ferent in the two cases, and the latter agreed well withthe observations. The deepening rate accelerated dur-ing the initial rise in wind stress, but decreasedabruptly as 8V was reduced during the second half ofthe inertial period, even though u2 continued to in-crease. They thus found no evidence of deepening dri-ven by wind stress alone on this time scale, althoughturbulence generated near the surface must still havecontributed to keeping the surface layer stirred.A particularly clear-cut series of observations on con-vective deepening was reported by Farmer (1975). Hehas also given an excellent account of the related lab-oratory and atmospheric observations and models inthe convective situation. The convection in the caseconsidered by Farmer was driven by the density in-crease produced by surface heating of water, which wasbelow the temperature of maximum density in an ice-covered lake. Thus there were no horizontal motions,and no contribution from a wind stress at the surface.From successive temperature profiles he deduced therate of deepening, and showed that this was on average17% greater than that corresponding to "nonpenetra-tive" mixing into a linear density gradient. Thus asmall, but not negligible, fraction of the convectiveenergy was used for entrainment. [The numerical val-ues of the energy ratio derived in this and earlier stud-ies will not be discussed here; but note that the rele-vance of the usual definition has been called intoquestion by Manins and Turner (1978).]In certain well-documented cases, models developedfrom that of Kraus and Turner (1967) (using a para-meterization in terms of the surface wind stress andthe surface buoyancy flux) have given a good predictionof the time-dependent behavior of deep surface mixedlayers. Denman and Miyake (1973), for example, wereable to simulate the behavior of the upper mixed layerat ocean weather station P over a 2-week period. Theyused observed values of the wind speed and radiation,and a fixed ratio between the surface energy input andthat needed for mixing at the interface.On the seasonal time scale, Gill and Turner (1976)have systematically compared various models with ob-servations at a North Atlantic weathership. They con-cluded that the Kraus-Turner calculation, modified toremove or reduce the penetrative convective mixingduring the cooling cycle, gives the best agreement withthe observed surface temperature Ts of all the modelsso far proposed. In particular, it correctly reproducesthe phase relations between the dates of maximumheating, maximum surface temperature, and minimumdepth, and it predicts a realistic hysteresis loop in aplot of Ts versus total heat content H (i.e., it properlyincorporates the asymmetry between heating and cool-ing periods). This behavior is illustrated in figure 8.3.The model also overcomes a previous difficulty andallows the potential energy to decrease during the cool-J t I - dz1I I I I I180 200 220 240 260Figure 8.3 The heat content in the surface layer as a functionof surface temperature T at ocean weather station Echo.(After Gill and Turner, 1976.) The reference temperature T, isthe mean of the temperature at 250 m and 275 m depth, andthe months are marked along the curve.ing period, instead of increasing continuously as im-plied by the earlier models.The mixed-layer depth and the structure of the ther-mocline are not, however, well predicted by thesemodels; this fact points again to the factors that havebeen neglected. Niiler (1977) has shown that improvedagreement is obtained by empirically allowing the en-ergy available for mixing to decrease as the layer depthincreases [though a similar behavior is implied by theuse of (8.23); see Thompson (1976) for a comparison ofthe two types of model]. Direct measurements of thedecay of turbulent energy with depth in the mixedlayer will clearly be important. In many parts of theocean it may also be necessary to consider upwelling.Perhaps the most important deficiency is the neglectof any mixing below the surface layer. There is nowstrong evidence that the density interface is neverreally sharp, but has below it a gradient region that isindirectly mixed by the surface stirring. At greaterdepths too, the density profile is observed to changemore rapidly than can be accounted for by advection,so that mixing driven by internal waves, alone or incombination with a shear flow, must become signifi-cant. These internal processes are the subject of thefollowing section.8.4 Mixing in the Interior of the OceanThe overall properties of the main thermocline appar-ently can be described rather well in terms of a balancebetween upwelling w and turbulent diffusion K in thevertical. Munk (1966), for example, after reviewing ear-lier work, summarized data from the Pacific that showthat the T and S distributions can be fitted by expo-nentials that are solutions of diffusion equations, forexample245Small-Scale Mixing Processes1400-1200-1000-[. -T i, -"'d2T dTKz -z = 0,with the scaleheight K/w 1 km. By using distribu-tions of a decaying tracer '4C, he also evaluated a scaletime K/w2, and the resulting upwelling velocity w 1.2 cm day-' and eddy diffusivity K 1.3 cm2s-1havebeen judged "reasonable" by modelers of the large-scaleocean circulation (chapter 15). Munk found the up-welling velocity consistent with the quantity of bot-tom water produced in the Antarctic, but he was notable to deduce K using any well-documented physicalmodel. The most likely candidate seemed to be themixing produced by breakdown of internal waves, butother possibilities are double-diffusive processes, andquasi-horizontal advection following vertical mixing inlimited regions (such as near boundaries or acrossfronts).Some progress has been made in each of these areasin the past 10 years, and they will be reviewed in turn.First, however, we shall discuss a set of interrelatedideas about the energetics of the process that are vitalto the understanding of all types of mixing in a strati-fied fluid.8.4.1 Mechanical Mixing Processes(a) Energy Constraints on Mixing The overall Richard-son number Rio [defined by equation (8.8)] based on thevelocity and density differences over the whole
View Full Document
Unlocking...