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Communications in Mathematical Physics

, Volume 83, Issue 2, pp 243–260 | Cite as

Nonlinear stability and instability of transonic flows through a nozzle

  • T.-P. Liu
Article

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.

Keywords

Neural Network Statistical Physic Shock Wave Complex System Nonlinear Dynamics 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • T.-P. Liu
    • 1
  1. 1.Department of MathematicsUniversity of MarylandCollege ParkUSA

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