Shock Waves

, Volume 28, Issue 2, pp 417–425 | Cite as

Analytical extension of curved shock theory

  • G. Emanuel
Original Article


Curved shock theory (CST) is limited to shock waves in a steady, two-dimensional or axisymmetric (2-Ax) flow of a perfect gas. A unique feature of CST is its use of intrinsic coordinates that result in an elegant and useful formulation for flow properties just downstream of a shock. For instance, the downstream effect of upstream vorticity, shock wave curvature, and the upstream pressure gradient along a streamline is established. There have been several attempts to extend CST, as mentioned in the text. Removal of the steady, 2-Ax, and perfect gas limitations, singly or in combination, requires an appropriate formulation of the shock wave’s jump relations and the intrinsic coordinate Euler equations. Issues discussed include flow plane versus osculating plane, unsteady flow, vorticity, an imperfect gas, etc. The extension of CST utilizes concepts from differential geometry, such as the osculating plane, streamline torsion, and the Serret–Frenet equations.


Curved shock theory Shock jump relations Intrinsic coordinate Euler equations Unsteady flow Three-dimensional flow Imperfect gas 



The author gratefully acknowledges the helpful comments of S. Mölder and B. Argrow of the Universities of Ryerson, Toronto, Canada, and Colorado, USA, respectively.


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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.School of Aerospace and Mechanical EngineeringUniversity of OklahomaNormanUSA

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