The variables are eastward, northward, and upward velocity, is the pressure perturbation divided by reference density, is buoyancy, is the constant buoyancy frequency, and is the equatorial approximation to the Coriolis parameter. The equations express, respectively:
- zonal momentum balance between acceleration, Coriolis force, and pressure gradient;
- meridional geostrophic balance, with meridional acceleration omitted by the long-wave approximation;
- incompressible mass conservation;
- adiabatic buoyancy evolution in the background stratification;
- hydrostatic pressure balance, .
Together they are the hydrostatic Boussinesq approximation for long equatorial waves.
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