140 Fluctuations 



Consider a layer of water of density p^, depth D, overlying a deep, 

 resting layer of density p^^. The upper layer has a velocity U at the Key 

 West-Havana section (a; = 0), and its vorticity is zero. Farther down- 

 stream (a: = Aa:), at the narrower Miami-Cat Key section, the Stream has 

 accelerated by a drop in the free surface A^. Because the lower layer is at 

 rest, the interface must slope upward to offset the eflFect of the free surface. 

 If the axial pressure gradient vanishes in the lower layer, then the following 

 relation must hold: 



( p2-pA dD^dh 



\ P2 J dx 8x' 



The hnearized vorticity equation in this simple case may be WTitten as 

 follows, where ^ is the vorticity of the upper layer : 



We assume that the vorticity vanishes at Key West ; hence the vorticity 

 at Miami is given approximately by 



A^ Po 

 D P2-P1 



The actual acceleration observed at Miami corresponds to a value of A^ of 

 about —20 cm. (This is somewhat in excess of the —4-9 cm. obtained by 

 leveUng between Key West and Miami [Montgomery, 1941a].) The 

 density difference of the two layers is approximately (P2~Pi)/P2 = 2 x 10~^. 

 The initial depth D of the current is roughly 250 m. ; and this yields a value 

 of the vorticity increase between Key West and Miami of A^= —0-4/, the 

 observed value given above. 



If the high anticyclonic shear at Miami is actually due to the vertical 

 shrinking of the upper layers, it should be possible, by careful hydro- 

 graphic observations on the two sections, to try to detect the average rise 

 of about 100 m. in the isopycnic surface at a depth of 100-300 m. It would 

 be difficult and tedious to measure this hypothetical rise, because the rise 

 may be partly masked by the large cross-stream slope of the isopycnic 

 surfaces, and by variations in depth caused by the tides. Present data 

 are insufficient to form a basis for a satisfactory test. 



The Miami tide gauge is most sensitive to fluctuations in the transport 

 through the Florida Straits, because it lies at the western end of the 

 shallowest section of the Stream. 



