Analysis of a Non-Equilibrium Vortex Pair as Aircraft Trailing Vortices

Shortly after the roll-up evolution of the vortex sheet behind the wings of an aircraft, a coherent counter-rotating vortex pair emerges. Presence of this vortex pair in the downstream of an aircraft, creates unsafe conditions for other aircraft. This study uses non-equilibrium pressure theory to develop an accurate model describing the physical behavior of the vortex pair created by an aircraft in the early to mid-field vortex regime.  An isolated aircraft vortex is first modeled and compared using several vortex models. Eddy viscosity to kinematic viscosity ratio correlation for aircraft trailing vortices has been introduced to satisfy the turbulent energy embedded in the vortex cores. Subsequently, the counter-rotating vortex pair is considered, and detailed derivation of the non-equilibrium vortex pair model is introduced. Existence of a vortex pair with non-equilibrium cores embedded in an inviscid fluid medium is discussed. Vortex pairs are characterized by an accompanying isolating “atmosphere”, commonly known as “Kelvin oval”. When aircraft vortex pair are close to merger or the vortex cores increasingly dilate, the non-equilibrium vortex pair model predicts instability. Non-equilibrium oval size changes drastically from the potential oval size.