We consider internal gravity waves in a stratified fluid layer with rigid horizontal boundaries and periodic boundary conditions on the sides at constant temperature with a small constant viscosity, modelled using the incompressible Navier-Stokes equations. Using operator-theoretic methods to study the damping rates of internal waves we prove there are non-oscillatory wave modes with arbitrarily small damping rates. We provide an asymptotic approximation for these non-oscillatory modes. Additionally, we find that the eigenvalues for damped oscillations are in an explicitly describable half-ring.