# The ¢â‚¬“ageostrophic wind¢â‚¬â€Œ...

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18-Apr-2020Category

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● QG model emphasizes role of horizontal divergence, i.e.

● geostrophic wind (on an f plane**) is non-divergent, so interest is the ageostrophic wind

● above the friction layer, horiz. mtm eqns. can be written

Dg η Dt

= − f 0 ∇⋅V⃗ ag

Du D t

= − 1ρ ∂P ∂ x

+ f v = f [v−V g] = f vag

D v D t

= − 1ρ ∂P ∂ y

− f u =− f [u−U g] =−f uag

or k̂ f

× [ DV⃗D t − F⃗fric ] = V⃗ ag

| î ĵ k̂0 0 1/ fD u Dt

D v Dt

0 | = uag î + vag ĵ + 0 k̂ = −1f D vD t î + 1f D uD t ĵ + 0 k̂

Terms (v-V g ) and (u-U

g ) are

identically the "geostrophic deficit"

and the "ageostrophic wind." In

absence of friction, acceleration of

the flow equals the ageostrophic

wind divided by the Coriolis time

scale f -1

The “ageostrophic wind” and the "isallobaric wind"

eas372_isallobaricwind.odp JDW, EAS U. Alberta Last modified: 17 Apr. 2015

The ageostrophic wind is in the horiz. plane, perpendicular (and oriented to the left of) the acceleration vector

**A local approximation of the spherical earth as a plane normal to the zenithal component of the earth's rotation... f is assumed to be constant on the plane... valid in describing motions with time scales smaller than or comparable to 1/f. (AMS Glossary)... [as distinct from "beta plane" which allows linear variation of f with y ]

V⃗ g = k̂ × 1 ρ f

∇ P

jet entrance

jet exit

k̂ f

× DV⃗ D t

= V⃗ ag

Acceleration vector

Gradient wind

Ageostrophic wind

“Ageostrophic wind” in relation to jet streaks: locations of con/divergence

C

C

D

D

V⃗ ag = k̂ f

× [ ∂ V⃗∂ t + [V⃗⋅∇ ] V⃗ + ω ∂ V⃗∂ p ] Define the "isallobaric wind" to be that part of the ageostrophic wind that is

contributed by the first term (non-stationarity). Under the approximation that terms

on the rhs are evaluated using the geostrophic wind, the isallobaric wind is

V⃗ ia = k̂ f

× ∂ V⃗ g ∂ t

= k̂ f

× ∂ ∂ t [ k̂ × 1ρ f ∇ P ] = −1ρ f 2 ∇ ∂ P∂ t

• lines of constant surface pressure tendency are “isallobars”

• isallobaric wind “driven” by spatial gradient in pressure tendency

• or (equivalently) by tendency in the pressure gradient

• isallobaric wind blows PERPENDICULAR to isallobars

The "isallobaric wind"

V⃗ g = k̂ × 1 ρ f

∇ P

The "isallobaric wind"

Let coordinate s increase down the isallobaric gradient, i.e.

● from where p is rising rapidly towards where p is rising less rapidly, or

● from where p is rising towards where p is falling, or

● from where p is falling slowly towards where p is falling faster

Then the isallobaric wind is

V⃗ ia = −1 ρ f 2

∂ ∂ s [ ∂ P∂ t ]

Is this a "real" wind? Yes, it is one component of the departure from the geostrophic

wind (within the ABL, and particularly near the surface, friction is liable to be a more

important deviation). Furthermore its divergence is important (our starting point),

given by ∇⋅V⃗ ia = −1 ρ f 2

∇2 ∂P ∂ t

Isallobaric chart (from Vizaweb) – relevant to 12Z winds and our fcst for Wed. 12Z**

**YEG reported "18010KT" at 12Z Wed.

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