<p>The Rossby radius of deformation tells you the distance when the Coriolis effect becomes just as important as the buoyancy or gravity.</p>

<p>Let the Rossby radius of deformation be denoted as $L_R$. According to Holton's Fifth Edition of "An introduction to Dynamic Meteorology,"  $$L_R=\frac{NH}{f_0}$$ where $N$ is the Brunt-Vaisala frequency, $H$ is the scale height, and $f_0$ is the Coriolis parameter.</p>

<p>For phenomena with length scale $L$, buoyancy can be neglected if $L&lt;&lt;L_R$.</p>

<p>In statically stable equatorial flows, $$\lim_{f_0\to 0} L_R=\infty$$</p>

<p>In certain coastal flows, $L \approx L_R$</p>

<p>So the author is saying that in equatorial flows, buoyancy can't be neglected, since the Rossby radius "blows up" and for coastal flows $L\approx L_R$</p>

CC BY-SA 3.0
2017-09-22T15:38:07.387Z
2017-09-22T15:38:07.387Z
BarocliniCplusplus
<p>In the introduction of "<a href="http://shoni2.princeton.edu/ftp/lyo/journals/Cai-etal-RossbyRadiusSCS-JMS2008.pdf" rel="nofollow noreferrer">Geographical and monthly variability of the first baroclinic Rossby radius of deformation in the South China Sea</a>", the authors states:</p>

<blockquote>
  <p>In both theoretical and observational studies of large and meso-scale oceanic processes, the first baroclinic Rossby radius of deformation (R1) is an important quantity in determining horizontal scales which characterize eddy sizes, trapping scales for coastal jets and equatorial flows.</p>
</blockquote>

<p>I am familiar with the fact that R1 can determine eddy sizes (e.g., <a href="https://earthscience.stackexchange.com/questions/2227/how-is-the-rossby-radius-used-to-determine-that-synoptic-weather-systems-are-100">this answer</a>), but I am having an hard time to find references about trapping scales for coastal jets and equatorial flows.</p>

<p>Can someone, please, give me some explanations and/or references?</p>

CC BY-SA 3.0
2018-04-06T17:29:23.083Z
For equatorial flows, please check for Matsuno 1966 Quasi-Geostrophic motions in the equatorial area.
Enver
<geophysics><oceanography>
Rossby radius as horizontal scale
shamalaia
# Rossby radius as horizontal scale

(Asked by: username_0 on 2017-09-22)

In the introduction of "[Geographical and monthly variability of the first baroclinic Rossby radius of deformation in the South China Sea](http://shoni2.princeton.edu/ftp/lyo/journals/Cai-etal-RossbyRadiusSCS-JMS2008.pdf)", the authors states:

> In both theoretical and observational studies of large and meso-scale oceanic processes, the first baroclinic Rossby radius of deformation (R1) is an important quantity in determining horizontal scales which characterize eddy sizes, trapping scales for coastal jets and equatorial flows.

I am familiar with the fact that R1 can determine eddy sizes (e.g., [this answer](https://earthscience.stackexchange.com/questions/2227/how-is-the-rossby-radius-used-to-determine-that-synoptic-weather-systems-are-100)), but I am having an hard time to find references about trapping scales for coastal jets and equatorial flows.

Can someone, please, give me some explanations and/or references?

**Tags:** geophysics, oceanography

> **Comments:**
> **username_1**: For equatorial flows, please check for Matsuno 1966 Quasi-Geostrophic motions in the equatorial area.  

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## 1 answers

### Answer by username_2 on 2017-09-22. Score: 5

The Rossby radius of deformation tells you the distance when the Coriolis effect becomes just as important as the buoyancy or gravity.

Let the Rossby radius of deformation be denoted as $L\_R$. According to Holton's Fifth Edition of "An introduction to Dynamic Meteorology," $$L\_R=\frac{NH}{f\_0}$$ where $N$ is the Brunt-Vaisala frequency, $H$ is the scale height, and $f\_0$ is the Coriolis parameter.

For phenomena with length scale $L$, buoyancy can be neglected if $L<<L\_R$.

In statically stable equatorial flows, $$\lim\_{f\_0\to 0} L\_R=\infty$$

In certain coastal flows, $L \approx L\_R$

So the author is saying that in equatorial flows, buoyancy can't be neglected, since the Rossby radius "blows up" and for coastal flows $L\approx L\_R$


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