Earth RotationSlide 2Slide 3Ve Decreases with LatitudePowerPoint PresentationSlide 6Rotation, cont.Slide 8Slide 9Slide 10Slide 11Slide 12Wind StressSlide 14Slide 15Slide 16Slide 17What are the units of C?Slide 19Slide 20Vertical Eddy ViscositySlide 22ReviewEkman TransportEarth Rotation•Earth’s rotation gives rise to a fictitious force called the Coriolis force•It accounts for the apparent deflection of motions viewed in our rotating frame•Analogies–throwing a ball from a merry-go-round–sending a ball to the sunEarth Rotation•Earth rotates about its axis wrt sun (2 rad/day)•Earth rotates about the sun (2 rad/365.25 day)•Relative to the “distant stars” (2 rad/86164 s)–Sidereal day = 86164 sec (Note: 24 h = 86400 sec)•Defines the Earth’s rotation frequency,  = 7.29 x 10-5 s-1 (radians per sec)Earth Rotation•Velocity of Earth surface•Ve(Eq) = Re Re = radius Earth (6371 km)Ve(Eq) = 464 m/s•As latitude, , increases, Ve() will decrease•Ve() =  Re cos()Ve Decreases with Latitude-80 -60 -40 -20 0 20 40 60 80050100150200250300350400450500latitude (N)Vearth (m/s)Ve() =  Re cos()Earth Rotation•Moving objects on Earth move with the rotating frame (Ve()) & relative to it (vrel)•The absolute velocity is vabs = vrel + Ve()•Objects moving north from Equator will have a larger Ve than that under them•If “real” forces sum to 0, vabs will not change, but the Ve() at that latitude willRotation, cont.•Frictionless object moving north vabs = const., but Ve() is decreasing vrel must increase (pushing the object east)•When viewed in the rotating frame, moving objects appear deflected to right (left SH) •Coriolis force accounts for this by proving a “force” acting to the right of motionCoriolis Forcean object with an initial east-west velocity will maintain that velocity, even as it passes over surfaces with different velocities. As a result, it appears to be deflected over that surface (right in NH, left in SH)Coriolis Force and Deflection of Flight Pathhttp://www.youtube.com/watch?v=_36MiCUS1rohttp://www.youtube.com/watch?v=49JwbrXcPjc http://www.youtube.com/watch?v=KdD3Wq2DCWQEarth Rotation•Motions in a rotating frame will appear to deflect to the right (NH)•Deflection will be to the right in the northern hemisphere & to left in southern hemisphere •No apparent deflection right on the equator•It’s a matter of frame of reference, there is NO Coriolis force…Wind Stress•Wind stress, w, accounts for the input of momentum into the ocean by the wind•Exact processes creating w is complex• w is a tangential force per unit area •Units are Newton (force) pre meter squaredF = ma -> 1 Newton = 1 N = 1 kg (m s-2)N m-2 = kg m-1 s-2Wind Stress•Wind stress is modeled as w = C U2 where C ~ 2x10-3 & U is wind speed•Values of C can vary by factor of 2Wind Stress•Calculations…If U = 15 knots, what is the wind stress?•Steps– Convert U in knots to U in m/s– Calculate wWind StressFacts: 1o latitude = 60 nautical miles = 111 km15 knots = 15 nautical miles / hour€ 15knots = ...15nm ilehour ⎛ ⎝ ⎜ ⎞ ⎠ ⎟1hour602sec ⎛ ⎝ ⎜ ⎞ ⎠ ⎟111x1000m60nmile ⎛ ⎝ ⎜ ⎞ ⎠ ⎟=7.7m/sWind StressFinishing up the calculation... w = C U2 = (2x10-3) (7.7 m/s)2 = 0.12 N/m2We’re done!!But what were the units of C?What are the units of C?•We know that w = C U2 w =[N/m2] = [kg m-1 s-2] & U2 = [(m/s)2] C = [kg m-1 s-2] / [m 2 s-2] = [kg m-3]-> C ~ 2x10-3 kg m-3•Typically, C is defined as a CD a = density air & CD = drag coefficientWind Stress•Many processes contribute to transfer of momentum from wind to the ocean– Turbulent friction– Generation of wind waves– Generation of capillary waves•Key is the recognition that the process is turbulentWind StressVertical eddy viscosity quantifies the air-sea exchanges of horizontal momentumVertical Eddy Viscosity•Vertical eddy viscosity, Az, controls the efficiency of wind momentum inputs•High values of Az suggest deeper penetration of momentum into the ocean•Values of Az are functions of – turbulence levels– wave state– stratification near the surfaceVertical Eddy Viscosity•Similar to discussion of eddy diffusion (turbulence mixes scalars & momentum similarly)–Values of Az (vertical) << Ah (horizontal)–Az decreases as stratification increases–Az is at its greatest in the mixed layerReview•Wind stress accounts for the input of momentum into the ocean by the wind •Calculated using wind speed, w = C U2 •Processes driving wind stress & vertical eddy viscosity are very complexEkman 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