1 Strictly, a mixed layer refers to a layer of Suid which is notstratiRed (vertical gradients of potential temperature, salinity andpotential density, averaged horizontally or in time, are zero). Theterminology is most precise in the case of a convectively forcedboundary layer. Elsewhere, oceanographers use the term looselyto describe the region of the ocean that responds most directly tosurface processes. Late in the day, following periods of strongheating, the mixed layer may be quite shallow (a few meters orless), extending to the diurnal thermocline. In winter and follow-ing series of storms, the mixed layer may extend vertically tohundreds of meters, marking the depth of the seasonal thermo-cline at midlatitudes.

warmer than the mixed layer. Intermediate temper-ature maxima in the Antarctic Ocean are less pro-nounced (up to 0.53C) but occur persistently aroundAntarctica.

See also

Ekman Transport and Pumping. Geophysical HeatFlow. Heat Transport and Climate. Satellite

Measurements of Salinity. Satellite Remote Sens-ing of Sea Surface Temperatures. ThermohalineCirculation. Wind and Buoyancy-forced UpperOcean. Wind Driven Circulation.

Further ReadingTomczak M and Godfrey JS (1994) Regional Oceano-

graphy: an Introduction. Oxford: Pergamon.

UPPER OCEAN MIXING PROCESSES

J. N. Moum and W. D. Smyth, Oregon StateUniversity, Corvallis, OR, USA

Copyright ^ 2001 Academic Press

doi:10.1006/rwos.2001.0156

Introduction

The ocean’s effect on weather and climate is govern-ed largely by processes occurring in the few tens ofmeters of water bordering the ocean surface. Forexample, water warmed at the surface on a sunnyafternoon may remain available to warm the atmo-sphere that evening, or it may be mixed deeper intothe ocean not to emerge for many years, dependingon near-surface mixing processes. Local mixing ofthe upper ocean is predominantly forced from thestate of the atmosphere directly above it. The dailycycle of heating and cooling, wind, rain, and cha-nges in temperature and humidity associated withmesoscale weather features produce a hierarchy ofphysical processes that act and interact to stir theupper ocean. Some of these are well understood,whereas others have deRed both observationaldescription and theoretical understanding.

This article begins with an example of in situmeasurements of upper ocean properties. Theseobservations illustrate the tremendous complexityof the physics, and at the same time reveal someintriguing regularities. We then describe a set ofidealized model processes that appear relevant tothe observations and in which the underlyingphysics is understood, at least at a rudimentarylevel. These idealized processes are Rrst summarized,then discussed individually in greater detail. Thearticle closes with a brief survey of methods forrepresenting upper ocean mixing processes in large-scale ocean models.

Over the past 20 years it has become possible tomake intensive turbulence proRling observationsthat reveal the structure and evolution of upper

ocean mixing. An example is shown in Figure 1,which illustrates mixed-layer1 evolution, temper-ature structure and small-scale turbulence. Thesmall white dots in Figure 1 indicate the depthabove which stratiRcation is neutral or unstable andmixing is intense, and below which stratiRcation isstable and mixing is suppressed. This representsa means of determining the vertical extent of themixed layer directly forced by local atmosphericconditions. (We will call the mixed-layer depth D.)Following the change in sign from negative (surfaceheating) to positive (surface cooling) of the surfacebuoyancy Sux, J0

b, the mixed layer deepens. (J0b rep-

resents the Sux of density (mass per unit volume)across the sea surface due to the combination ofheating/cooling and evaporation/precipitation.) Themixed layer shown in Figure 1 deepens each night,but the rate of deepening and Rnal depth vary. Eachday, following the onset of daytime heating, themixed layer becomes shallower.

SigniRcant vertical structure is evident within thenocturnal mixed layer. The maximum potentialtemperature (�) is found at mid-depth. Above this,� is smaller and decreases toward the surface at therate of about 2 mK in 10 m. The adiabatic changein temperature, that due to compression of Suidparcels with increasing depth, is 1 mK in 10 m. Theregion above the temperature maximum is super-adiabatic, and hence prone to convective instability.

UPPER OCEAN MIXING PROCESSES 3093

2

0

_ 2

_ 4

_ 20

_ 40

_ 60

_ 80

Dep

th (

m)

_ 20

_ 40

_ 60

_ 80

Dep

th (

m)

_ 20_ 40 0� (mK)

_ 10 _ 5 0

_ 6_ 8

log (m s )10 �2 _ 3

03/1803/16

_ 6_ 8 _ 4

10(W

kg

)7

0_ 1

Jb

(A)

(B)

(C)

J0b

log (m s )10 �2 _ 3

� (mK)

Figure 1 Observations of mixing in the upper ocean over a five-day period. These observations were made in March 1987 in theNorth Pacific using a vertical turbulence profiler and shipboard meteorological sensors. (A) The variation in the surface buoyancyflux, J 0

b, which is dominated by surface heating and cooling. The red (blue) areas represent daytime heating (nighttime cooling).Variations in the intensity of nighttime cooling are primarily due to variations in winds. (B) Potential temperature referenced to theindividual profile mean in order to emphasize vertical rather than horizontal structure (�; K). To the right is an averaged verticalprofile from the time period indicated by the vertical bars at top and bottom of each of the left-hand panels. (C) The intensity ofturbulence as indicated by the viscous dissipation rate of turbulence kinetic energy, �. To the right is an averaged profile with themean value of J 0

b indicated by the vertical blue line. The dots in (B) and (C) represent the depth of the mixed layer as determinedfrom individual profiles.

3094 UPPER OCEAN MIXING PROCESSES

Cool skin

Convection

� ( )xShear-induced

turbulence

Thermocline

Breakinginternal waves

Sea surface

Wind row

Wind row

Wind row

Cooling

� ( )x

Langmuir

circulation

Wind

Breaking wavebubble injection

� ( )z

Mixedlayer

Velocityshear

� (K)0.1

z (m)0.01

Surfacelayer

Figure 2 Diagram showing processes that have been identified by a wide range of observational techniques as importantcontributors to mixing the upper ocean in association with surface cooling and winds. The temperature (�) profiles shown here havethe adiabatic temperature (that due to compression of fluid parcels with depth) removed; this is termed potential temperature. Theprofile of velocity shear (vertical gradient of horizontal velocity) indicates no shear in the mixed layer and nonzero shear above. Theform of the shear in the surface layer is a current area of research. Shear-induced turbulence near the surface may be responsiblefor temperature ramps observed from highly resolved horizontal measurements. Convective plumes and Langmuir circulations bothact to redistribute fluid parcels vertically; during convection, they tend to move cool fluid downward. Wind-driven shear concentratedat the mixed-layer base (thermocline) may be sufficient to allow instabilities to grow, from which internal gravity waves propagateand turbulence is generated. At the surface, breaking waves inject bubbles and highly energetic turbulence beneath the sea surfaceand disrupt the ocean’s cool skin, clearing a pathway for more rapid heat transfer into the ocean.

Below this superadiabatic surface layer is a layer ofdepth 10}30 m in which the temperature change isless than 1 mK. Within this mixed layer, the inten-sity of turbulence, as quantiRed by the turbulentkinetic energy dissipation rate, �, is relatively uni-form and approximately equal to J0

b. (� representsthe rate at which turbulent motions in a Suid aredissipated to heat. It is an important term in theevolution equation for turbulent kinetic energy,signifying the tendency for turbulence to decay inthe absence of forcing.) Below the mixed layer, �generally (but not always) decreases, whereas above,� increases by 1}2 factors of 10.

Below the mixed layer is a region of stable stratiR-cation that partially insulates the upper ocean fromthe ocean interior. Heat, momentum, and chemicalspecies exchanged between the atmosphere and theocean interior must traverse the centimeters thickcool skin at the very surface, the surface layer, andthe mixed layer to modify the stable layer below.These vertical transports are governed by a combi-nation of processes, including those that affect onlythe surface itself (rainfall, breaking surface gravity

waves), those that communicate directly from thesurface throughout the entire mixed layer (convec-tive plumes) or a good portion of it (Langmuircirculations) and also those processes that are forcedat the surface but have effects concentrated at themixed-layer base (inertial shear, Kelvin}Helmholtzinstability, propagating internal gravity waves). Sev-eral of these processes are represented in schematicform in Figure 2. Whereas Figure 1 represents theobserved time evolution of the upper ocean ata single location, Figure 2 represents an idealizedthree-dimensional snapshot of some of the processesthat contribute to this time evolution.

Heating of the ocean’s surface, primarily by solar(short-wave) radiation, acts to stabilize the watercolumn, thereby reducing upper ocean mixing. Solarradiation, which peaks at noon and is zero at night,penetrates the air}sea interface (limited by absorp-tion and scattering to a few tens of meters), but heatis lost at the surface by long-wave radiation, evapor-ative cooling and conduction throughout both dayand night. The ability of the atmosphere to modifythe upper ocean is limited by the rate at which heat

UPPER OCEAN MIXING PROCESSES 3095

and momentum can be transported across theair}sea interface. The limiting factor here is theviscous boundary layer at the surface, which permitsonly molecular diffusion through to the upperocean. This layer is evidenced by the ocean’s coolskin, a thin thermal boundary layer (a few milli-meters thick), across which a temperature differenceof typically 0.1 K is maintained. Disruption of thecool skin permits direct transport by turbulent pro-cesses across the air}sea interface. Once disrupted,the cool skin reforms over a period of some tens ofseconds. A clear understanding of processes thatdisrupt the cool skin is crucial to understanding howthe upper ocean is mixed.

Convection

Cooling at the sea surface creates parcels of cool,dense Suid, which later sink to a depth determinedby the local stratiRcation in a process known asconvection. Cooling occurs almost every night andalso sometimes in daytime in association withweather systems such as cold air outbreaks fromcontinental landmasses. Convection may also becaused by an excess of evaporation over precipita-tion, which increases salinity, and hence density, atthe surface. Winds aid convection by a variety ofmechanisms that agitate the sea surface, therebydisrupting the viscous sublayer and permitting rapidtransfer of heat through the surface (see below).Convection in the ocean is analogous to that foundin the daytime atmospheric boundary layer, which isheated from below, and which has been studied ingreat detail. Recourse to atmospheric studies ofconvection has helped in understanding the ocean’sbehavior.

Surface tension and viscous forces initially preventdense, surface Suid parcels from sinking. Once theSuid becomes sufRciently dense, however, theseforces are overcome and Suid parcels sink in theform of convective plumes. The relative motion ofthe plumes helps to generate small-scale turbulence,resulting in a turbulent Reld encompassing a rangeof scales from the depth of the mixed layer (typically100 m) to a few millimeters.

A clear feature of convection created by surfacecooling is the temperature proRle of the upper ocean(Figure 1). Below the cool skin is an unstable sur-face layer that is the signature of plume formation.Below that is a well-mixed layer in which density(as well as temperature and salinity) is relativelyuniform. The depth of convection is limited by thelocal thermocline. Mixing due to penetrative con-vection into the thermocline represents anothersource of cooling of the mixed layer above. Within

the convecting layer, there is an approximate bal-ance between buoyant production of turbulent kin-etic energy and viscous dissipation, as demonstratedby the observation �+J0

b.The means by which the mixed layer is restratiRed

following nighttime convection are not clear.Whereas some one-dimensional models yield realis-tic time series of sea surface temperature, suggestingthat restratiRcation is a one-dimensional process (seebelow), other studies of this issue have shown one-dimensional processes to account for only 60% ofthe stratiRcation gained during the day. It has beensuggested that lateral variations in temperature, dueto lateral variations in surface Suxes, or perhapslateral variations in salinity due to rainfall vari-ability, may be converted by buoyant forces intovertical stratiRcation. These indicate the potentialimportance of three-dimensional processes torestratiRcation.

Wind Forcing

Convection is aided by wind forcing, in part becausewinds help to disrupt the viscous sublayer at the seasurface, permitting more rapid transport of heatthrough the surface. In the simplest situation, windsproduce a surface stress and a sheared currentproRle, yielding a classic wall-layer scaling of turbu-lence and Suxes in the surface layer, similar to thesurface layer of the atmosphere. (Theory, supportedby experimental observations, predicts a logarithmicvelocity proRle and constant stress layer in theturbulent layer adjacent to a solid boundary. This istypically found in the atmosphere during neutralstratiRcation and is termed wall-layer scaling.) Thissimple case, however, seems to be rare. The reasonfor the difference in behaviors of oceanic and atmo-spheric surface layers is the difference in the bound-aries. The lower boundary of the atmosphere issolid (at least over land, where convection is well-understood), but the ocean’s upper boundary is freeto support waves, ranging from centimeter-scalecapillary waves, through wind waves (10s of meters)to swell (100s of meters). The smaller wind waveslose coherence rapidly, and are therefore governedby local forcing conditions. Swell is considerablymore persistent, and may therefore reSect conditionsat a location remote in space and time from theobservation, e.g., a distant storm.

Breaking Waves

Large scale breaking of waves is evidenced at thesurface by whitecapping and surface foam, allowingvisual detection from above. This process, which isnot at all well understood, disrupts the ocean’s cool

3096 UPPER OCEAN MIXING PROCESSES

skin, a fact highlighted by acoustic detection ofbubbles injected beneath the sea surface by breakingwaves. Small-scale breaking, which has no visiblesignature (and is even less well understood but isthought to be due to instabilities formed in concertwith the superposition of smaller-scale waves) alsodisrupts the ocean’s cool skin. An important chal-lenge for oceanographers is to determine the preva-lence of small-scale wave breaking and the statisticsof cool skin disruption at the sea surface.

The role of wave breaking in mixing is an issue ofgreat interest at present. Turbulence observations inthe surface layer under a variety of conditions haveindicated that at times (generally lower winds andsimpler wave states) the turbulence dissipation rate(and presumably other turbulence quantities includ-ing Suxes) behaves in accordance with simple wall-layer scaling and is in this way similar to the atmo-spheric surface layer. However, under higher winds,and perhaps more complicated wave states, turbu-lence dissipation rates greatly exceed those predictedby wall-layer scaling. This condition has been ob-served to depths of 30 m, well below a signiRcantwave height from the surface, and constituting a sig-niRcant fraction of the ocean’s mixed layer. (ThesigniRcant wave height is deRned as the averageheight of the highest third of surface displacementmaxima. A few meters is generally regarded asa large value.) Evidently, an alternative to wall-layerscaling is needed for these cases. This is a problemof great importance in determining both transferrates across the air}sea interface to the mixed layerbelow and the evolution of the mixed layer itself. Itis at times when turbulence is most intense thatmost of the air}sea transfers and most of the mixedlayer modiRcation occurs.

Langmuir Circulation

Langmuir circulations are coherent structures withinthe mixed layer that produce counterrotating vor-tices with axes aligned parallel to the wind. Theirsurface signature is familiar as windrows: lines ofbubbles and surface debris aligned with the windthat mark the convergence zones between the vor-tices. These convergence zones are sites of down-wind jets in the surface current. They concentratebubble clouds produced by breaking waves, orbubbles produced by rain, which are then carrieddownward, enhancing gas-exchange rates with theatmosphere. Acoustical detection of bubbles pro-vides an important method for examining the struc-ture and evolution of Langmuir circulations.

Langmuir circulations appear to be intimately re-lated to the Stokes drift, a small net current parallelto the direction of wave propagation, generated by

wave motions. Stokes drift is concentrated at thesurface and is thus vertically sheared. Small per-turbations in the wind-driven surface current gener-ate vertical vorticity, which is tilted toward thehorizontal (downwind) direction by the shear of theStokes drift. The result of this tilting is a Reld ofcounterrotating vortices adjacent to the ocean sur-face, i.e., Langmuir cells. It is the convergence asso-ciated with these vortices that concentrates thewind-driven surface current into jets. Langmuir cellsthus grow by a process of positive feedback. Ongo-ing acceleration of the surface current by the wind,together with convergence of the surface current bythe Langmuir cells, provides a continuous source ofcoherent vertical vorticity (i.e., the jets), which istilted by the mean shear to reinforce the cells.

Downwelling speeds below the surface conver-gence have been observed to reach more than0.2 m s�1, comparable to peak downwind horizontalSow speeds. By comparison, the vertical velocityscale associated with convection, wH"(J0

bD)1�3 iscloser to 0.01 m s�1. Upward velocities representingthe return Sow to the surface appear to be smallerand spread over greater area. Maximum observedvelocities are located well below the sea surface butalso well above the mixed-layer base. Langmuircirculations are capable of rapidly moving Suidvertically, thereby enhancing and advecting theturbulence necessary to mix the weak near-surfacestratiRcation which forms in response to daytimeheating. However, this mechanism does not seem tocontribute signiRcantly to mixing the base of thedeeper mixed layer, which is inSuenced more bystorms and strong cooling events.

In contrast, penetration of the deep mixed layerbase during convection (driven by the conversion ofpotential energy of dense Suid plumes created bysurface cooling/evaporation into kinetic energy andturbulence) is believed to be an important means ofdeepening the mixed layer. So also is inertial shear,as explained next.

Wind-Driven Shear

Wind-driven shear erodes the thermocline at themixed-layer base. Wind-driven currents often veerwith depth due to planetary rotation (cf. the Ekmanspiral). Fluctuations in wind speed and directionresult in persistent oscillations at near-inertialfrequencies. Such oscillations are observed almosteverywhere in the upper ocean, and dominate thehorizontal velocity component of the internal waveReld. Because near-inertial waves dominate the ver-tical shear, they are believed to be especially impor-tant sources of mixing at the base of the mixedlayer. In the upper ocean, near-inertial waves are

UPPER OCEAN MIXING PROCESSES 3097

generally assumed to be the result of wind forcing.Rapid diffusion of momentum through the mixedlayer tends to concentrate shear at the mixed layerbase. This concentration increases the probability ofsmall-scale instabilities. The tendency toward insta-bility is quantiRed by the Richardson number,Ri"N2/S2, where N2

"!(g/�) ) d�/dz, represents thestability of the water column, and shear, S, repres-ents an energy source for instability. Small values ofRi ((1/4) are associated with Kelvin}Helmholtzinstability. Through this instability, the inertialshear is concentrated into discrete vortices (Kelvin}Helmholtz billows) with axes aligned horizontallyand perpendicular to the current. Ultimately, thebillows overturn and generate small-scale turbulenceand mixing. Some of the energy released by theinstabilities propagates along the stratiRed layer ashigh frequency internal gravity waves. These pro-cesses are depicted in Figure 2. The mixing of Suidfrom below the mixed layer by inertial shear con-tributes to increasing the density of the mixed-layerand to mixed-layer deepening.

Temperature Ramps

Another form of coherent structure in the upperocean has been observed in both stable and unstableconditions. In the upper few meters temperatureramps, aligned with the wind and marked by hori-zontal temperature changes of 0.1 K in 0.1 m, indi-cate the upward transport of cool/warm Suid duringstable/unstable conditions. This transport is drivenby an instability triggered by the wind and perhapssimilar to the Kelvin}Helmholtz instability discussedabove. It is not yet clearly understood. Because itbrings water of different temperature into close con-tact with the surface, and also because it causeslarge lateral gradients, this mechanism appears tobe a potentially important factor in near-surfacemixing.

Effects of Precipitation

Rainfall on the sea surface can catalyze several im-portant processes that act to both accentuate andreduce upper ocean mixing. Drops falling on thesurface disrupt the viscous boundary layer, and maycarry air into the water by forming bubbles.

Rain is commonly said to ‘knock down the seas.’The evidence for this is the reduction in breakingwave intensity and whitecapping at the sea surface.Smaller waves ((20 cm wavelength) may be dam-ped by subsurface turbulence as heavy rainfall actsto transport momentum vertically, causing drag onthe waves. The reduced roughness of the small-scalewaves reduces the probability of the waves exciting

Sow separation on the crests of the long waves, andhence reduces the tendency of the long waves tobreak.

While storm winds generate intense turbulencenear the surface, associated rainfall can conRne thisturbulence to the upper few meters, effectively insu-lating the water below from surface forcing. This isdue to the low density of fresh rainwater relative tothe saltier ocean water. Turbulence must workagainst gravity to mix the surface water downward,and turbulent mixing is therefore suppressed. Solong as vertical mixing is inhibited, Suid heatedduring the day will be trapped near the sea surface.Preexisting turbulence below the surface will con-tinue to mix Suid in the absence of direct surfaceforcing, until it decays due to viscous dissipationplus mixing, typically over the time scale of a buoy-ancy period, N�1.

Deposition of pools of fresh water on the seasurface, such as occurs during small-scale squalls,raises some interesting prospects for both lateralspreading and vertical mixing of the fresh water. Inthe warm pool area of the western equatorial Paci-Rc, intense squalls are common. Fresh light puddlesat the surface cause the surface density Reld to beheterogeneous. Release of the density gradient maythen occur as an internal bore forming on the sur-face density anomaly, causing a lateral spreading ofthe fresh puddle. Highly resolved horizontal proRlesof temperature, salinity and density reveal sharpfrontal interfaces, the features of which depend onthe direction of the winds relative to the buoyancy-driven current. These are portrayed in Figure 3.When the wind opposes the buoyancy current, thedensity anomaly at the surface is reduced, possiblyas a result of vertical mixing in the manner sugges-ted in Figure 3(B). This mechanism results in a rapidvertical redistribution of fresh water from thesurface pool and a brake on the propagation of thebuoyancy front. Similarly, an opposing ambient cur-rent results in shear at the base of the fresh layer,which may lead to instability and consequent mix-ing. The nature of these features has yet to beclearly established, as has the net effect on upperocean mixing.

Ice on the Upper Ocean

At high latitudes, the presence of an ice layer (up toa few meters thick) partially insulates the oceanagainst surface forcing. This attenuates the effects ofwind forcing on the upper ocean except at thelowest frequencies. The absence of surface wavesprevents turbulence due to wave breaking and Lang-muir circulation. However, a turbulence source is

3098 UPPER OCEAN MIXING PROCESSES

Wind

Wind

Buoyancy-drivencurrent

No entrainment

Dense water

No convection

Wind driftcurrent

Buoyancy-drivencurrent

Entrainment

DensewaterConvection

Wind driftcurrent

(A)

(B)

Figure 3 Two ways in which the frontal interface of a freshsurface pool may interact with ambient winds and currents. (A)The case in which the buoyancy-driven current, wind and ambi-ent current are all in the same direction. In this case, thebuoyancy-driven current spreads and thins unabated. In (B), thebuoyancy-driven current is opposed by wind and ambient cur-rent. In this case, the frontal interface of the buoyancy-drivencurrent may plunge below the ambient dense water, so thatconvection near the surface intensifies mixing at the frontalinterface. Simultaneously, shear-forced mixing at the base ofthe fresh puddle may increase entrainment of dense water frombelow.

provided by the various topographic features foundon the underside of the ice layer. These range in sizefrom millimeter-scale dendritic structures to 10 mkeels, and can generate signiRcant mixing near thesurface when the wind moves the ice relative to thewater below or currents Sow beneath the ice.

Latent heat transfer associated with melting andfreezing exerts a strong effect on the thermal struc-ture of the upper ocean. Strong convection canoccur under ice-free regions, in which the watersurface is fully exposed to cooling and evaporativesalinity increase. Such regions include leads (formedby diverging ice Sow) and polynyas (where wind orcurrents remove ice as rapidly as it freezes). Convec-tion can also be caused by the rejection of salt bynewly formed ice, leaving dense, salty water nearthe surface.

Parameterizations of Upper OceanMixing

Large-scale ocean and climate models are incapableof explicitly resolving the complex physics of the

upper ocean, and will remain so for the foreseeablefuture. Since upper ocean processes are crucial indetermining atmosphere}ocean Suxes, methods fortheir representation in large-scale models, i.e., para-meterizations, are needed. The development ofupper-ocean mixing parameterizations has drawn onextensive experience in the more general problem ofturbulence modeling. Some parameterizations em-phasize generality, working from Rrst principles asmuch as possible, whereas others sacriRce generalityto focus on properties speciRc to the upper ocean.An assumption common to all parameterizationspresently in use is that the upper ocean is horizon-tally homogeneous, i.e., the goal is to representvertical Suxes in terms of vertical variations inocean structure, leaving horizontal Suxes to be han-dled by other methods. Such parameterizations arereferred to as ‘one-dimensional’ or ‘column’ models.

Column modeling methods may be classiRed aslocal or nonlocal. In a local method, turbulentSuxes at a given depth are represented as functionsof water column properties at that depth. Forexample, entrainment at the mixed-layer basemay be determined solely by the local shear andstratiRcation. Nonlocal methods allow Suxes to beinSuenced directly by remote events. For example,during nighttime convection, entrainment at themixed-layer base may be inSuenced directly by cha-nges in the surface cooling rate. In this case, the factthat large convection rolls cannot be representedexplicitly in a column model necessitates the non-local approach. Nonlocal methods include ‘slab’models, in which currents and water properties donot vary at all across the depth of the mixed layer.Local representations may often be derived system-atically from the equations of motion, whereas non-local methods tend to be ad hoc expressions ofempirical knowledge. The most successful modelscombine local and nonlocal approaches.

Many processes are now reasonably well repre-sented in upper ocean models. For example, entrain-ment via shear instability is parameterized using thelocal gradient Richardson number and/or a nonlocal(bulk) Richardson number pertaining to the wholemixed layer. Other modeling issues are subjects ofintensive research. Nonlocal representations of heatSuxes have resulted in improved handling of night-time convection, but the corresponding momentumSuxes have not yet been represented. Perhaps themost important problem at present is the representa-tion of surface wave effects. Local methods are ableto describe the transmission of turbulent kinetic en-ergy generated at the surface into the ocean interior.However, the dependence of that energy Sux onsurface forcing is complex and remains poorly

UPPER OCEAN MIXING PROCESSES 3099

understood. Current research into the physics ofwave breaking, Langmuir circulation, wave-precipi-tation interactions, and other surface wave phe-nomena will lead to improved understanding, andultimately to useful parameterizations.

See also

Breaking Waves and Near-surface Turbulence.Bubbles. Deep Convection. Heat and MomentumFluxes at the Sea Surface. Internal Tides.Langmuir Circulation and Instability. Penetrating

Shortwave Radiation. Surface, Gravity and Capil-lary Waves. Three-dimensional (3D) Turbulence.Under-ice Boundary Layer. Upper Ocean VerticalStructure. Whitecaps and Foam. Wave Generationby Wind.

Further ReadingGarrett C (1996) Processes in the surface mixed layer of

the ocean. Dynamics of Atmospheres and Oceans 23:19}34.

Thorpe SA (1995) Dynamical processes at the sea surface.Progress in Oceanography 35: 315}352.

UPPER OCEAN RESPONSES TO STRONGFORCING EVENTS

L. K. Shay, University of Miami, Miami, FL, USA

Copyright ^ 2001 Academic Press

doi:10.1006/rwos.2001.0159

Introduction

Strong atmospheric forcing events occur over theoceans during both summer and winter months.Cyclonically (anticyclonically) rotating wind Reldsaround a surface low-pressure region in the North-ern (Southern) Hemisphere excite an energetic oceanresponse. For example, winter storms and extra-tropical cyclones originating in the Gulf of Alaska(north-east PaciRc Ocean) or over the Gulf Stream(western Atlantic Ocean) signiRcantly impact thenorth-west and north-east coasts of the UnitedStates, respectively. Similarly, tropical storm forma-tion and their subsequent development into tropicalcyclones (called hurricanes in the Eastern PaciRc andAtlantic Ocean basins, and typhoons in the WesternPaciRc Ocean) cause an energetic ocean response inthese basins. In this context, the ocean’s response ispronounced as manifested in the upper ocean cool-ing patterns that are modulated by the three-dimensional current structure excited by storms.

Observationally, studies over the past decade havedemonstrated the importance of the current struc-ture on the oceanic mixed layer (OML) thermalresponse. Thermal structure changes using temper-ature proRles and remotely sensed data acquiredduring hurricane conditions have been welldocumented. However, the oceanic current responseto the surface winds has focused primarily onanalytical and numerical solutions with simplifyingassumptions. A key component of the current

response is associated with the divergence andconvergence of the OML currents that induceupwelling and downwelling regimes, respectively, inthe thermocline. The wind-forced currents rotateanticyclonically with time with a period of oscilla-tion close to the local inertial period. In addition,this wind-forced, near-inertial current vector rotatesanticyclonically with depth and creates signiRcantshear across the OML base that causes vertical mix-ing and upper ocean cooling. Although the currentresponse has been thought to be conRned to theupper part of the water column, fortuitous encoun-ters of hurricanes with spatially limited current metermoorings indicate that the response extends throughthe thermocline to as deep as 1000 m. These datahave provided a new view of the oceanic currentresponse to storms, and have challenged theories andmodels concerning strongly forced conditions.

Accordingly, the ocean’s current response en-compasses both the directly forced or near-Reldregion, and the evolving three-dimensional wake orfar-Reld regime. In the near-Reld region, the cycloni-cally rotating wind Reld of a tropical cyclone forcesthe OML currents of about 1}2 m s~1 to divergefrom the storm track starting within one-quarter ofan inertial wavelength (") behind the eye, deRned asthe product of the storm translation speed Uh andthe local inertial period (IP). This OML currentdivergence and net Ekman transport away from thestorm track cause the upwelling of cooler water thatdecreases the OML depth (Figure 1). Over the nexthalf of a near-inertial cycle, OML currents convergetoward the storm track, causing an increase in theOML depth as warmer water is downwelled intothe thermocline. This alternating cycle of upwellingand downwelling of the isotherms occurs over

3100 UPPER OCEAN RESPONSES TO STRONG FORCING EVENTS