580 



5 



2n(-t) 



N^(i<) 



J ^ 5 6 8 10 



20 



FIGURE 6. The one tenth law as confirmed by laboratory 

 experiments of A. G. Zatsepin, K. N. Fedorov, S. I. 

 Voropaev, and A. M. Pavlov. 



50 



100 



zoo 



• — iV = 0.63 sec" 



'< — /T" = 1.00 sec^ 



AV«a>— jvj=0.58 sec' 



square of time; at the intermediate stage it is 

 proportional to the square root of time for a cylin- 

 drical spot and to the cube root of time for an axi- 

 symmetric spot. At the viscous stage the extension 

 is proportional to time; to one sixth in the case of 

 a cylindrical spot and to one tenth in the case of 

 an axisymmetric spot. Thus the extension of the 

 spot is sharply decelerated at the viscous stage in 

 comparison with the initial stages. 



It seems plausible to us that the "blini" shaped 

 regions of constant density and temperature observed 

 in the ocean are turbulent spots of various scales 

 generated by the loss of stability or breaking of 

 internal waves, local instability of shear flows, 

 penetration of cooled turbulized fluid from the 

 turbulized surface layer, etc. which are mainly in 

 the last, viscous stage of their evolution. Note 

 that along with the states in which turbulence is 

 preserved within the spot, the states are possible 

 and apparently rather frequent, especially for spots 

 of small scales, in which turbulence within the spot 

 has disappeared but the fluid remains mixed and homog- 

 eneous. This assumption is supported qualitatively 

 by some data of simultaneous measurements of vertical 

 distributions of density and velocity gradient 

 [Federov (1975) ] . These distributions have the form 

 presented by solid lines in Figure 1. Indeed, if 

 the regions of constant density are intrusions, then 

 the shear should increase near their boundaries com- 

 pared to ambient fluid (cf . , Figure 2) . However, in 

 this case the shear should be reduced near the cen- 

 tral line of intrusion (dashed line in Figure 1) . 

 It is plausible that the resolution in these mea- 

 surements was not sufficient to observe this shear 

 reduction. 



it is of interest from the point of view of the 

 evolution of turbulent spots in stratified fluid. 

 A characteristic example - the intrusion of the 

 bottom Mediterranean water into the body of the 

 Atlantic (Figure 7) . The bottom water descends 

 through the Straits of Gibraltar down the contin- 

 ental slope and enters the body of the ocean in an 

 intermediate layer where the density of the ocean 

 water is equal to its own density. The intrusion 

 of the bottom water of the Red Sea into the body of 

 the Indian Ocean is completely analogous. The in- 

 trusion of bottom water is a slow process and we 

 may assume that for its description, Eq. (22), 

 corresponding to a pure viscous mechanism of the 

 intrusion drag, is valid. 



The intrusion of bottom sea water into the body 

 of the ocean goes by separate portions [Federov 

 (1976) ] and it is possible to assvune that, at the 

 beginning of the intrusion of a new portion, the 

 bottom fluid that intruded earlier is carried suf- 

 ficiently far away so that the initial condition 

 holds 



h(x,0) = (x > 0) 



(35) 



Here h, as before, is the height of the intrusion 

 tongue, x the horizontal coordinate in the direction 

 of intrusion from its origin. Let us suppose that 



5. 



THE INTRUSION OF BOTTOM SEA WATER INTO THE 

 BODY OF THE OCEAN 



The intrusion of mixed fluid into a continuously 

 stratified medium is widely distributed in nature; 



FIGURE 7. The intrusion of sea bottom water into the 

 body of the ocean. 



