  Acoustic phonons play a special role in lattice heat transport, and confining
these low-energy modes in low-dimensional materials may enable nontrivial
transport phenomena. By applying lowest-order anharmonic perturbation theory to
an atomistic model of a carbon nanotube, we investigate numerically and
analytically the spectrum of three-phonon scattering channels in which at least
one phonon is of low energy. Our calculations show that acoustic longitudinal
(LA), flexural (FA), and twisting (TW) modes in nanotubes exhibit a distinct
dissipative behavior in the long-wavelength limit, $|k| \rightarrow 0$, which
manifests itself in scattering rates that scale as $\Gamma_{\rm{LA}}\sim
|k|^{-1/2}$, $\Gamma_{\rm{FA}}\sim k^0$, and $\Gamma_{\rm{TW}}\sim |k|^{1/2}$.
These scaling relations are a consequence of the harmonic lattice approximation
and critically depend on the condition that tubes are free of mechanical
strain. In this regard, we show that small amounts of tensile lattice strain
$\epsilon$ reduce the strength of anharmonic scattering, resulting in
strain-modulated rates that, in the long-wavelength limit, obey $\Gamma \sim
\epsilon^{r} |k|^{s}$ with $r\leq 0$ and $s\geq 1$, irrespectively of acoustic
mode polarization. Under the single-mode relaxation time approximation of the
linearized Peierls-Boltzmann equation (PBE), the long-tube limit of lattice
thermal conductivity in stress-free and stretched tube configurations can be
unambiguously characterized. Going beyond relaxation time approximations,
analytical results obtained in the present study may help to benchmark
numerical routines which aim at deriving the thermal conductivity of nanotubes
from an exact solution of the PBE.
