Rossby waves

[Ari Epstein <awe@pimms.mit.edu>]

Kyle Forinash writes:

> Here are a couple of general references that might be relevant. I don't
> recall if Rossby waves are explicitly mentioned but the idea of internal
> waves (as opposed to surface waves) are:

and a number of others follow up on internal waves. The problem is
that, although they are *extremely* interesting (e.g.  under certain
conditions the phase velocity is normal to the group velocity; also,
in an ocean where density varies smoothly with depth--as opposed to
those two-fluid internal-wave gizmos that you can buy in the
store--internal waves propagate vertically as well as horizontally,
and the angle at which they propagate depends on the waves' frequency;
and lots of other cool stuff) internal waves are *not* Rossby waves.

Rossby waves are essentially a product of the earth's curvature and
rotation. They can exist only in regions large enough (in the
North-South direction) that the Coriolis parameter varies
significantly from one part of the region to another. (In the example
I gave involving coins and potential vorticity, recall that things
only started to work when one water column was displaced far enough
that its planetary vorticity--i.e. the Coriolis parameter--changed
significantly.)  Internal gravity waves can exist in inertial
reference frames, in uniformly-spinning reference frames (where they
have some *very* interesting properties) or on a curved, spinning
planet. I'd be happy to say a bit more about them if folks would like
to hear it.

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Jim Green writes:

> BUT the Chelton/Schlax Science paper (12Apr96 p234) reports TOPEX/POSEIDON
> ocean surface height data and then says these transverse waves move the
> water/weather/currents horizontally.  What do I miss???  Probably a lot as
> the paper uses copious oceanography jargon.
>
> Chelton emails me that the ocean tides have nothing to do with Rossby Waves
> -- it is hard to see why there is no interaction -- I confess that I *want*
> there to be interaction as I am expecting to find long wavelength tidal
> waves -- when I first heard of Rossby Waves, I happily thought I had found
> them in disguise.  This to educate those who still think there is a "tidal
> bulge".  I guess I will have to look elsewhere.


In the linear approximation, Rossby waves do not interact with the
ocean tides. Tides are a forced oscillation, and Rossby waves can
propagate freely; I suppose it's possible that tidal phenomena could
gnerate Rossby waves, which would then travel freely, but I don't know
where this might happen (I could ask around, if you want me to). You
are correct that the "tidal bulge" is pretty mythical, at least on a
planet with continents.


It's not so much that Rossby waves move the (warm or cold) water
around, as that they cause the displacement of the isotherms to
propagate, so that cold water upwells (or warm water downwells)
somewhere very far away from the initial disturbance. That in turn
affects the weather over long distances.

Tomorrow I'll try to post an example in which a Rossby wave causes a
current field to propagate, again without moving the water around very
much.




As far as references go, I've been looking around and I'm not
completely satisfied about any of the textbooks I've got on the
subject. Some good ones are:

Introductory Dynamical Oceanography, by Pond and Pickard

Atmosphere-Ocean Dynamics, by Gill

Principles of Ocean Physics, by Apel

If folks would like, I'd be willing to post a quick mathamatical
description of Rossby waves.





Ari Epstein