shear, shear, and migration

[David Eric Smith]

Hi Nick,

Unfortunately, given that I find them interesting, the amount I don't
know about Hurricanes fills volumes.  On the other hand, I think you
are a victim of language, created because weather people, like
everyone else, never speak in complete sentences.  

So first, to shear and Shear.  Scale matters here.  A Hurricane is a
structure of shear flows.  Unless I am terribly missing the point,
that is why it spins, why the eyewall has the structure it does, etc.
Shear is what makes the coriolis force matter.  A net influx of air
toward the eye (shear over the ocean) at low level causes
more-equatorial air to move northward and more-polar air southward.
Because they keep some of their angular momentum, the more-equatorial
air has a net eastward velocity relative to the more-polar component.
This angular momentum conservation creates the vortex, and the fact
that the low pressure in the central regions is only capable of
supporting a limited centripetal force causes the influx to stop at a
nonzero radius, leaving the eye.  I think that this is why wind speed
in the storm is directly related to (and caused by) the pressure
reduction in the eye (there is also some Bernoulli relation relating
pressure and velocity in the eyewall with pressure and stillness in
the eye, which would provide a different-looking equation to arrive at
the same result).

Some of the angular momentum is not convected, because the air has
friction, so the total angular momentum at the top of the convection
system, where it must flow back out (shear at high altituted) is not
what it brought in with it.  Hence there is a negative velocity of the
more-equatorial air near the eye now going back toward the equator,
and the more-polar air near the eye going back toward the pole.  So we
get spiral flow at the top in the antisense of the flow at the
bottom.  All this is shear, but it is shear at the scale of the
substructure of the storm itself, rather than net Shear at the scale
of the whole atmosphere.  

I assume, though I can't back it up, that the form of shear weathermen
speak of as disruptive of hurricanes, is Shear on the scale of the
whole atmosphere, which is transporting and dissipating angular
momentum in lattitude in other ways than those that form a clean
vortex.  Think of stirring the water going down the drain, and how
that can inhibit the formation of a drain vortex.  That is a
disruptive Shear phenomenon, but the vortex itself, when it forms, is
also a shear phenomenon.  

Re polar migration.  Thank you for providing a lot of detail I didn't
know about that.  Perhaps I should have been thinking of the oceans as
the place to look for the original polar motion, though that seems too
limited.  I thought that the gulf stream runs northward near the
surface, warming England and Scotland, but where it gives that heat up
to the atmosphere, the water cools and dives, returning to the equator
in the deep mid-atlantic, where it eventually wells up, is reheated by
the sun, and meanders (via loop currents or however) back northward.
If that is correct, then what you say about Hurricanes following ocean
tracks would be consistent with northward tendencies, because the
ocean currents go north at the surface to be cooled.  (Please pardon
the intentional language here.  They do what they do because they
solve differential equations, where sinking leaves a low pressure that
draws in warm surface water, etc.  It is easier to assume we all know
there is some such mechanics behind it and encode that in saying "to
be cooled".)  I still tend to expect that, with all sorts of
variations and stochasticity, there is a larger principle here that
governs atmosphere and oceans through whatever coordinated currents:
that heat is delivered mostly in the equator and tropics, and
dissipates as uniformly as it can (meaning, limited by the degree to
which temperature can be equalized) over the globe.  Thus net
transport of heat from equator and tropics to poles is the background
leading to all the various currents.  There is a lot more heat in the
oceans than atmosphere, in addition to which that is where most of
the sunlight is actually absorbed and converted to heat.  So it would
be reasonable that the oceans are the big engine, and the atmosphere
follows along.

Anyway, all most interesting...

Eric