  In weakly-collisional plasma environments with sufficiently low electron
beta, Alfv\'enic turbulence transforms into inertial Alfv\'enic turbulence at
scales below the electron skin-depth, $k_\perp d_e\gtrsim 1$. We argue that, in
inertial Alfv\'enic turbulence, both energy and generalized kinetic helicity
exhibit direct cascades. We demonstrate that the two cascades are compatible
due to the existence of a strong scale-dependence of the phase alignment angle
between velocity and magnetic field fluctuations, with the phase alignment
angle scaling as $\cos\alpha_k\propto k_{\perp}^{-1}$. The kinetic and magnetic
energy spectra scale as $\propto k_{\perp}^{-5/3}$ and $\propto
k_{\perp}^{-11/3}$, respectively. As a result of the dual direct cascade, the
generalized-helicity spectrum scales as $\propto k^{-5/3}_{\perp}$, implying
progressive balancing of the turbulence as the cascade proceeds to smaller
scales in the $k_{\perp} d_e \gg 1$ range. Turbulent eddies exhibit a
phase-space anisotropy $k_{\parallel} \propto k_{\perp}^{5/3}$, consistent with
critically-balanced inertial Alfv\'en fluctuations. Our results may be
applicable to a variety of geophysical, space, and astrophysical environments,
including the Earth's magnetosheath and ionosphere, solar corona,
non-relativistic pair plasmas, as well as to strongly rotating non-ionized
fluids.
