lect_14 - Thermal Wind Equation We begin by writing the...

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1 Thermal Wind Equation We begin by writing the vector form of the geostrophic wind equation in isobaric coordinates for two levels: ( ) ( ) () () k ˆ Z f g V k ˆ Z f g V p g p g × = × = 2 2 1 1 r r ( ) ( ) () () k ˆ Z f g V k ˆ Z Z f g V V V V p T p T g g T × = × = Δ r r r r r 1 2 1 2 Now we compute the difference in geostrophic wind between the two levels: thermal wind equation Thermal Wind • The thermal wind is the vertical shear of the geostrophic wind between two levels. • The thermal wind is a vector that is oriented parallel to the thickness isolines with lower values to the left (in the N. Hemisphere). Its magnitude is proportional to the thickness gradient. low high Δ Z 1 Δ Z 2 Δ Z 3 T V r
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2 Geostrophic Wind Shear and Thermal Advection cold warm T V r ( ) 1 g V r ( ) 2 g V r Case 1: Geostrophic wind veers (i.e., turns clockwise) with height. Lower level wind is from SW. Upper level wind is from W. Since colder air must lie to the left of the thermal wind, the layer average wind blows from warm to cold, which implies warm advection. Geostrophic Wind Shear and Thermal Advection
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lect_14 - Thermal Wind Equation We begin by writing the...

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