Math 2.0

Fluid mechanics Definition

Transonic flow

Builds on Compressible flowMach numberSpeed of soundTricomi equationShock wave

Definition

Consider a steady compressible flow past a body, with local Mach number M(x)=∣𝐮(x)∣/c(x)M(x) = \abs{\mathbf{u}(x)} / c(x), where c(x)c(x) is the local speed of sound. The flow is transonic if the set where M<1M < 1 and the set where M>1M > 1 are both nonempty. The surface {x:M(x)=1}\set{x : M(x) = 1} that separates them is the sonic surface, or sonic line in a plane flow. The critical Mach number of the body is the free stream Mach number at which M=1M = 1 is first reached somewhere on the body.

Remarks

Example: a typical airfoil at free stream Mach number 0.80.8 has a supersonic pocket above its upper surface, closed downstream by a shock wave. The flow elsewhere is subsonic, so the flow is transonic. Non-example: the same airfoil at free stream Mach number 0.30.3 has M<1M < 1 everywhere, so the flow is subsonic. In engineering usage the transonic range is roughly 0.8<M∞<1.20.8 < M_\infty < 1.2. For steady irrotational flow, the potential equation is elliptic where M<1M < 1 and hyperbolic where M>1M > 1. So a transonic flow solves a PDE of mixed type, a nonlinear relative of the Tricomi equation.

Reading path

To understand this page from the ground up, read these 6 pages in order. The foundations come first.

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Compressible flow, concept, no evidence levelCompressible flowconceptMach number, concept, no evidence levelMach numberconceptShock wave, concept, no evidence levelShock waveconceptSpeed of sound, concept, no evidence levelSpeed of soundconceptTricomi equation, concept, no evidence levelTricomi equationconceptTransonic flow, definition, no evidence levelTransonic flowdefinition
Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.
  • no evidence level
  1. Compressible flow concept
  2. Mach number concept
  3. Shock wave concept
  4. Speed of sound concept
  5. Tricomi equation concept
  6. Transonic flow definition

Further reading

  1. Web https://en.wikipedia.org/wiki/Transonic
About this page
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DefinesTransonic flow
UsesCompressible flow, Mach number, Speed of sound, Tricomi equation, Shock wave
Changed3 November 2026

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