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regime $T \sim T_Q$ - the thermal conductivity plateau

1986 Phonon localization in aggregates J. E. Graebner and B.Golding

1978 The low-temperature thermal properties of amorphous arsenic D. P. Jones , N. Thomas & W. A. Phillips

.... High-frequency longitudinal modes may also contribute : if the scattering by non-propagating ' transverse ' modes has any resonant character (since both transverse and longitudinal modes have the same frequency), the scattering may well decrease as the longitudinal frequency increases. Careful calculations are, of course, necessary to establish if the strength of this phonon-phonon scattering is sufficient to explain the plateau in K.