1. linearized vorticity equation that governs barotropic dynamics is a(' ag' dzu at + u dy2 = 0 ax Starting from the horizontal momentum equations, show the steps in deriving the linearized vorticity equation, but this time allow the planet's rotation rate to vary: f = fo + By. (Because of this change, your final linearized equation will differ slightly from what's given above.). linearize around a background state with a zonal wind that varies with y only; there is no meridional component to the background wind. horizontal momentum equations: Du 1 ap Dt fv = - pox Dv 1 ap Dt + fu = - pdy