A note on the Ekman numbers at the interface of a two-layer, quasi-geostrophic flow

In a recent paper, the parameterisation of turbulence of a two-layer, quasi-geostrophic flow has been derived on the basis of a generalisation of the classical Ekman theory. While this generalisation does not pose any constraint on the vertical Ekman numbers relative to the turbulent sublayers just above and below the interface, energy arguments, pointed out in the present note, show that these numbers have, of necessity, the same value. Moreover, a oversimplified two-layer model, expounded at the end of the note, allows us to draw the same conclusion oil symmetry grounds.