A zonal mean flow with small perturbations was assumed, , and a meridional flow with a zero mean, . Since it was assumed that the perturbations are small, a linearization can be performed on the barotropic vorticity equation above, ignoring all the non-linear terms (terms where two or more small variables, i.e. , are multiplied with one another). Also the derivative of  in the zonal direction, the time derivative of the mean flow  and the time derivative of  are zero. This results in a simplified equation:
With  as defined above () and  and  the small perturbations in the zonal and meridional components of the flow.