The zeros of \(J^ 2_ 1(\zeta)-J_ 0(\zeta)J_ 2(\zeta)=0\) with an application to swirling flow in a tube. (English) Zbl 0716.33005
The complex roots in the first quadrant of the equation in the title are made available through tabulation (25 roots, 7 digits) and the remaining through an asymptotic formula. The roots play a role in the Lavan- Nielsen-Fejér solution of the steady motion of a viscous fluid in a long tube which rotates about its axis with an angular velocity that abruptly changes at one location of the axis. A discussion of the physical vortex breakdown phenomenon is included.
Reviewer: N.M.Temme
MSC:
| 33C10 | Bessel and Airy functions, cylinder functions, \({}_0F_1\) |
| 41A60 | Asymptotic approximations, asymptotic expansions (steepest descent, etc.) |
| 76B47 | Vortex flows for incompressible inviscid fluids |
| 76U05 | General theory of rotating fluids |
