  Kelvin-Helmholtz {instability induced} turbulence is one promising mechanism
by which loops in the solar corona can be heated by MHD waves. In this paper we
present an analytical model of the dissipation rate of {Kelvin-Helmholtz
instability induced} turbulence $\varepsilon_{\rm D}$, finding it scales as the
wave amplitude ($d$) to the third power ($\varepsilon_{\rm D}\propto d^3$).
Based on the concept of steady-state turbulence, we expect the turbulence
heating throughout the volume of {the} loop to match the total energy injected
through its footpoints. In situations where this holds, the wave amplitude has
to vary as the cube-root of the injected energy. Comparing the analytic results
with those of simulations shows that our analytic formulation captures the key
aspects of the turbulent dissipation from the numerical work. Applying this
model to the observed characteristics of decayless kink waves we predict that
the amplitudes of these observed waves is insufficient to turbulently heat the
solar corona.
