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Notes on the Linearised Equation for the Velocity Potential of the Steady Supersonic flow of a Compressible Fluid
Author(s) -
Tempest R. K.,
Rosenhead L.
Publication year - 1949
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/s2-51.3.197
Subject(s) - supersonic speed , choked flow , compressible flow , compressibility , mathematics , flow (mathematics) , differential equation , wave equation , motion (physics) , equations of motion , partial differential equation , mechanics , classical mechanics , mathematical analysis , physics
This paper deals with solutions of the “linearised” differential equation of the velocity potential of a compressible fluid in steady supersonic motion. The linearised equation is identical in form with that of two‐dimensional subsonic wave motion. Known solutions of the two‐dimensional wave equation can be interpreted in terms of supersonic flow. Some of these, which have been used by various investigators, are brought together and are shown to be special cases of the general solution. Two new types of solution, which are of special interest and are appropriate to special systems of coordinates, are developed.