You have still not explained, how you justify the assumption that atmosphere is isothermal horizontally, but allows for horizontal pressure gradients. (judithcurry.com)
4 in the post) is that all potential energy released from condensation is locally converted into the power of the large - scale horizontal pressure gradient force u ∇ p. (judithcurry.com)
You can get horizontal pressure gradients from uneven distributions of molecular nitrogen (N2) ice, and you can get horizontal temperature gradients from uneven heating from the sun. (space.com)