Re: double tide cause

["John S. Denker" <jsd@MONMOUTH.COM>]

At 04:05 PM 9/3/01 -0600, Jim Green wrote:

> I repeat: the "size" of the oscillating body doesn't matter nearly as much
> as its natural frequency.

There's a valid idea hiding in there, but it is so overstated as to lose
most of its meaning, and it is supported by invalid arguments.

By way of analogy:  When discussing torque measured in foot-pounds, it
would be absurd to say that the "feet" don't matter nearly as much as the
"pounds".  That's worse than comparing apples and oranges.

In fact what matters for torque is the PRODUCT of the feet TIMES the
pounds. Both factors in this product are indispensable.

In fact what matters for tides is the PRODUCT of the tide-producing force
TIMES some response function.  Both factors in this product are indispensable.

        (Footnote:  Yeah, I know it's actually a convolution, but
        the idea is the same, and I'm trying to keep the discussion
        from getting unduly complicated.)

Each of these factors has complexities of its own:
 1a) The magnitude of the tide-producing force depends on the size of the
body, as I have been saying.
 1b) It also depends on the extent to which the body is coupled to the
tidal motions of other bodies.

 2a) The response function depends on whether the body has resonances near
any of the relevant frequencies.
 2b) It, too, depends on coupling to other bodies.
 2c) It also depends on damping factors (internal friction, et cetera).

As an illustration, it would be straightforward for me to construct an
isolated inland canal (say 1 km long) with a sloshing resonance exactly at
one of the primary tidal frequencies.  I am quite confident that my canal
would not exhibit tides comparable to the Bay of Fundy -- or even an
ordinary New Jersey beach.  That's because it is too small to have much of
a driving force, and the Q of the resonance wouldn't be big enough to
change the story.