On the Integrability of Subsonic Compressible Potential Flow Around Bodies of Revolution

This work applies differential geometry concepts involving integrability to the linearized potential equation for steady, compressible flow around axisymmetric bodies in space. The classical problem of flow past a sphere is analyzed for free-stream Mach numbers that yield subsonic flow fields. For this scenario, after casting the relevant linearized potential equation as an exterior differential system, the isovector method may be used to construct infinitesimal vector fields or Lie group generators encoding the invariance properties of the coordinate-free representation. This vector field then has a number of important applications to the underlying mathematical model, including categorization of its underlying Lie symmetries, association of those symmetries with readily observable flow behaviors, interrogation of conditions for local integrability, and identification and characterization of obstructions in extending from local to global integrability. This analysis is intended to provide a direct connection between these abstract geometric concepts and a classical, thoroughly understood physical model.