“…Vortex research in Cartesian coordinates includes the Green-Taylor vortex [Taylor and Green, 1937] and the helicoid vortex developed in Section 5.1.1 [Rodriguez andEl-Genk, 2008a, 2010d]. Various researchers selected spherical coordinates [Tsukker, 1955;Gol'Dshtik and Yavorskii, 1986;Hwang and Chwang, 1992], but the vast majority of the research found in the literature is in cylindrical coordinates [Rankine, 1858;Lamb-Oseen, 1932;Burgers, 1948;Loitsyanskiy, 1953;Gortler, 1954;Newman, 1959;Sullivan, 1959;Batchelor, 1964;Squire, 1965;Chepura, 1969;Martynenko, 1989;Aboelkassem, Vatistas, and Esmail, 2005;Rodriguez andEl-Genk, 2008a, 2010d]. Cylindrical coordinates are chosen primarily due to its geometric simplicity and excellent mapping of the vortex behavior onto a coordinate system-in particular, as a 3D vortex spins azimuthally as it stretches about the z axis, the vortex velocity field shape fills up a cylindrical geometry.…”