<p>Recently I found <a href="https://www.youtube.com/watch?v=svke_051zzc" rel="nofollow noreferrer">this tutorial video</a> about Jet streaks (want to mention I'm only in second term so my knowledge is not advanced yet). Originally I was looking for the topic because of a particular exercise I have to solve but now I got stuck here:</p>
<p><a href="https://i.sstatic.net/bunqU.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/bunqU.png" alt="enter image description here" /></a></p>
<p>Mathematically it is clear for me that ageostrophic wind calculates according to</p>
<p><span class="math-container">$$\vec v_{ag} = \frac{1}{f} \cdot \vec k \times \frac{d \vec v}{d t}$$</span></p>
<p>But now my problem:</p>
<p>It is assumed that the real wind flows in x direction from W to (blue) E. Therefore, the ageostrophic wind is oriented towards north direction (green arrow). But, vectorially, this means that the geostrophic wind (red) must be directed a little to south so that read + green = blue.</p>
<p>But isn't that in contradiction to the fact, that geostrophic wind is always oriented along contours of constant height? Especially in this image, the contour through the point of interest is the straight line from W to E and not oriented towards south.</p>
<p>Moreover, its is shown in the video that the regions of convergence/divergence are N/S to the entrance and the opposite at the exit.</p>
<p>I would have guessed, that region of divergence is on the entrance and convergence at the exit, because</p>
<p><span class="math-container">$$\vec \nabla \cdot  \vec v = \partial u/\partial x + \partial v/\partial y$$</span></p>
<p>Since in the picture <span class="math-container">$v=0$</span> everywhere, we would have</p>
<p><span class="math-container">$$\vec \nabla \cdot  \vec v = \partial u/\partial x $$</span></p>
<p>and this depends only on the zonal position, not on meridional.</p>
<p>Do I maybe need to consider also w along z to calculate divergence? But we have been told, that vertical motion is neglectable.</p>
<p>Something is weird here...what is wrong in my understanding?</p>

CC BY-SA 4.0
2023-03-12T14:17:17.067Z
I cannot follow, what your hint shall be. I know what natural coordinates are. How does this relate to my question?
MichaelW
CC BY-SA 4.0
2023-03-12T15:47:46.680Z
Don't have time for a full answer right now, but noticed up front... yes geodtrophic is parallel to height contours.  But ageostrophic means non-geostrophic, so you're adding the geo and non geo
JeopardyTempest
CC BY-SA 4.0
2023-03-12T18:01:15.750Z
My main problem is that the real wind shown has only a zonal component and therefore gives divergence on the left and convergence on the right. I can't see what could be wrong with that. However, divergence and convergence zones are as indicated in the video and differ in the north and south.
MichaelW
<meteorology><wind><atmosphere-modelling><fluid-dynamics><jet-stream>
How is Wind oriented in a Jet Streak?
MichaelW
# How is Wind oriented in a Jet Streak?

(Asked by: username_0 on 2023-03-11)

Recently I found [this tutorial video](https://www.youtube.com/watch?v=svke_051zzc) about Jet streaks (want to mention I'm only in second term so my knowledge is not advanced yet). Originally I was looking for the topic because of a particular exercise I have to solve but now I got stuck here:

[![enter image description here](https://i.sstatic.net/bunqU.png)](https://i.sstatic.net/bunqU.png)

Mathematically it is clear for me that ageostrophic wind calculates according to

$$\vec v\_{ag} = \frac{1}{f} \cdot \vec k \times \frac{d \vec v}{d t}$$

But now my problem:

It is assumed that the real wind flows in x direction from W to (blue) E. Therefore, the ageostrophic wind is oriented towards north direction (green arrow). But, vectorially, this means that the geostrophic wind (red) must be directed a little to south so that read + green = blue.

But isn't that in contradiction to the fact, that geostrophic wind is always oriented along contours of constant height? Especially in this image, the contour through the point of interest is the straight line from W to E and not oriented towards south.

Moreover, its is shown in the video that the regions of convergence/divergence are N/S to the entrance and the opposite at the exit.

I would have guessed, that region of divergence is on the entrance and convergence at the exit, because

$$\vec \nabla \cdot \vec v = \partial u/\partial x + \partial v/\partial y$$

Since in the picture $v=0$ everywhere, we would have

$$\vec \nabla \cdot \vec v = \partial u/\partial x $$

and this depends only on the zonal position, not on meridional.

Do I maybe need to consider also w along z to calculate divergence? But we have been told, that vertical motion is neglectable.

Something is weird here...what is wrong in my understanding?

**Tags:** meteorology, wind, atmosphere-modelling, fluid-dynamics, jet-stream

> **Comments:**
> **username_0**: I cannot follow, what your hint shall be. I know what natural coordinates are. How does this relate to my question?  
> **username_1**: Don't have time for a full answer right now, but noticed up front... yes geodtrophic is parallel to height contours.  But ageostrophic means non-geostrophic, so you're adding the geo and non geo  
> **username_0**: My main problem is that the real wind shown has only a zonal component and therefore gives divergence on the left and convergence on the right. I can't see what could be wrong with that. However, divergence and convergence zones are as indicated in the video and differ in the north and south.  

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## 0 answers

