Abstract
By using characteristic analysis of the linear and nonlinear parabolic stability equations (PSE), PSE of primitive disturbance variables are proved to be parabolic intotal. By using sub-characteristic analysis of PSE, the linear PSE are proved to be elliptical and hyperbolic-parabolic for velocity U, in subsonic and supersonic, respectively; the nonlinear PSE are proved to be elliptical and hyperbolic-parabolic for relocity U+u in subsonic and supersonic, respectively. The methods are gained that the remained ellipticity is removed from the PSE by characteristic and sub-characteristic theories, the results for the linear PSE are consistent with the known results, and the influence of the Mach number is also given out. At the same time, the methods of removing the remained ellipticity are further obtained from the nonlinear PSE.
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Communicated by Dai Shi-qiang and Wu Wang-yi
Foundation items: the National Natural Science Foundation of China (10032050); the National 863 Program Foundation of China (2002AA633100)
Biography: Li Ming-jun (1968≈)
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Ming-jun, L., Zhi, G. Analysis and application of ellipticity of stability equations on fluid mechanics. Appl Math Mech 24, 1334–1341 (2003). https://doi.org/10.1007/BF02439657
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DOI: https://doi.org/10.1007/BF02439657