CSU AT 540 - Balance Winds (136 pages)

Previewing pages 1, 2, 3, 4, 5, 6, 7, 8, 9, 64, 65, 66, 67, 68, 69, 70, 71, 72, 128, 129, 130, 131, 132, 133, 134, 135, 136 of 136 page document View the full content.
View Full Document

Balance Winds



Previewing pages 1, 2, 3, 4, 5, 6, 7, 8, 9, 64, 65, 66, 67, 68, 69, 70, 71, 72, 128, 129, 130, 131, 132, 133, 134, 135, 136 of actual document.

View the full content.
View Full Document
View Full Document

Balance Winds

72 views


Pages:
136
School:
Colorado State University- Fort Collins
Course:
At 540 - Synoptic Weather Analysis

Unformatted text preview:

Balance Winds Geostrophic Balance Gradient Wind Cyclostrophic Wind Balance Balance with Friction Ekman Balance Geostrophic Balance The equation of motion can be written as r r r r r dV 1 p 2 V F G dt r where is the angular velocity of the earth positive pointing upward from the north pole 2 day corresponding to the rotation rate of the earth r r 2 V is called the Coriolis term r F represents the effects of friction r r r G is the gravitational vector G gk Coriolis Term i r r 2 V 2 0 u j cos v k sin w r r r 2 cos w sin v i sin u j cos u k r r r r r 2 V fv f w i fu j f uk where f 2 cos and f 2 sin The horizontal components of the equation of motion can therefore be written as du 1 p fv f w Fu dt x dv 1 p fu Fv dt y where f 2 sin and f 2 cos and is the latitude For the case of no friction Fu Fv 0 no acceleration du dt dv dt 0 u v w which is typical on the synoptic scale then 1 p 0 fu y 1 p 0 fv x 1 p u ug f y 1 p v vg f x where ug and vg are the geostrophic wind components defined by these relations The geostrophic wind relation can be written in vector notation as r r 1 Vg k z p f r r j where z is the horizontal gradient operator i x y r r 1 Vg k z p f This can be checked using the definition of the vector cross product r r r Vg u g i v g j i j k 0 1 p f x 0 1 p f y 1 0 r r 1 Vg k z p f The geostrophic wind is the balance between the pressure gradient force and the Coriolis force r Vg must be horizontal and perpendicular to z p the wind direction is parallel to the isobars r Vg is directed such that the high pressure is to the right in the northern hemisphere and to the left in the southern hemisphere r As is nearly constant at a given height Vg is almost linearly r proportional to the pressure gradient the larger z p the larger Vg r A given value of z p will result in stronger Vg at lower latitudes because f 0 at low latitudes Geostrophic balance is rarely achieved at low latitudes It is assumed that the flow is straight for the geostrophic wind 1 p ug f y 1 p vg f x



View Full Document

Access the best Study Guides, Lecture Notes and Practice Exams

Loading Unlocking...
Login

Join to view Balance Winds and access 3M+ class-specific study document.

or
We will never post anything without your permission.
Don't have an account?
Sign Up

Join to view Balance Winds and access 3M+ class-specific study document.

or

By creating an account you agree to our Privacy Policy and Terms Of Use

Already a member?