The existence of temporally growing spatially damped long waves in western boundary current extensions is suggested by various authors from both an observational and theoretical point of view. Here the nature of such waves is reconsidered based on both a local analysis of a simple analytical model and numerical experiments. The analytical calculation consists of an investigation of the possible solutions of the quasi-geostrophic equation in a barotropic ocean, when a spatially constant zonal mean flaw and Laplacian lateral dissipation are considered. A previously unexplored case of a low frequency wave that undergoes amplitude growth in time but is spatially damped is explained based on energy convergence in the downstream direction. In the numerical experiments, in addition to an investigation on the realizability of the analytical solutions, effects of a tilting western boundary on the wind-driven circulation are explored. It is found that the tilt of the western boundary has a very strong effe... Abstract The existence of temporally growing spatially damped long waves in western boundary current extensions is suggested by various authors from both an observational and theoretical point of view. Here the nature of such waves is reconsidered based on both a local analysis of a simple analytical model and numerical experiments. The analytical calculation consists of an investigation of the possible solutions of the quasi-geostrophic equation in a barotropic ocean, when a spatially constant zonal mean flaw and Laplacian lateral dissipation are considered. A previously unexplored case of a low frequency wave that undergoes amplitude growth in time but is spatially damped is explained based on energy convergence in the downstream direction. In the numerical experiments, in addition to an investigation on the realizability of the analytical solutions, effects of a tilting western boundary on the wind-driven circulation are explored. It is found that the tilt of the western boundary has a very strong effe...