# Earth Rotation Earth’s rotation gives rise to a fictitious force called the Coriolis force It accounts for the apparent deflection of motions viewed in.

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Earth 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 sun

Earth 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 V e (Eq) = R e  R e = radius Earth (6371 km) V e (Eq) = 464 m/s As latitude, , increases, V e (  ) will decrease V e (  ) =  R e cos(  ) 

V e Decreases with Latitude V e (  ) =  R e cos(  )

Earth Rotation Moving objects on Earth move with the rotating frame (V e (  )) & relative to it (v rel ) The absolute velocity is v abs = v rel + V e (  ) Objects moving north from Equator will have a larger V e than that under them If “real” forces sum to 0, v abs will not change, but the V e (  ) at that latitude will

Rotation, cont. Frictionless object moving north v abs = const., but V e (  ) is decreasing v rel 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 motion

Coriolis Force an 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 Path

Earth 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 squared F = ma -> 1 Newton = 1 N = 1 kg (m s -2 ) N m -2 = kg m -1 s -2

Wind Stress Wind stress is modeled as  w = C U 2 where C ~ 2x10 -3 & U is wind speed Values of C can vary by factor of 2

Wind Stress Calculations… If U = 15 knots, what is the wind stress? Steps – Convert U in knots to U in m/s – Calculate  w

Wind Stress Facts: 1 o latitude = 60 nautical miles = 111 km 15 knots = 15 nautical miles / hour

Wind Stress Finishing up the calculation...  w = C U 2 = (2x10-3) (7.7 m/s) 2 = 0.12 N/m 2 We’re done!! But what were the units of C?

What are the units of C? We know that  w = C U 2  w =[N/m 2 ] = [kg m -1 s -2 ] & U 2 = [(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 C D  a = density air & C D = drag coefficient

Wind 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 turbulent

Wind Stress Vertical eddy viscosity quantifies the air- sea exchanges of horizontal momentum

Vertical Eddy Viscosity Vertical eddy viscosity, A z, controls the efficiency of wind momentum inputs High values of A z suggest deeper penetration of momentum into the ocean Values of A z are functions of – turbulence levels – wave state – stratification near the surface

Vertical Eddy Viscosity Similar to discussion of eddy diffusion (turbulence mixes scalars & momentum similarly) –Values of A z (vertical) << A h (horizontal) –A z decreases as stratification increases –A z is at its greatest in the mixed layer

Review Wind stress accounts for the input of momentum into the ocean by the wind Calculated using wind speed,  w = C U 2 Processes driving wind stress & vertical eddy viscosity are very complex

Ekman 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]

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