Revisit to frozen-in property of vorticity
Yang Shuai1, 2, Zuo Qun-Jie1, , Gao Shou-Ting1, 3
       

(color online) (a) and (b) Ideal case where the fluid elements ( and ) tilt from horizontal to vertical directions by only updraft, and related vorticity vector tied in material element evolves. Large and thick arrows denote updraft in panel (a) and convergence of airflows in panel(b). Thin solid lines with blue arrows refer to vortex lines, red arrows denote material line element vectors. (c) and (d) Another ideal case where the vertical component of fluid element grows associated vorticity intensifies and vortex lines are concentrated because of its frozen-in property. Large opposite arrows denote convergence of airflows, thin solid lines with blue arrows refer to vortex lines and vorticity vectors, red arrow represents material line vector. (e) The same as panel (b), except for low-level material line element developing upwards and the associated near-ground vorticity generation after the downdraft (purple arrow) joins the team.