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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 14-19 Newton’s Second Law: dV F ma m dt Lab 1 - Coriolis Then the summation of F ( SF ) involves several forces. Thus, SF = 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 2 V 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” r xiˆ yˆj zkˆ And, (1) dr Dr V r dt Dt or V V r Lab 1 - Coriolis Now the same for the acceleration in a moving system: (2) Then put (1) into (2): dV DV a V dt Dt dV d V dr V r dt dt dt Coriolis Centrifugal Lab 1 - Coriolis r (recall cross product – the resultant has to be mutually perpendicular to all three!) dV d V 2 2 V r sin rˆc dt dt Coriolis Centrifugal Acc. (points to or away from axis of rotation) Lab 1 - Coriolis Then, substitute above expression into the Equation of Motion. The Coriolis Force: ( -2xV ) 0iˆ cos ˆj sin kˆ Lab 1 - Coriolis When the vertical velocity is small compared to the horizontal motions, the horizontal component of the Coriolis force is: f = 2sin() “” 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 p/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!