<p>You can, but the form changes. it is</p>
<p><span class="math-container">$N^2=\frac{g}{T}(\frac{dT}{dz} + Γ)$</span></p>
<p>where <span class="math-container">$Γ$</span> is the dry adiabatic lapse rate, given by <span class="math-container">$g/c_p$</span></p>
<p>where <span class="math-container">$c_p$</span> is the specific heat of air at constant pressure.</p>

CC BY-SA 4.0
2023-04-22T09:24:09.487Z
2023-04-23T02:00:27.530Z
2023-04-23T02:00:27.530Z
Edward Carroll
<p>The buoyancy frequency, $N$ is defined as $N^2=\frac{gd\theta}{\theta dz}$, where $\theta$ is the potential temperature (I see it as a measure of the deviation from the adiabatic nature), 
$z$ is the vertical co-ordinate and 
$g$ is the acceleration due to gravity and sometimes $\theta$ is replaced with potential density. My question is why not use $T(z)$ (usual temperature) instead of $\theta(z)$ to define $N$?</p>

CC BY-SA 3.0
2016-06-22T17:23:58.813Z
If you start from the derivation of the frequency (https://en.wikipedia.org/wiki/Brunt%E2%80%93V%C3%A4is%C3%A4l%C3%A4_frequency#Derivation_for_a_general_fluid), you see that in reality it is based on density. In the atmosphere, potential temperature has the same properties with regards to buoyancy as density and they can be substituted.
arkaia
CC BY-SA 4.0
2023-04-24T09:38:27.580Z
Because $\theta(z) = const.$ for an isentropc i.e. adiabatic atmosphere, whereas  $T(z) \neq const.$.
AtmosphericPrisonEscape
<atmosphere><temperature><atmospheric-circulation>
Buoyancy frequency
vijay
# Buoyancy frequency

(Asked by: username_0 on 2016-06-22)

The buoyancy frequency, $N$ is defined as $N^2=\frac{gd\theta}{\theta dz}$, where $\theta$ is the potential temperature (I see it as a measure of the deviation from the adiabatic nature),
$z$ is the vertical co-ordinate and
$g$ is the acceleration due to gravity and sometimes $\theta$ is replaced with potential density. My question is why not use $T(z)$ (usual temperature) instead of $\theta(z)$ to define $N$?

**Tags:** atmosphere, temperature, atmospheric-circulation

> **Comments:**
> **username_1**: If you start from the derivation of the frequency (https://en.wikipedia.org/wiki/Brunt%E2%80%93V%C3%A4is%C3%A4l%C3%A4_frequency#Derivation_for_a_general_fluid), you see that in reality it is based on density. In the atmosphere, potential temperature has the same properties with regards to buoyancy as density and they can be substituted.  
> **username_2**: Because $\theta(z) = const.$ for an isentropc i.e. adiabatic atmosphere, whereas  $T(z) \neq const.$.  

---

## 1 answers

### Answer by username_3 on 2023-04-22. Score: 3

You can, but the form changes. it is

$N^2=\frac{g}{T}(\frac{dT}{dz} + Γ)$

where $Γ$ is the dry adiabatic lapse rate, given by $g/c\_p$

where $c\_p$ is the specific heat of air at constant pressure.


---

