Atmospheric Science 4320 / 7320 Lab Portion / Anthony R. Lupo

Lab 1 - Coriolis  “Thursday is Lab Day”  Lab 1: Real and Apparent Forces, The Coriolis Force  Read Ch. 1 from Holton p  Newton’s Second Law:

Lab 1 - Coriolis  Then the summation of F ( F ) involves several forces. Thus,  F = PGF + CO + Gravity + Friction + Viscous forces  where gravity = absolute gravity + centrifugal force

Lab 1 - Coriolis  Other forces such as electrostatic forces or magnetic forces are negligible for typical scales of atmospheric motions and are thus neglected!  Real forces: PGF, Gravity, Friction, and Viscous forces!  Must exist in both inertial (non accelerating) and non-intertial coordinate systems.

Lab 1 - Coriolis  Apparent forces: Coriolis force   Coriolis Force is due to the fact that the coordinate system we use is on a rotating earth, which is of course, NOT an inertial coordinate system. (V != 0).

Lab 1 - Coriolis  A “derivation”:  First, let’s define our “position vector”  And, (1)

Lab 1 - Coriolis  Now the same for the acceleration in a moving system: (2)  Then put (1) into (2):  Coriolis Centrifugal

Lab 1 - Coriolis  (recall cross product – the resultant has to be mutually perpendicular to all three!)  CoriolisCentrifugal Acc. (points to or away from axis of rotation)

Lab 1 - Coriolis  Then, substitute above expression into the Equation of Motion.  The Coriolis Force: ( -2xV )

Lab 1 - Coriolis  When the vertical velocity is small compared to the horizontal motions, the horizontal component of the Coriolis force is:  f = 2sin()  “” is your latitude.

Lab 1 - Coriolis  Coriolis force deflects moving objects on sufficient time and space scales to the right in the Northern Hemisphere and to the left in the Southern Hemisphere.  For horizontal motions:  This “sine” relationship (cross product) assures that when the rotation vector is perpendicular to the motion vector, but in the same plane as V ( = 0), and thus  x V (at the equator) is perpendicular to the horizontal plane, f = 0. The Coriolis force is all in the vertical!

Lab 1 - Coriolis  f = 0  No horizontal comp!!!  Then when the rotation vector is perpendicular to the motion vector (angle  = 90, or /2), thus  x V perpendicular to the vector V and lies in the same plane, f = 2 coriolis force, or is at a maximum.

Lab 1 - Coriolis  f is the coriolis parameter of “planetary vorticity”. Recall vorticity is the curl of the velocity vector!