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Lower bound for transient growth of inclined buoyancy layer

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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 P r = 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.

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Acknowledgements

The work was carried out at National Supercomputer Center in Tian**, and the calculations were performed on TianHe-1(A).

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Authors and Affiliations

  1. 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, Bei**g, 100871, China

    **angming **ong & Jianjun Tao

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  1. **angming **ong
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  2. Jianjun Tao
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Correspondence to **angming **ong.

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Project supported by the National Natural Science Foundation of China (Nos. 11225209, 11490553, and 11521091)

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**ong, X., Tao, J. Lower bound for transient growth of inclined buoyancy layer. Appl. Math. Mech.-Engl. Ed. 38, 779–796 (2017). https://doi.org/10.1007/s10483-017-2202-8

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  • DOI: https://doi.org/10.1007/s10483-017-2202-8

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