The role of cross sectional geometry in the passive tracer problem

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  • March 20, 2019
Creator
  • Aminian, Manuchehr
    • Affiliation: College of Arts and Sciences, Department of Mathematics
Abstract
  • This dissertation is concerned with how the longitudinal moments (mean, variance, skewness) of a tracer distribution undergoing an advective-diffusive process in Poiseiulle flow depend in a nontrivial way upon the cross section of the pipe. The main focus of this dissertation is on the distribution’s skewness, which is the simplest statistic to describe upstream/downstream asymmetry in the tracer distribution. The results of both analysis and numerics show that the distribution’s skewness depends significantly on the cross section of the pipe. Typically, cross sections with an exaggerated aspect ratio (e.g., thin ellipses or rectangles) result in negative skewess in the distribution, that is, having a sharp front and a long tail upstream. The opposite is true for nearly circular or square cross sections, with a long tail downstream and the bulk of the distribution upstream. As a result, there are “golden" aspect ratios for each class of cross section – critical aspect ratios which maintain the initial symmetry through the advective timescale – and other critical aspect ratios which symmetrize the distribution at a faster rate than any other aspect ratio on diffusive timescales.
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  • In Copyright
Advisor
  • Camassa, Roberto
  • Newhall, Katherine
  • McLaughlin, Richard
  • Adalsteinsson, David
  • Miller, Laura
Degree
  • Doctor of Philosophy
Degree granting institution
  • University of North Carolina at Chapel Hill Graduate School
Graduation year
  • 2016
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