The downstream flow of a transonic aircraft: a small disturbance, high Reynolds number analysis

Small disturbance equations for the downstream flow of a transonic aircraft are derived from the steady, viscous, compressible Reynolds-averaged Navier–Stokes equations. These equations are then simplified further for the relevant case of high Reynolds numbers. The given analysis appears not to be trivial, implying a mild form of ambiguity, leading to two acceptable strategies to solve the equations. The physical mechanisms that play a role in vortex decay and the consequent downstream transition of crossflow kinetic energy into viscous/thermodynamic streamwise momentum deficit are identified. The case of discrete trailing vortices having a distinct vortex core is briefly discussed. Four invariant vorticity moments playing a role in the wake roll-up process are re-derived.