RAYLEIGH-TAYLOR INSTABILITY FOR COMPRESSIBLE ROTATING FLOWS

doi:10.1016/S0252-9602(15)30060-6

数学物理学报(英文版) ›› 2015, Vol. 35 ›› Issue (6): 1359-1385.doi: 10.1016/S0252-9602(15)30060-6

RAYLEIGH-TAYLOR INSTABILITY FOR COMPRESSIBLE ROTATING FLOWS

段然¹, 江飞², 尹俊平³

1. School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China;
2. College of Mathematics and Computer Science, Fuzhou University, Fuzhou 361000, China;
3. Institute of Applied Physics and Computational Mathematics, Beijing 100088, China

收稿日期:2015-02-15 修回日期:2014-08-26 出版日期:2015-11-01 发布日期:2015-11-01
作者简介:Ran DUAN, E-mail: duanran@mail.ccnu.edu.cn;Fei JIANG, E-mail: jiangfei0591@163.com;Fei JIANG, E-mail: yinjp@163.com
基金资助:
The research of Ran Duan was supported by three grants from the NSFC (11001096, 11471134), Program for Changjiang Scholars and Innovative Research Team in University (IRT13066); the research of Fei Jiang and Junping Yin was supported by NSFC (11101044, 11301083).

RAYLEIGH-TAYLOR INSTABILITY FOR COMPRESSIBLE ROTATING FLOWS

Ran DUAN¹, Fei JIANG², Fei JIANG³

1. School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China;
2. College of Mathematics and Computer Science, Fuzhou University, Fuzhou 361000, China;
3. Institute of Applied Physics and Computational Mathematics, Beijing 100088, China

Received:2015-02-15 Revised:2014-08-26 Online:2015-11-01 Published:2015-11-01
Supported by:
The research of Ran Duan was supported by three grants from the NSFC (11001096, 11471134), Program for Changjiang Scholars and Innovative Research Team in University (IRT13066); the research of Fei Jiang and Junping Yin was supported by NSFC (11101044, 11301083).

摘要/Abstract

摘要：

In this paper, we investigate the Rayleigh-Taylor instability problem for two compressible, immiscible, inviscid flows rotating with a constant angular velocity, and evolving with a free interface in the presence of a uniform gravitational field. First we construct the Rayleigh-Taylor steady-state solutions with a denser fluid lying above the free interface with the second fluid, then we turn to an analysis of the equations obtained from linearization around such a steady state. In the presence of uniform rotation, there is no natural variational framework for constructing growing mode solutions to the linearized problem. Using the general method of studying a family of modified variational problems introduced in e^t√c|ξ|-1,where ξ is the spatial frequency of the normal mode and the constant c depends on some physical parameters of the two layer fluids. A Fourier synthesis of these normal mode solutions allows us to construct solutions that grow arbitrarily quickly in the Sobolev space H^k, and leads to an ill-posedness result for the linearized problem. Moreover, from the analysis we see that rotation diminishes the growth of instability. Using the pathological solutions, we then demonstrate the ill-posedness for the original non-linear problem in some sense.

关键词: Rayleigh-Taylor instability, rotation, Hadamard sense

Abstract:

Key words: Rayleigh-Taylor instability, rotation, Hadamard sense

中图分类号:

35L65

段然, 江飞, 尹俊平. RAYLEIGH-TAYLOR INSTABILITY FOR COMPRESSIBLE ROTATING FLOWS[J]. 数学物理学报(英文版), 2015, 35(6): 1359-1385.

Ran DUAN, Fei JIANG, Fei JIANG. RAYLEIGH-TAYLOR INSTABILITY FOR COMPRESSIBLE ROTATING FLOWS[J]. Acta mathematica scientia,Series B, 2015, 35(6): 1359-1385.

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RAYLEIGH-TAYLOR INSTABILITY FOR COMPRESSIBLE ROTATING FLOWS

RAYLEIGH-TAYLOR INSTABILITY FOR COMPRESSIBLE ROTATING FLOWS

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