2025ApJ...989..141W

We extend the description of equivalent-barotropic equations for exoplanets to the diabatic case-that is, with explicit heating and/or cooling representation, rather than with a stationary deflection of the bottom bounding surface. In the diabatic case, the equation for potential temperature (or entropy) is directly forced and cannot be decoupled from the equations for momentum and nonlinear pressure (the mass-like variable); hence, the isentropic surfaces do not remain coincident with material surfaces. Here the formalism is presented for an atmosphere with the Lamb vertical structure, as the formalism is substantially simplified while still remaining physically useful under the structure. The equations presented set the stage for accurate global simulations, which permit small-scale vortices, gravity waves, and fronts observed in current three-dimensional global simulations to be studied in detail.