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Recently I found this tutorial video about Jet streaks. Originally I was looking for the topic because of a particular exercise I have to solve but now I got stuck here:

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

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

Recently I found this tutorial video 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:

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?

Recently I found this tutorial video about Jet streaks. Originally I was looking for the topic because of a particular exercise I have to solve but now I got stuck here:

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.

What is wrong in my understanding?

Recently I found this tutorial video about Jet streaks. Originally I was looking for the topic because of a particular exercise I have to solve but now I got stuck here:

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

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

Recently I found this tutorial video about Jet streaks. Originally I was looking for the topic because of a particular problem I have to solve but now I got stuck here:

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.

What is wrong in my understanding?

Recently I found this tutorial video about Jet streaks. Originally I was looking for the topic because of a particular exercise I have to solve but now I got stuck here:

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.

What is wrong in my understanding?