THE ZEROS OF J1(2)(ZETA)-J0(ZETA)J2(ZETA)=0 WITH AN APPLICATION TO SWIRLING FLOW IN A TUBE

The roots of the equation J12(zeta) - J0(zeta)J2(zeta) = 0 are presented correctly to six decimal places, or better. The first 25 roots in the first quadrant of the zeta plane are tabulated, and an asymptotic formula that describes all subsequent roots correctly to at least six decimal places is derived. The roots are used to plot representative streamlines for the steady motion of a viscous fluid in a long tube, of constant radius, which rotates about its axis (the z-tripple-over-dot axis) with an angular velocity that changes discontinuously at z-tripple-over-dot = 0 from one constant value to another of the same sign. The results are discussed with reference to the vortex breakdown phenomenon.