# CSU AT 540 - Balance Winds (136 pages)

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# Balance Winds

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## Balance Winds

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At 540 - Synoptic Weather Analysis
##### Synoptic Weather Analysis Documents

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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

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