Date

2018

Document Type

Thesis

Degree

Master of Science

Department

Mechanical Engineering

First Adviser

Jaworski, Justin W.

Abstract

In formation flight, the wings of a leader aircraft generate trailing vortices that travel downstream and interact with the wings of a follower aircraft. The pressure field of the follower wing can effect the trajectory and stability of these trailing vortices prior to their direct impingement. This upstream influence is examined here by analytical and numerical means using the boundary layer approximation of the incompressible Navier-Stokes equations. Under these slenderness assumptions, the classical Batchelor q-vortex is evolved over a finite domain with a prescribed axisymmetric background pressure gradient using a Green's function approach. The presented analysis is restricted by the linearity of the boundary approximations and the requirement that the vortex and axisymmetric imposed pressure gradient are aligned. Results are presented for constant and linear pressure gradients, as well as for pressure fields representative of canonical axisymmetric follower bodies. This work may be extended and applied to the stability analysis of streamwise finite-core vortices arising in formation flight.

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