Rossby radius as horizontal scale

Question

In the introduction of "Geographical and monthly variability of the first baroclinic Rossby radius of deformation in the South China Sea", 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), 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?

Answer 1

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 $L\approx L_R$