The effect of linear waves on the Charney–Hasegawa–Mima model of drift and geostrophic turbulence is studied numerically for a slowly decaying field. It is shown that wave effects can reduce the efficiency of nonlinear mode coupling, effectively ‘freezing’ the spectrum to a narrow band in wavenumber space. Selective nonlinear interactions tend to favour velocities parallel to the direction of propagation of the waves. Accordingly, anisotropic spectra are observed, steeper in the direction of wave propagation, and shallower in the perpendicular direction.