We extend the Kolmogorov phenomenology for the scaling of energy spectra in
high-Reynolds number turbulence, to explicitly include the effect of helicity.
There exists a time-scale ΟHβ for helicity transfer in homogeneous,
isotropic turbulence with helicity. We arrive at this timescale using the
phenomenological arguments used by Kraichnan to derive the timescale ΟEβ
for energy transfer (J. Fluid Mech. {\bf 47}, 525--535 (1971)). We show that in
general ΟHβ may not be neglected compared to ΟEβ, even for rather low
relative helicity. We then deduce an inertial range joint cascade of energy and
helicity in which the dynamics are dominated by ΟEβ in the low wavenumbers
with both energy and helicity spectra scaling as kβ5/3; and by ΟHβ at
larger wavenumbers with spectra scaling as kβ4/3. We demonstrate how,
within this phenomenology, the commonly observed ``bottleneck'' in the energy
spectrum might be explained. We derive a wavenumber khβ which is less than
the Kolmogorov dissipation wavenumber, at which both energy and helicity
cascades terminate due to dissipation effects. Data from direct numerical
simulations are used to check our predictions.Comment: 14 pages, 5 figures, accepted to Physical Review