The resultant QG vorticity equation is D g(! g+f) Dt =f 0 #$ #p or ! g!t =#V g$%( g+f)+f 0!&!p (6.19) —– In Cartesian coordinates the geostrophic wind (with constant-f) is defined as V g!f 0 1k#$% Thus, the geostrophic vorticity, ! g=k#$V g, can be expressed as g! g= v x # u g y = 1 f 0 2$ x2 + 2$ y2 % &’ ()* = 1 f 0 +2$ (6.15) For a pure 2-D motion, the vorticity equation can be written as !!t 2#=$$ 1 f.
The QG Vorticity Equation The quasi-geostrophic vorticity is ?g = k·?×Vg = 1 f0 ?2? This enables ?g to be computed immediately once the geopo-tential is known. It also means that the geopotential can be deduced from the vorticity by inverting the Laplacian operator. This invertibility principle holds in.
QG Equations QG Vorticity Equation The vorticity equation can be written in isobaric and vector form as: () ?? ? ? ?? ? ? ? ? ? ? ? ??+ ? ? ?? ? ? ? ? ? ? ? ? ? ? ? ??? ? ? ?? ? ? ? ? + ? ? ? + ? ? ? ? ? ? ? ? ? ? ? =? ? ? y F x F p u p y v y x v x u f y f v y p v x u t ? ? ? ?? ? ? ? ry rx A number of simplifications are made to transform this into the QG Vorticity …
The prediction equation for QG flow that does not explicitly reference the divergent flow component is called the QG potential vorticity equation. Although it can be derived quite generally, the focus here is on its simplified linearized version, when the zonal-mean flow ?U is independent of latitude.
QG Equations: Vorticity Equation Blue contours = Relative vorticity Red contours = Geopotential height More on Term 3 (Planetary Vorticity Advection): Remember that the geostrophic flow (implied by black arrows) is parallel to the geopotential height contours (in red) Note the regions of southward flow that correspond to regions, QG Potential Vorticity Paul Ullrich Quasi-Geostrophic Theory March 2014 @ @t 1 f 0 r2 + f + @ @p f 0 @ @p + u g · r 1 f 0 r2 + f + @ @p f 0 @ @p =0 De!nition: The quasi-geostrophic potential vorticity is de#ned as q = 1 f 0 r2 + f + @ @p f 0 @ @p D gq Dt =0 QG Potential Vorticity Equation q is conserved following geostrophic motion.
11/10/1975 · QG Potential Vorticity Equation The prediction equation for QG flow that does not explicitly reference the divergent flow component is called the QG potential vorticity equation. Although it can be derived quite generally, the focus here is on its simplified linearized version, when the zonal-mean flow ?U is independent of latitude.
QUASI-GEOSTROPHIC VORTICITY EQUATION The wind shear component of relative vorticity ( ? ) is equal to (i.e.
change in the north-south wind in the direction [to the east] minus change in the east-west wind in the direction [to the north]). If considering only QG relative vorticity, is.
Vorticity & Geopotential @? g @t = f 0 @! @p u g · r? g v g QG Vorticity Equation Advection Terms Geostrophic Wind u g = 1 f 0 @ @y v g = 1 f 0 @ @x ? g = @v g @x @u g @y = 1 f 0 @2 @x2 + @2 @y2 = 1 f 0 r2 Geostrophic Vorticity Paul Ullrich Quasi-Geostrophic Theory March 2014 Relates geostrophic vorticity and geopotential
