Re: CoTidal Map

[David Bowman <David_Bowman@GEORGETOWNCOLLEGE.EDU>]

Regarding Jim Green's comment:

> As a matter of fact, Joel, the Co-Tidal Map a couple of pages above is
> better -- The lines show high water all at the same time.  For me it is
> plain that there is no "bulge"  but I wouldbe happy to hear from others.
>
> Jim

You really *would* "be happy to hear from others"?

Ok.  First off, if there was no tidal bulge then there would be no
tidal breaking of the Earth's spin with its lost spin angular
momentum being transferred to the orbital angular momentum of a
receding Moon.  But it just so happens that actual measurements
indicate that the Moon *is* receding from the Earth at an average
rate of around 3.7 cm/yr *and* the earth's spin rate *is* being
braked at a rate of about 15 microsec/day/yr.  This angular momentum
transfer can only be accomplished via a tidal coupling between the
Moon's gravitational field gradient and the induced mass-quadrupole
moment of the earth such that that quadrupole moment is not aligned
exactly with the moon.  The phase shift in the alignment is an
artifact of a combination of the Earth's spin rate and the finite
relaxation time of the induced moment in the Earth.  The rotation of
the earth carries the induced quadrupole moment out ahead of the Moon
by a few degrees while it continuously relaxes and is being
re-induced directly under the Earth-Moon line of sight.  The
relaxation time is dependent on the size & shape of the ocean basins
and intervening continents as well as the rate of a host of
dissipative effects affecting the relaxation of such deformations.

Since the Moon *is* receding from the Earth, and since the Earth *is*
spinning down we know that the tidal bulge (i.e. the difference
between the shape of the earth in the absence of the tidal effects of
the Sun & the Moon and the actual shape which *is* influenced by
these tidal forces and which has the induced mass-quadrupole moment
in place) *does* exist.  Whether or not it can be seen in cotidal
maps is a completely *different* issue.  As I recall the average
amplitude of the tidal bulge is something on the order of 10-11 cm
anyway.  Not something that is easily seen under all the sloshing of
the much larger tidally-induced water displacements here and there
with their various local basin resonances, reflections, sieches, and
assorted other local amplifications and attenuations.

To claim that there is no tidal bulge is tantamount to claiming that
angular momentum is manifestly not conserved.  Do you really want to
claim that, Jim?

David Bowman