Transcript atms4320lab
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!