Date of Award

Summer 2021

Document Type


Degree Name

Doctor of Philosophy (PhD)


Mechanical & Aerospace Engineering


Aerospace Engineering

Committee Director

Robert L. Ash

Committee Member

Colin P. Britcher

Committee Member

Shizhi Qian


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, especially near airport runways. Fundamental knowledge of the physics that govern the formation, duration and dissipation of aircraft wake vortices is desirable in order to improve aircraft operational safety. 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 considered, modeled and compared using several vortex models found in the literature. Additionally, the non-equilibrium model for an isolated vortex is compared with existing wind tunnel data. 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. The model is based on a two-dimensional steady state vortex pair in an unbounded atmosphere. Existence of a vortex pair with nonequilibrium cores embedded in an inviscid fluid medium is discussed. Vortex pairs are characterized by an accompanying isolating “atmosphere”, commonly known as “Kelvin oval”. The non-equilibrium vortex pair model predicts a complete departure from the potential oval size when the pair are near merger.


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