Wrap, tilt and stretch of vorticity lines around a strong thin straight vortex tube in a simple shear flow

The mechanism of wrap, tilt and stretch of vorticity lines around a strong thin straight vortex tube in a simple shear flow is analytically investigated. An asymptotic expressions for the vorticity field is obtained at a large Reynolds number and during the initial time S t≪1 of evolution as well as S t≪(Γ/ν)^1/2. The asymptotic solutions are expected to be closely related to the flow structures around intense vortex tubes observed in various kinds of turbulence such as helical winding of vorticity lines around a vortex tube, the dominance of cyclonic vortex tubes, the appearance of opposite-signed vorticity, and the zig-zag arrangement of streamwise vortices in homogeneous isotropic turbulence, shear turbulence and near-wall turbulence.