Applied Mathematics and Mechanics >
Lower bound for transient growth of inclined buoyancy layer
Received date: 2016-04-15
Revised date: 2016-09-27
Online published: 2017-06-01
Supported by
Project supported by the National Natural Science Foundation of China (Nos. 11225209, 11490553, and 11521091)
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.
Xiangming XIONG, Jianjun TAO . Lower bound for transient growth of inclined buoyancy layer[J]. Applied Mathematics and Mechanics, 2017 , 38(6) : 779 -796 . DOI: 10.1007/s10483-017-2202-8
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