stability. We prove that, with a weighted energy method, the basic flow of the vertical buoyancy boundary layer is stable to finite-amplitude streamwise-independent disturbances.

关键词: interpolation, singular perturbation method, nonlinear, natural convection, boundary layer, energy method, transient growth

Abstract:

Key words: interpolation, singular perturbation method, nonlinear, energy method, natural convection, boundary layer, transient growth

中图分类号:

76E06
76R10

Xiangming XIONG, Jianjun TAO. Lower bound for transient growth of inclined buoyancy layer[J]. Applied Mathematics and Mechanics (English Edition), 2017, 38(6): 779-796.

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Lower bound for transient growth of inclined buoyancy layer

Lower bound for transient growth of inclined buoyancy layer

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