(l) inversely proportional to the previous mixed-layer thickness (h), (2) 

 inversely proportional to the mean density gradient (G) in the thermocline, 

 and (3) directly proportional to the amount of denser water (M=J — : — dt) 



produced at the surface during the given time period. An expression com- 

 hining these factors is: 



*.=&/-*-« (1) 



■where R is a proportionality factor dependent on type of units used, 

 amount of water added from the thermocline, horizontal components of 

 motion associated with the increase of density, conduction of heat from 

 and to the mixed layer below the thin surface stratum of density change, 

 and local conditions such as permanent flow, convergence or divergence, 

 etc. Thus the proportionality factor is a sum of several minor or indi- 

 vidually nondeterminable components and can hardly be expected to remain 

 constant; however, it can probably be treated as a constant in practical 

 use for at least more or less restricted areas. If sufficiently accurate 

 determinations of the increase of mixed-layer density and of mean density 

 gradient in the thermocline could be made in a case where only instability 

 mixing occurs, the factor R could be determined empirically. 



During spring the increasing temperature gradient in the thermocline 

 constantly increases stability. If no advection occurs, small variations 

 of salinity caused by evaporation cannot offset this increasing stability; 

 hence, instability mixing can be neglected. Instability mixing is also 

 negligible during summer because of limited evaporation, increasing surface 

 temperature, and the magnitude of the density gradient in the thermocline. 



Instability mixing becomes important during late fall, when surface 

 cooling starts to reduce the temperature gradient in the thermocline. At 

 this same time, wind waves and drift caused by severe storms increase the 

 mixed-layer thickness to nearly the maximum possible by mechanical mixing. 

 Rapid cooling and active evaporation, which cause instability mixing, 

 usually occur with heavy seas. 



Subsequent to a fall storm, a thermocline deeper than one produced by 

 mechanical mixing can be expected. Under given stability and surface con- 

 ditions, the thermocline depth is determined by the combined effects of 

 mechanical mixing and instability mixing. If a storm with slightly deeper 

 mixing penetration occurs soon after another storm, the thermocline depth, 

 which is already beyond the influence of mechanical mixing, would not be 

 altered. As surface cooling proceeds, further mixing and increase of the 

 thermocline depth are caused only by instability mixing. The influence of 

 mechanical mixing on the thermocline depth gradually ceases. Even the 

 heaviest storms during winter do not affect the thermocline, because 

 turbulence does not extend to the bottom of the mixed layer. 



13 



