Re: Rossby waves

[Bowman_David/tiger_mpc@tiger.gtc.georgetown.ky.us]

Jim G. writes:

> I was hoping that an understanding of Rossby waves would shed some light so
> I brought the topic up for discussion.  But I find it difficult to penetrate
> the oceanographic language barrier. I seem to be too old and senile to
> understand that stuff.  (Heavens, I forgot about retrograde motion the other
> day and still haven't recovered.)

It is possible to explain Rossby waves without referring to terms such as
absolute and relative potential vorticity as well as to the Coriolis parameter
(directly).  It's just that the description will not be as elegant (and
short).  I find it easier to explain Rossby waves in a meteorological context
than in an oceanographic one.  In this case Rossby waves can be seen as sort
of a modulation on a geostrophic wind.  (Oops. I shouldn't use meteorlogical
jargon.)  A geostrophic wind is a relatively straight line steady flow of a
belt of air over long distances at a high enough altitude that friction at the
surface is negligible.  This motion is a direct hydrodynamical analog of the
Hall Effect for electric currents in conductors or a velocity selector for
charged particle beams using crossed E and B fields.  The midlatitude jet
stream is a classic example of this.  Due to details of planetary-wide
circulation patterns (at the latitude of the boundary (front) of the mid-
latitude westerlies and the polar northeasterlies) there tends to be a
horizontal pressure gradient at a high altitude such that the higher pressure
side is to the south and the lower pressure side is to the north.  This means
that a parcel of air at this level will be pushed to the north by the pressure
gradient.  Since the friction is low the parcel and its neighbors pick up
speed and accelerate due to this unbalanced force.  As their speed increases
the Coriolis effect acting on the parcels kicks in since the Coriolis effect
magnitude is proportional to the speed.  In the Northern Hemisphere the
earth's angular velocity vector has an upward vertical component (and a north-
pointing horizontal component).  Since the Coriolis "force" acts perpendic-
ularly to both the velocity and this spin axis direction (due to the vector
cross procuct) there is a horizontal component to the Coriolis "force" which
tends to deflect horizontal motion to the right (from the upward vertical
component of the angular velocity vector).  (There is also a vertical
component to the Coriolis "force" acting on horizontal motion coming from the
horizontal component of the angular velocity but this component is dwarfed and
swamped by the much stronger gravitational forces, the vertical pressure
gradient, etc.)  Now this rightward Coriolis "force" acting on the northbound
air parcels deflects their motion to the east.  As the speed increases the
Coriolis "force" gets stronger and the direction turns evermore to the east.
Eventually a steady-state develops where the air motion is essentially due
east and there is no further acceleration.  In this state the air parcels
feel a leftward (north-pointing) pressure gradient force which is exactly
balanced by the rightward Coriolis "force" allowing the parcel and its
neighbors to coast at a constant velocity to the east.  This easterly flow IS
the jet stream (or more generically the geostrophic wind).  In the E&M analogy
the horizontal pressure gradient is the electric field, the angular velocity
vector of the earth is the magnetic field, the Coriolis effect is the magnetic
force, and the wind flow is the electric current flow.  (If the original
pressure gradient force was toward the south rather than the north, then the
geostrophic wind would have ended up flowing to the west.  In the Southern
Hemisphere a similar jet stream flow to the east occurs, except in this case
the Coriolis "force" is to the north and the pressure gradient force is to the
south.)

If there were no perturbations on this system the jet stream would just
continue to flow to the east following a parallel of latitude.  Now suppose
that for some reason that the flow gets disturbed (maybe jet stream is blowing
over a lower altitude front or a localized blocking weather system and gets
disrupted) and the flow is deflected north and flows in a northeasterly
direction.  As the air parcels in the stream get further north the horizontal
Coriolis "force" gets more intense (since the Earth's angular velocity vector
has a more vertical upward orientation the further north one goes).  This
excess Coriolis "force" curves the motion to the right and causes the flow to
head back south and now flows in a southeasterly direction.  Eventually the
flow stream overshoots and crosses its original latitude going too far the
south.  Now the horizontal Coriolis "force" is weaker than before and does
not tend to deflect the flow to the right as much as the (now stronger)
pressure gradient force tends to deflect the flow to the left (north).  The
flow direction now curves off to the north all-the-while still maintaining an
overall flow to the east.  These wiggly north-south excursions on the overall
flow to the east of the jet stream ARE the Rossby waves on the jet stream.
BTW, the speed at which the pattern of Rossby waves propagate along the jet
stream is MUCH slower than the jet stream current itself and (I think I
remember) can even result in a standing wave pattern or a western motion of
the modulation on the east-going jet stream.

Rossby waves on ocean currents are a similar phenomenon.  A major difference  
is that the wavelength of oceanic Rossby waves is about an order of magnitude
shorter than for those on the jet streams.  (After all, the jet streams move
much faster than ocean currents).

David Bowman
Georgetown College
dbowman@gtc.georgetown.ky.us

P.S.  If someone who really understands meteorology (such as an actual
meteorologist) notices that I have said something incorrect or misleading
here, please correct my errors.  Meteorology is definitely not my field.

P.P.S  BTW, I don't wear suspenders, and I fail to see what posting messages
at odd hours has to do with how one holds up one's trousers. :)