A numerical study of the two‐dimensional flow of linearly stratified Boussinesq fluid past a vertical flat plate in a channel of finite depth is described. It is found that there are time‐dependent oscillations in each vertical mode of the upstream advancing columnar disturbances which correspond to the unsteadiness in the drag coefficient found in previous experiments. The long‐time behavior of the upstream columnar disturbances shows that the time‐averaged strength of each mode approaches some constant value that is not zero. This determines the drag coefficient in the long‐time limit. In many points the numerical solutions of the Navier–Stokes equation agree with the solutions of the forced Korteweg–de Vries (KdV) equation with a cubic nonlinear term or the forced KdV–Burgers equation. It is also suggested that the strong downstream columnar disturbances predicted by linear theory for steady flow do not exist.