http://www.ocean.fsu.edu/~bunge/page/art1.pdf
1. Introduction [2] The Gulf of Mexico is a semi-enclosed sea with connections to the Caribbean Sea through the Yucatan Channel and to the Atlantic Ocean through the Florida Straits. The total mean transport flowing from the Caribbean into the Gulf of Mexico through the Yucatan Channel is close to 24 Sv, with RMS fluctuations of 4.6 Sv [Ochoa et al., 2001; Sheinbaum et al., 2002]. The Yucatan Current, which accounts for most of this transport, passes through the Yucatan Channel, where it becomes the Loop Current. This warm surface current shows great variability, either crossing directly toward the Florida Straits, or forming large loops inside the Gulf of Mexico, often followed by the shedding of large anticyclonic eddies. The dynamic reasons for the variations in the path of the current and for the eventual shedding of eddies are poorly understood. Nonetheless, some hypothesis have been explored using mass conservation. Maul [1977] suggested that changes in the Loop Current volume needed to be compensated by deep flows which, ****because of the large difference between the sill depth at the Yucatan Channel (2040 m) and at the Florida Straits (730 m at its shallowest poin*****t, between Miami and Bimini), may only occur at Yucatan. Maul et al. [1985] examined their idea by comparing observations made over a 3 year period with a current meter placed at the bottom of the Yucatan Channel, to the surface area of the Loop Current inferred from satellite infrared observations, but found no relation between the two data sets. Maul and Vukovich [1993] compared the volume transports in the Florida Straits and the Loop Current extension, but again found little correlation.


The difference between the ***sill*** depths at the Yucatan Channel and the Florida Straits suggests the use of a two-layer model, with the lower layer extending from the bottom of the Gulf of Mexico to the level of the deepest isotherm found in the Florida Straits, and the upper layer from that isotherm to the surface (Figure 1).


Strictly speaking, TF should correspond to the transport across the Key West to Havana section, where all the contribution to the Florida Current originates from the Yucatan Channel and the **sill*** depth is close to 900 m, but the deepest connection with the Atlantic Ocean at the Miami-Bimini section, is shallower than that (730 m) and the minimum temperature observed there is about 6 C [Schmitz and Richardson, 1991].

A while back I found a Glosario de Geología Inglés – Español, at:
http://ceramica.wikia.com/wiki/Glosario_de_Geología_Inglés_–...
It is English-Spanish only, but back-checking on "sill" I found this:
sill [marine geol] : umbral submarino [geol marino]