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A weakly dispersive sub-range (WDR) of kinetic Alfv\'en turbulence isdistinguished and investigated for the first time in the context of MHD/kineticturbulence 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 theMHD and strongly dispersive KAW sub-ranges, which results in a specificdouble-kink (2-k) pattern often seen in observed turbulent spectra. The firstkink occurs where MHD turbulence transforms into weakly dispersive KAWturbulence; the second one is between weakly and strongly dispersive KAWsub-ranges. Our analysis suggests that the partial turbulence dissipation dueto amplitude-dependent super-adiabatic ion heating may occur in the vicinity ofthe first spectral kink. A threshold-like nature of this process results in aconditional selective dissipation affecting only largest over-thresholdamplitudes and decreasing intermittency in the range below the first spectralkink. Several recent counter-intuitive observational findings can be explainedby the selective dissipation coupled to the nonlinear interaction among weaklydispersive KAWs.

Turbulent spectra and spectral kinks in the transition range from MHD to kinetic Alfv\'en turbulence