The present study provides a unified and consistent theory for the three types of linear waves of the Shallow Water Equations (SWE) on the β-plane – Kelvin, inertia-gravity (Poincare) and planetary (Rossby). The unified theory obtains by formulating the linearized SWE as an eigenvalue problem that is a variant of the classical Schrödinger equation. The results of the new theory show that Kelvin...
