  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 $\tau_H$ 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 $\tau_E$
for energy transfer (J. Fluid Mech. {\bf 47}, 525--535 (1971)). We show that in
general $\tau_H$ may not be neglected compared to $\tau_E$, 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 $\tau_E$ in the low wavenumbers
with both energy and helicity spectra scaling as $k^{-5/3}$; and by $\tau_H$ at
larger wavenumbers with spectra scaling as $k^{-4/3}$. We demonstrate how,
within this phenomenology, the commonly observed ``bottleneck'' in the energy
spectrum might be explained. We derive a wavenumber $k_h$ 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.
