Ekman TransportFridtjof NansenPowerPoint PresentationSlide 4Slide 5Slide 6Slide 7Slide 8Ekman SpiralEkman SpiralsSlide 11Ekman LayerSlide 13Slide 14Slide 15Slide 16Current Meter MooringSlide 18Slide 19LOTUSEkman Transport Works!!Slide 22Slide 23Slide 24Inertia CurrentsInertial CurrentsSlide 27Slide 28Slide 29Slide 30Inertial PeriodInertial OscillationsSlide 33Slide 34Ekman Transport•Ekman transport is the direct wind driven transport of seawater •Boundary layer process•Steady balance among the wind stress, vertical eddy viscosity & Coriolis forces•Story starts with Fridtjof Nansen [1898]Fridtjof Nansen•One of the first scientist-explorers•A true pioneer in oceanography •Later, dedicated life to refugee issues •Won Nobel Peace Prize in 1922Nansen’s Fram•Nansen built the Fram to reach North Pole•Unique design to be locked in the ice•Idea was to lock ship in the ice & wait •Once close, dog team set out to NPFram Ship Locked in Ice1893 -1896 - Nansen got to 86o 14’ NEkman Transport•Nansen noticed that movement of the ice-locked ship was 20-40o to right of the wind•Nansen figured this was due to a steady balance of friction, wind stress & Coriolis forces•Ekman did the mathEkman TransportMotion is to the right of the windEkman Transport•The ocean is more like a layer cake •A layer is accelerated by the one above it & slowed by the one beneath it•Top layer is driven by w•Transport of momentum into interior is inefficientEkman Spiral•Top layer balance of w, friction & Coriolis•Layer 2 dragged forward by layer 1 & behind by layer 3•Etc.Ekman Spirals•Ekman found an exact solution to the structure of an Ekman Spiral•Holds for a frictionally controlled upper layer called the Ekman layer•The details of the spiral do not turn out to be importantEkman Layer•Depth of frictional influence defines the Ekman layer•Typically 20 to 80 m thick – depends on Az, latitude, w•Boundary layer process–Typical 1% of ocean depth (a 50 m Ekman layer over a 5000 m ocean)Ekman Transport•Balance between wind stress & Coriolis force for an Ekman layer– Coriolis force per unit mass = f u• u = velocity• f = Coriolis parameter = 2  sin  = 7.29x10-5 s-1 &  = latitude•Coriolis force acts to right of motionEkman TransportCoriolis = wind stressf ue = w / ( D)Ekman velocity = ueue = w / ( f D)Ekman transport = QeQe = w / ( f) = [m2 s] = [m3 s-1 m-1](Volume transport per length of fetch)Ekman Transport•Ekman transport describes the direct wind-driven circulation•Only need to know w & f (latitude)•Ekman current will be right (left) of wind in the northern (southern) hemisphere•Simple & robust diagnostic calculationCurrent Meter MooringCurrent MetersVector Measuring Vector AveragingCurrent Meter Current MeterCurrent Meter MooringLOTUSEkman Transport Works!!•Averaged the velocity profile in the downwind coordinates•Subtracted off the “deep” currents (50 m)•Compared with a model that takes into account changes in upper layer stratification•Price et al. [1987] ScienceEkman Transport Works!!Ekman Transport Works!!theoryobserverdEkman Transport Works!!•LOTUS data reproduces Ekman spiral & quantitatively predicts transport•Details are somewhat different due to diurnal changes of stratification near the sea surfaceInertia Currents•Ekman dynamics are for steady-state conditions •What happens if the wind stops? •Ekman dynamics balance wind stress, vertical friction & Coriolis•Then only force will be Coriolis force...Inertial Currents•Motions in rotating frame will veer to right•Make an inertial circle•August 1933, Baltic Sea, ( = 57oN) •Period of oscillation is ~14 hoursInertial Currents•Inertial motions will rotate CW in NH & CCW in the SH•These “motions” are not really in motion•No real forces only the Coriolis forceInertial Currents•Balance between two “fake” forces– Coriolis &– Centripetal forcesInertial Currents•Balance between centripetal & Coriolis force– Coriolis force per unit mass = f u• u = velocity• f = Coriolis parameter = 2  sin  = 7.29x10-5 s-1 &  = latitude– Centripetal force per unit mass = u2 / r– fu = u2 / r -> u/r = fInertial Currents•Inertial currents have u/r = f•For f = constant– The larger the u, the larger the r– Know size of an inertial circle, can estimate u•Period of oscillation, T = 2r/u (circumference of circle / speed going around it)– T = 2r/u = 2 (r/u) = 2 (1/f) = 2 /fInertial Period•f = 2  sin() •For  = 57oN, f = 1.2x10-4 s-1•T = 2  / f = 51,400 sec = 14.3 hours•Matches guess of 14 hInertial Oscillations D’Asaro et al. [1995] JPOInertial Currents•Balance between Coriolis & centripetal forces•Size & speed are related by value of f - U/R = f–Big inertial current (U) -> big radius (R)–Vice versa… •Example from previous slide - r = 8 km &  = 47oN–f = 2  sin(47o) = 1.07x10-5 s-1–U = f R ~ 0.8 m/s –Inertial will dominate observed currents in the mixed layerInertial Currents•Period of oscillations = 2  / f–NP = 12 h; SP = 12 h; SB = 21.4 h; EQ = Infinity•Important in open ocean as source of shear at base of mixed layer–A major driver of upper ocean mixing–Dominant current in the upper