The tangential velocity profile of the Lamb-Oseen vortex is given by r ug -2 (1-6-2/40), where...

  

Transcribed Image Text:

The tangential velocity profile of the Lamb-Oseen vortex is given by r ug -2 (1-6-2/40), where r is the radial ordinate, t is time, I' is the circulation and is the kinematic viscosity. With drug zero radial velocity the axial vorticity w, in cylindrical coordinates (r, 0) is given by w rr i) Show that 2/Aut W=== 4avt ii) Show that the maximum value of up is at position r* given by the expression 2/Avt 1+ 2vt The tangential velocity profile of the Lamb-Oseen vortex is given by r ug -2 (1-6-2/40), where r is the radial ordinate, t is time, I' is the circulation and is the kinematic viscosity. With drug zero radial velocity the axial vorticity w, in cylindrical coordinates (r, 0) is given by w rr i) Show that 2/Aut W=== 4avt ii) Show that the maximum value of up is at position r* given by the expression 2/Avt 1+ 2vt