Abstract: For the two-layer quasi-geostrophic flow on β plane,there is a minimum enstrophy if the energy,momentum and circulation are specified.This minimum enstrophy flow is obtained by variational calculation.The form of the minimum enstrophy solutionrelies on the aspect ratio of the channel.If the zonal length of the channel is substantially greater than its meridional width,the solution is always a Rossby wave except a special case.Otherwise,if this inequality is reversed,the form of the solution is decided by the ratio of the energy to the square of momentum.