The Isallobaric Wind

 

The real wind can always be broken into a geostrophic and an ageostrophic component

 

V = Vg + Va                                                                                             (1)

 

 

We have spent much time discussing both the real wind and the geostrophic wind.  Now let's get some insight into the ageostrophic component of the real wind.

 

The portion of the wind that is ageostrophic can be shown to be related to divergence and convergence at the given level.  Hence, part of the way to understand divergence patterns is to examine the isallobars. 

 

You can reason this out yourself by examining the following equation, where V is the horizontal wind.

 

                         (2)

 

 

You already showed in Lab 1 that the divergence of the geostrophic wind is zero (this is not really true, but the reasoning for that awaits future lectures).  Thus the horizontal divergence is really due to the divergence of the ageostrophic wind.

 

                                                         (3)

 

If there is no ageostrophic wind, therefore, there can be no divergence.

 

 

Remember that the geostrophic wind is, in s, n, p components

 

                                                  (4)

 

Also, recall that the equation of horizontal motion in natural coordinates can be rewritten for straight flow

 

 

                                (4a)

 

Solving for the horizontal wind (4a) can be rewritten

 

 

                                (4b)

 

Substituting equation (4) into (4b)

 

                                                                                                         (5)

 

So, it is clear from equation (1) that

 

                                                (6a)

 

              (6b)

 

 

At the synoptic scale,  equation (7) reduces to

 

                                             (7)

 

 

Substitute (4) into (7) and remembering that changing the order of differentiation does not alter the accuracy of the result, one gets:

 

                       (8)

 

Equation (8) states that, at the synoptic scale, the real wind differs from the geostrophic wind by an ageostrophic wind that is dominated by a term proportional to the height tendency (in x,y,p) (or pressure tendency in x,y,z).  This portion of the ageostrophic wind is known at the ISALLOBARIC WIND. 

 

The isallobaric wind is the wind that “blows” at right angles to the isallobars (pressure or thickness change contours) from more positive values to more negative values. 

 

Substitution of (8) into (1) shows that vectorially, at the synoptic scale, the isallobaric wind vector is that which must be added to the geostrophic wind vector (at a given level…don’t get this confused with the thermal wind relation) to obtain the real wind. 

 

Another way to look at this is that the wind will be geostrophic until the height or pressure gradient increases or decreases.  Then the wind will be out of geostrophic balance  and the wind will flow down or, actually, up the pressure gradient again (since the pressure gradient acceleration will be out of balance with the Coriolis acceleration until the wind is in geostrophic balance again).

 

Note, if the isallobaric component of the wind was the ONLY ageostrophic component, then the difference between the actual wind at any level and the geostrophic wind would be that due to pressure tendencies (development).  However, at the surface, terms dominated by friction effects and curvature effects, may partially mask the isallobaric wind.  In the upper troposphere the centripetal accelerations related to curvature of the trajectories is very strong and contributes a much larger portion of the ageostrophic wind.  (pp. 178-181 in Bluestein).