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Nonlinear stability and instability of transonic flows through a nozzle

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Abstract

We study transonic flows along a nozzle based on a one-dimensional model. It is shown that flows along the expanding portion of the nozzle are stable. On the other hand, flows with standing shock waves along a contracting duct are dynamically unstable. This was conjectured by the author based on the study of noninteracting wave patterns. The author had shown earlier that supersonic and subsonic flows along a duct with various cross sections are stable. Basic to our analysis are estimates showing that shock waves tend to decelerate along an expanding duct and accelerate along a contracting duct.

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Authors and Affiliations

  1. Department of Mathematics, University of Maryland, 20742, College Park, Maryland, USA

    T.-P. Liu

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  1. T.-P. Liu
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Communicated by J. Glimm

Sponsored by the United States Army under Contract No. DAAG29-80-C-0041. This material is based upon work supported by the National Science Foundation under Grant No. MCS 7802202 and by the Sloan Foundation

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Liu, TP. Nonlinear stability and instability of transonic flows through a nozzle. Commun.Math. Phys. 83, 243–260 (1982). https://doi.org/10.1007/BF01976043

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  • DOI: https://doi.org/10.1007/BF01976043

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