We consider the dynamics of axial velocity and of scalar transport in the s
tretched-spiral vortex model of turbulent fine scales. A large-time asympto
tic solution to the scalar advection-diffusion equation, with an azimuthal
swirling velocity field provided by the stretched spiral vortex, is used to
gether with appropriate stretching transformations to determine the evoluti
on of both the axial velocity and a passive scalar. This allows calculation
of the shell-integrated three-dimensional spectra of these quantities for
the spiral-vortex flow. The dominant term in the velocity (energy) spectrum
contributed by the axial velocity is found to be produced by the stirring
of the initial distribution of axial velocity by the axisymmetric component
of the azimuthal velocity. This gives a k(-7/3) spectrum at large wave num
bers, compared to the k(-5/3) component for the azimuthal velocity itself.
The spectrum of a passive scalar being mixed by the vortex velocity field i
s the sum of two power laws. The first is a k(-1) Batchelor spectrum for wa
ve numbers up to the inverse Batchelor scale. This is produced by the axisy
mmetric component of the axial vorticity but is independent of the detailed
radial velocity profile. The second is a k(-5/3) Obukov-Corrsin spectrum f
or wave numbers less than the inverse Kolmogorov scale. This is generated b
y the nonaxisymmetric axial vorticity and depends on initial correlations b
etween this vorticity and the initial scalar field. The one-dimensional sca
lar spectrum for the composite model is in satisfactory agreement with expe
rimental measurement. (C) 2001 American Institute of Physics.