AbstractLinear wave modelling about a zonally symmetric state is often assumed to be able to simulate accurately time‐averaged planetary wave geopotential heights in the stratosphere during quiescent winter periods. We test this linear assumption by using a time‐dependent three‐dimensional primitive equation model of the stratosphere and mesosphere to simulate the quiescent winter stratospheric circulation during December 1980. The results from this simulation, together with two other idealized integrations, indicate that nonlinear wave interactions were crucial in accounting for the observed monthly mean wavenumber‐1 planetary wave amplitude, particularly in the upper stratosphere. Our results suggest that, in general, such interactions cannot be ignored for quantitatively accurate simulations of the middle atmosphere.