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</o:shapelayout></xml><![endif]--></head><body lang=EN-US link=blue vlink=purple><div class=WordSection1><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal><span style='font-size:9.0pt'><o:p> </o:p></span></p><p class=MsoNormal align=center style='text-align:center;page-break-after:avoid'><b><span style='font-size:16.0pt;font-family:"Tahoma","sans-serif"'>MS Thesis Defense<o:p></o:p></span></b></p><p class=MsoNormal align=center style='text-align:center;page-break-after:avoid'><b><span style='font-size:16.0pt;font-family:"Tahoma","sans-serif"'><o:p> </o:p></span></b></p><p class=MsoNormal align=center style='text-align:center;page-break-after:avoid'><b><span style='font-size:16.0pt;font-family:"Tahoma","sans-serif"'>INSTABILITY OF A VORTEX COLUMN DUE TO TURBULENCE GENERATED AXIAL FLOW<o:p></o:p></span></b></p><p class=MsoNormal><b><span style='font-size:14.0pt;font-family:"Tahoma","sans-serif"'><o:p> </o:p></span></b></p><p class=MsoNormal align=center style='text-align:center'><b><span style='font-size:14.0pt;font-family:"Tahoma","sans-serif"'>Eric Stout<o:p></o:p></span></b></p><p class=MsoNormal align=center style='text-align:center'><b><span style='font-size:12.0pt'><o:p> </o:p></span></b></p><p class=MsoNormal align=center style='text-align:center'><b><span style='font-size:12.0pt'>Date: Wednesday, August 14<sup>th</sup>, <sup> </sup>2013<o:p></o:p></span></b></p><p class=MsoNormal align=center style='text-align:center'><b><span style='font-size:12.0pt'><o:p> </o:p></span></b></p><p class=MsoNormal align=center style='text-align:center'><b><span style='font-size:12.0pt'>Location:</span></b> <span style='font-size:12.0pt'>Mechanical Engineering (large) Conference Room<o:p></o:p></span></p><p class=MsoNormal align=center style='text-align:center'><b><span style='font-size:12.0pt'>Time: 2:30 PM<o:p></o:p></span></b></p><p class=MsoNormal align=center style='text-align:center'><b><span style='font-size:12.0pt'><o:p> </o:p></span></b></p><p class=MsoNormal align=center style='text-align:center'><b><span style='font-size:12.0pt'>Committee Chair: <o:p></o:p></span></b></p><p class=MsoNormal align=center style='text-align:center'><span style='font-size:12.0pt'>Dr. Fazle Hussain<o:p></o:p></span></p><p class=MsoNormal align=center style='text-align:center'><o:p> </o:p></p><p class=MsoNormal align=center style='text-align:center'><b><span style='font-size:12.0pt'>Committee Members: <o:p></o:p></span></b></p><p class=MsoNormal align=center style='text-align:center'>Dr. Ralph Metcalfe<o:p></o:p></p><p class=MsoNormal align=center style='text-align:center'>Dr. Gemunu Gunaratne<o:p></o:p></p><p class=MsoNormal align=center style='text-align:center'><o:p> </o:p></p><p class=MsoNormal><span style='font-size:12.0pt'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:12.0pt'><o:p> </o:p></span></p><p class=MsoNormal style='text-align:justify'>Axial flow generated by turbulence on an initially two-dimensional vortex column, the Lamb-Oseen vortex, is studied theoretically and by direct numerical simulation of the Navier-Stokes equations. Azimuthally wrapped filaments of opposite circulations, discussed for the case of two oppositely oriented filaments, advect radially in opposite directions, leading to radial separation of the filaments and net axial flow on the vortex axis. Axial velocity is found to grow as <i>t<sup>5/2</sup></i> from the simulation results, closely matching the analytically determined growth rate. Derivation of the axial flow magnitude predicts the onset of instability due to axial flow via the <i>q</i>($B"a(Bpeak azimuthal velocity/peak axial velocity) criterion. Simulation results show (limited) renewed growth when <i>q</i> decreases below the unstable limit, likely dominating the previously discussed parent-offspring hairpin vortex mechanism for regenerative growth and suggesting possible breakup of the initially normal mode stable vortex at higher Re due to ambient turbulence. <o:p></o:p></p><p class=MsoNormal style='text-align:justify'><o:p> </o:p></p></div></body></html>