  A weakly dispersive sub-range (WDR) of kinetic Alfv\'en turbulence is
distinguished and investigated for the first time in the context of MHD/kinetic
turbulence transition. We found perpendicular wavenumber spectra ~ k^{-3} and ~
k^{-4} formed in WDR by strong and weak turbulence of kinetic Alfv\'en waves
(KAWs), respectively. These steep WDR spectra connect shallower spectra in the
MHD and strongly dispersive KAW sub-ranges, which results in a specific
double-kink (2-k) pattern often seen in observed turbulent spectra. The first
kink occurs where MHD turbulence transforms into weakly dispersive KAW
turbulence; the second one is between weakly and strongly dispersive KAW
sub-ranges. Our analysis suggests that the partial turbulence dissipation due
to amplitude-dependent super-adiabatic ion heating may occur in the vicinity of
the first spectral kink. A threshold-like nature of this process results in a
conditional selective dissipation affecting only largest over-threshold
amplitudes and decreasing intermittency in the range below the first spectral
kink. Several recent counter-intuitive observational findings can be explained
by the selective dissipation coupled to the nonlinear interaction among weakly
dispersive KAWs.
