<p>How do you derive the components of the inertial advective wind in natural coordinates?</p>
<p>The vector form of the inertial advective wind is:</p>
<p><a href="https://i.sstatic.net/Ec4LH.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/Ec4LH.png" alt="enter image description here" /></a></p>
<p>I have been able to find the components in cartesian coordinates as shown here:</p>
<p><a href="https://i.sstatic.net/DNSkz.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/DNSkz.png" alt="enter image description here" /></a></p>
<p>I want to find the components in natural coordinates (such as shown below), but I have been unsuccessful so far.</p>
<p><a href="https://i.sstatic.net/3gpRu.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/3gpRu.png" alt="enter image description here" /></a></p>
<p>Any help would be greatly appreciated! Thanks</p>

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2021-04-26T21:19:03.987Z
Hi for reference the first equation comes from 

Rochette 2006, "A primer of the ageostrophic wind," (http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.663.2094&rep=rep1&type=pdf)

 And the second equation comes from the Encyclopedia of Atmospheric Sciences (2nd edition) volume 5 under the entry on Jet Streaks - a preview with the relevant equation can be found here under the heading "SYNOPTIC METEOROLOGY | Jet Streaks" https://www.sciencedirect.com/topics/earth-and-planetary-sciences/ageostrophic-flow
Will Watson
<meteorology><wind>
How to find inertial advective component of ageostrophic wind in natural coordinates
Will Watson
# How to find inertial advective component of ageostrophic wind in natural coordinates

(Asked by: username_0 on 2021-04-26)

How do you derive the components of the inertial advective wind in natural coordinates?

The vector form of the inertial advective wind is:

[![enter image description here](https://i.sstatic.net/Ec4LH.png)](https://i.sstatic.net/Ec4LH.png)

I have been able to find the components in cartesian coordinates as shown here:

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

I want to find the components in natural coordinates (such as shown below), but I have been unsuccessful so far.

[![enter image description here](https://i.sstatic.net/3gpRu.png)](https://i.sstatic.net/3gpRu.png)

Any help would be greatly appreciated! Thanks

**Tags:** meteorology, wind

> **Comments:**
> **username_0**: Hi for reference the first equation comes from   Rochette 2006, "A primer of the ageostrophic wind," (http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.663.2094&rep=rep1&type=pdf)   And the second equation comes from the Encyclopedia of Atmospheric Sciences (2nd edition) volume 5 under the entry on Jet Streaks - a preview with the relevant equation can be found here under the heading "SYNOPTIC METEOROLOGY | Jet Streaks" https://www.sciencedirect.com/topics/earth-and-planetary-sciences/ageostrophic-flow  

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## 0 answers

