•The dynamics of steady circulations in a equatorial mixed
layer can be approximated by a set of linear equations analogous to the equatorial wave equations ,
but with the time derivative terms replaced by linear damping terms.
•In the momentum
equations the surface eddy stress is taken to be proportional to
the mean velocity in the mixed layer.
•In the continuity
equation the perturbation in the mixed layer height is proportional to
the mass convergence in the layer, with a coefficient that is smaller in the
presence of convection than in its absence, due to ventilation of the
boundary layer by convection.