tides

From: Ken Poulton (poulton@zonker.hpl.hp.com-DeleteThis)
Date: Sun Aug 27 1995 - 11:09:20 PDT


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Date: Sun, 27 Aug 1995 11:09:20 -0700
From: Ken Poulton <poulton@zonker.hpl.hp.com-DeleteThis>
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To: wind_talk@zonker.hpl.hp.com-DeleteThis
Subject: tides

On the topic of tide models, I'm afraid good old Newtonian mechanics
suffice to explain tides. Relativistic effects are present (as always),
but I estimate them to be at least 10^11 times smaller.

The big picture:

The earth+moon system rotate around their *common* center of gravity,
which is near, but not at the center of the earth. The non-intuitive
result (no math today, folks) is that gravity is reduced slightly both
on the part of the earth nearest the moon and on the part farthest away
from the moon! Thus, two tidal bulges and two high tides a day.

There is a second, smaller tidal effect from the sun, which is why the
tides seem so complicated.

In the open ocean, these tidal bulges are unobstructed, and the
actual height change (as in Hawaii) is small - a foot or two.
More substantial tidal changes occur when the tidal bulges run into
continents - we get about 6 feet daily variation at the Gate.

The small-scale picture:

This is the interation of the ocean tides with the Bay shape. For the
circuit-impaired, we can make a Bay model with a network of springs and
rocks: the rocks represent regions of the Bay to be moved up or down and
the springs represent the channels that couple the regions together.
Larger areas are represented by larger rocks. Deeper and wider channels
are represented by stiff springs (the coupling is strong) while narrow
channels are represented by softer springs. When there are branches,
add a massless (whoops, that physics sneaking in) horizontal stick to
allow us to couple from one mass out to two springs (like a hanging
mobile).

When you move the top spring (the Gate) up quickly, the lower rocks
don't move at once - there is a transmission delay. If you apply a
gentle cyclic up and down motion, the whole network will move up and
down at the same frequency, but various points will have different
delays from the driving motion and different points will have different
amplitudes of motion. Some rocks, which are coupled by very long, soft
springs, will have smaller motions (Rio), and others, which just happen
to have the right combination of rock and spring, will actually have
larger amplitudes (Coyote).

More modeling details:

The above model omits friction, which is probably very important for
places like Rio. Imagine the whole mobile immersed in oil as a first
pass. Also, large open areas like the South Bay can be better modeled
as arrays of small rocks all coupled together with springs to their
nearest neighbors. This is the basic idea behind finite-element
modeling, which is how you would really go about this if you were
serious.

Tides vs currents:

The currents are represented here by the extension of the springs
beyond their resting lengths. You can see that since the South Bay
rocks are still moving after the ocean has stopped (reached low tide)
that the springs must still be getting longer - meaning that the
current is still running.

Great. How can I know the tides w/o a PhD and a supercomputer?

Tides at the Golden Gate have been carefully measured and modeled so
that tide tables can be calculated. There are public-domain programs
that calculate tide heights at the Golden Gate as well.

So how the heck do I avoid breaking off my fin at 3rd Ave?

This is the sticky part. All we get from NOAA are time and amplitude
offsets from the Gate for high and low tide (also for max and slack
currents). For Coyote Point, the height differences are +0.1 ft at low
tide and +1.8 ft at high - the average amplitude is 30% larger than
at the Gate. These are *averages* however, and tidal heights are quite
variable. It seems physically unlikely when we get a 3-foot low and a
4-foot high (e.g., Aug 19) that Coyote will get a 3.1-foot low and a
5.8-foot high (a 170% increase). So it is not very clear how to
apply the average differences to get the adjusted tides at any time.

After some discussion with NOAA's expert on the matter, I implemented
a simple model that essentially amplifies the tides from the Gate
by 30% and gives them a variable delay depending on height. I
improved the model somewhat over the last year but some muddy days at
Palo Alto have made me think that it is reading high for high low tides
(like that 3-foot low).

Other sources seem to be even more simplistic for application of
local offsets.

All of this has motivated the tidal measurement project I'll discuss
in the next message.

Ken Poulton
poulton@opus.hpl.hp.com-DeleteThis

"I have made this letter longer than usual because I lack the time to
make it shorter." -- Blaise Pascal



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