575 



?, Iffl 



sz 



FIGURE 1. Schematic form of syn- 

 chronous vertical distribution of 

 density and shear in the ocean. The 

 dashed line shows the shear distri- 

 bution for intrusions. 



after the breaking [Belyaev et al. (1975)]. 



The evolution of a newly-formed turbulent spot 

 appears to be the following. The turbulent mixing 

 makes the spot vertically quasi-homogeneous, there- 

 fore, within the spot the density of the water be- 

 comes uniform. For stable stratification, when the 

 density grows with depth, the density in the upper 

 half of the mixed spot is higher and in the lower 

 half of the spot lower than at the same levels in 

 ambient fluid. Therefore, under the action of the 

 buoyancy forces, the upper half of the spot should 

 go down and the lower half of the spot should rise 

 to its middle level. Therefore, the spot should 

 "collapse," simultaneously spreading and transform- 

 ing itself into a thin "blin." The intrusion of 

 such a "blin" into the body of surrounding strati- 

 fied fluid creates in it a new layer of microstruc- 

 ture. 



If the initial internal wave has a long period 

 and wave length (e.g., internal waves with tide 

 periods may be generated by tide forming forces 

 and tides themselves) turbulent spots formed by 

 this wave are large and corresponding turbulent 

 layers are very thick. Internal waves of smaller 

 periods and lengths may develop on these layers 

 forming turbulent spots of smaller sizes and layers 

 of microstructure of smaller thicknesses, etc.; 

 internal waves of minimum periods and lengths, 

 turbulent spots of minimum sizes and layers of 

 microstructure of minimum thicknesses. Thus, the 

 answer to the question "which came first, the chicken 

 or the egg?" consists for this case in the indica- 

 tion of a cascade process "internal waves ^ turbulent 

 spots -* layers of microstructure -*■ internal waves 

 etc." This cascade process may lead to the forma- 

 tion of a quasi-steady spectrum of internal waves, 

 intermittent turbulence , and layers of microstructure 

 (although in real nature the action of some other 

 processes influencing real spectra is possible, in- 

 cluding storms and quasi-steady horizontal inhomo- 

 geneities of geographic and dynamic origin) . The 

 turbulent spots also take part in a rising cascade 

 generated by local instabilities of available shear 

 flows, breaking of surface waves, sinking of cooled 



fluid from the turbulized surface layer, etc. As 

 distinct from the classical Kolmogorov cascade in 

 non-stratified fluid, here, in passing from a larger 

 scale to a smaller one, the energy is not preserved, 

 being left in turbulent spots in the final stage of 

 their evolution where internal waves do not gener- 

 ate. Thus, in stratified fluid turbulent spots of 

 various scales are continuously generated and the 

 process of their evolution is of considerable 

 interest. 



The first stages of the evolution of turbulent 

 spots where the radiation of internal waves takes 

 place are rather short: by estimates of J. Wu 

 (1969) and T. W. Kao (1976) they come to an end in 

 a time interval of the order of several tens of 

 N~ (N is the Brunt-Vaisala frequency) after the 

 beginning of the process. The final stage of the 

 evolution of turbulent spots is much longer. This 

 stage is much less known: in the paper of J. Wu 

 (1969) concerning this stage it is mentioned only 

 that viscosity is of significance at this stage and 

 it is noted that the profile of the spot is pre- 

 served during this stage. The analysis presented 

 here shows that the velocity of the extension of 

 turbulent spots at the viscous stage is essentially 

 lower than at the initial stages. It is our opin- 

 ion that the "blini"-shaped turbulent structures 

 are the intrusions of the turbulent spots of various 

 scales into surrounding stratified fluid which are 

 mainly at the final stage of their evolution. 



Thus, let a turbulent spot (Figure 1) be formed in 

 a stable continuously density-stratified (linearly 

 for definiteness) fluid due to some reason (breaking 

 of internal waves, local loss of stability of shear 

 flow, penetration of denser fluid from the turbulent 

 surface layer, etc.). The density of fluid within 

 the turbulent spot due to mixing is uniform in con- 

 trast to an ambient continuously stratified fluid 

 being in a state of rest or laminar motion. Certain 

 potential energy is stored due to mixing in the tur- 

 bulent spot, so the state of the mixed fluid- 

 stratified environment system ceases to be in 

 equilibrium. Mixed turbulent fluid starts to strike 

 (Figure 2) into stratified non-turbulent fluid by 

 tongues - "intrusions" which are formed at the 

 level, z = zj, (z is the vertical coordinate) where 

 the density of stratified fluid is equal to the 

 density of mixed fluid. 



Potential energy, stored by the fluid at initial 

 turbulization and mixing in the spot, dissipates 

 during the intrusion of mixed fluid into stratified 

 non-turbulent fluid. It is natural to consider 

 three stages of the evolution of the spot: 



(1) Initial stage of free intrusion. The motive 

 force of the intrusion at this stage exceeds greatly 

 the drag forces. The turbulent spot extends slightly 

 but the internal waves are intensively formed by the 

 spot. 



(2) Intermediate steady state. The motive force 

 at this stage is balanced mainly by form drag and 

 wave drag due to radiation of internal waves by an 

 extending turbulent spot. The acceleration of the 

 tongue is negligible. 



The classification of stages of the evolution of the spot of 

 mixed fluid in the continuously density-stratified fluid goes 

 back to the fundamental work of J. Wu (1969) where the ex- 

 perimental investigation of the initial stages of this process 

 was performed for the wake of circular initial cross-section. 

 T. W. Kao (1976) performed semi-empirical theoretical investi- 

 gation for the initial stages of the evolution of such wakes. 



