<p>In the question, T was not specifically mentioned to be a constant. So by also expanding <span class="math-container">$T = \overline{T} + t’$</span>, we end up with the following answer. Where, the covariance term containing <span class="math-container">$\overline{c’t’}$</span> reflects that turbulence still plays a role in determining the mean quantity of C.</p>
<p><a href="https://i.sstatic.net/YZZAb.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/YZZAb.jpg" alt="enter image description here" /></a></p>

CC BY-SA 4.0
2020-10-27T01:56:11.050Z
2020-10-27T02:03:12.147Z
2020-10-27T02:03:12.147Z
meteo_96
<p>In deriving the prognostic equation for the mean quantity of pollutant C, as shown in my solution below:</p>
<ol>
<li>Am I right in that I do not need to separate T (temperature) into its mean and turbulent parts (like <span class="math-container">$T = \overline{T}$</span> + t’)? If I am right, is it because T does not depend on anything in this equation?</li>
<li>When assuming horizontal homogeneity in the x-direction, this means that the change in c with respect to x (dc/dx = 0) is zero. So does that leave the final prognostic equation with no advective terms since I aligned U to be in X also?</li>
</ol>
<p><a href="https://i.sstatic.net/iyr9w.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/iyr9w.jpg" alt="enter image description here" /></a></p>
<p>Thanks for any help!</p>

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2020-10-26T15:17:14.623Z
What happened to $\overline{c’T’}$?
BarocliniCplusplus
CC BY-SA 4.0
2020-10-26T16:03:35.347Z
^That is, what makes you think that temperature is uniform?
BarocliniCplusplus
CC BY-SA 4.0
2020-10-27T01:58:46.190Z
Well, actually the question does not state this. I may have overlooked the statement that specifically says that the decomposition of C depends on T. Thanks!
meteo_96
<meteorology><planetary-boundary-layer>
Question on the derivation of a prognostic equation for the mean concentration (Assume horizontal homogeneity in X)
meteo_96
# Question on the derivation of a prognostic equation for the mean concentration (Assume horizontal homogeneity in X)

(Asked by: username_0 on 2020-10-26)

In deriving the prognostic equation for the mean quantity of pollutant C, as shown in my solution below:

1. Am I right in that I do not need to separate T (temperature) into its mean and turbulent parts (like $T = \overline{T}$ + t’)? If I am right, is it because T does not depend on anything in this equation?
2. When assuming horizontal homogeneity in the x-direction, this means that the change in c with respect to x (dc/dx = 0) is zero. So does that leave the final prognostic equation with no advective terms since I aligned U to be in X also?

[![enter image description here](https://i.sstatic.net/iyr9w.jpg)](https://i.sstatic.net/iyr9w.jpg)

Thanks for any help!

**Tags:** meteorology, planetary-boundary-layer

> **Comments:**
> **username_1**: What happened to $\overline{c’T’}$?  
> **username_1**: ^That is, what makes you think that temperature is uniform?  
> **username_0**: Well, actually the question does not state this. I may have overlooked the statement that specifically says that the decomposition of C depends on T. Thanks!  

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## 1 answers

### Answer by username_0 on 2020-10-27. Score: 1

In the question, T was not specifically mentioned to be a constant. So by also expanding $T = \overline{T} + t’$, we end up with the following answer. Where, the covariance term containing $\overline{c’t’}$ reflects that turbulence still plays a role in determining the mean quantity of C.

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


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