Lower bound for transient growth of inclined buoyancy layer

doi:10.1007/s10483-017-2202-8

Abstract

Abstract:

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.

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

2010 MSC Number:

76E06
76R10

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

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