The ¢â‚¬“ageostrophic wind¢â‚¬â€Œ...

The ¢â‚¬“ageostrophic wind¢â‚¬â€Œ and the isallobaric wind and the "ageostrophic wind." In absence of friction,
The ¢â‚¬“ageostrophic wind¢â‚¬â€Œ and the isallobaric wind and the "ageostrophic wind." In absence of friction,
The ¢â‚¬“ageostrophic wind¢â‚¬â€Œ and the isallobaric wind and the "ageostrophic wind." In absence of friction,
The ¢â‚¬“ageostrophic wind¢â‚¬â€Œ and the isallobaric wind and the "ageostrophic wind." In absence of friction,
The ¢â‚¬“ageostrophic wind¢â‚¬â€Œ and the isallobaric wind and the "ageostrophic wind." In absence of friction,
download The ¢â‚¬“ageostrophic wind¢â‚¬â€Œ and the isallobaric wind and the "ageostrophic wind." In absence of friction,

of 5

  • date post

    18-Apr-2020
  • Category

    Documents

  • view

    12
  • download

    0

Embed Size (px)

Transcript of The ¢â‚¬“ageostrophic wind¢â‚¬â€Œ...

  • ● 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.

    Slide 1 Slide 2 Slide 3 Slide 4 Slide 5 Slide 6 Slide 7 Slide 8 Slide 9 Slide 10 Slide 11 Slide 12 Slide 13 Slide 14 Slide 15 Slide 16 Slide 17 Slide 18 Slide 19 Slide 20 Slide 21 Slide 22