Update README.md

Author: Jwely

README.md

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-# Abstract
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 # pivpr
 
 [![DOI](https://zenodo.org/badge/16003/Jwely/pivpr.svg)](https://zenodo.org/badge/latestdoi/16003/Jwely/pivpr)
 
 Exploration of the Pressure Relaxation phenomena with Particle Image Velocimetry, or `pivpr` for short. 
 
+## Abstract
+Vortices are a common phenomenon in fluid flows that arise as kinetic 
+	energy dissipates into heat via viscous interaction. They arise naturally 
+	at large scales in the form of dust devils, tornadoes, and as a 
+	counter-rotating vortex pair in the wake of 
+	aircraft. It is important to understand the conditions leading to their 
+	formation, their duration, and their dissipation in order to forecast or 
+	prevent undesirable effects. Among these deleterious effects is a decrease 
+	in safety of aircraft 
+	operations in the wake of other aircraft, an extremely common situation at 
+	airports around the world. A large number of mathematical models and 
+	experimental data sets exists to help explain various aspects of axial wake 
+	vortex behavior, but current models fail to explain why many vortices 
+	remain tightly wound with slowly decaying azimuthal 
+	velocities about their cores the length of time for which they 
+	have been observed. The current study builds upon the theoretical work of 
+	Ash, Zardadkhan and Zuckerwar, and tests specific attributes 
+	of a turbulent axial vortex for agreement with non-equilibrium pressure 
+	relaxation theory. This theory provides an exact solution to a modified 
+	version of the Navier-Stokes equations for an 
+	axial vortex, with a resulting velocity model that agrees with leading 
+	empirical models. In the present investigation, axial wake vortices were 
+	created with a bi-wing vortex 
+	generator in a low speed wind tunnel, at free stream velocities between 15 
+	and 33 $m/s$. Stereo particle image velocimetry was employed to 
+	map three dimensional velocity vectors at positions between 5.4 and 10 
+	chord lengths downstream of the vortex generator, and at a sampling rate of 
+	1Hz for 200 seconds. A Reynolds time averaging approach was employed to 
+	express instantaneous velocity measurements as localized mean and 
+	fluctuating components and to study turbulent structures within the 
+	vortices. Periodicity in turbulent energy and Reynolds stress structures 
+	was observed by comparing vortex velocity fields normalized by age, based 
+	on free stream velocity and downstream distance. The cores of these 
+	vortices appeared to periodically ingest turbulent energy and compress it 
+	into approximately one half of local core radii. The cyclical ingestion of 
+	turbulence was shown to have the effect of tightening the core radius in 
+	the wake of the vortex generator center body. If this phenomenon persists 
+	for the life of the vortex, it could provide an explanation for the 
+	longevity of the azimuthal velocity component, as observed in natural wake 
+	vortices.
+	
+## About
 This repository is for code and resources for my masters thesis in Aerospace Engineering at [Old Dominion University](https://www.odu.edu/mae). The code revolves around synthesis and display of test data taken of an axial wake vortex with Particle Image Velocitmetry (PIV) in the ODU Low Speed Wind Tunnel (LSWT).
 
 The data is discussed in the context of the pressure relaxation phenomena which is theorized to allow the longevity of axial wake vortex flow structures. "Raw" vector data is calculated from raw stereo image data and instrument calibration parameters by comercial software using particle displacement tracking methods, and is stored in tabular `v3d` files. These v3d files are considered the starting point for this code base, though some additional code has been writen to demonstrate uncertainty principles behind correlation techniques used to calculate 3d vector fields from stereo frame stradled image pairs.