Pd. Killworth et Nr. Mcdonald, MAXIMAL REDUCED-GRAVITY FLUX IN ROTATING HYDRAULICS, Geophysical and astrophysical fluid dynamics, 70(1-4), 1993, pp. 31-40
A simple but general upper bound is given for the flux of a reduced-gr
avity fluid with non-negative, but otherwise arbitrary, potential vort
icity through a sill of arbitrary shape. This bound is a modified form
of the zero potential vorticity limit. A weaker bound is given for th
e flux in any layer of an (n + 1/2) layer fluid.