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Home , Gulf of Maine, Tidal range

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Time and in the of A dockside dialogue between two old friends

by David A. Brooks

It's impossible to visit Maine's coast and not notice the tides. The twice-daily rise and fall of level never fails to impress, especially downeast, toward the Canadian border, where the tidal range can exceed twenty feet. Proceeding northeastward into the of Fundy, the range grows steadily larger, until at the head of the bay, "" tides of greater than fifty feet can leave ships wallowing in the mud, awaiting the water's return.

My dockside companion, nodding impatiently, interrupts:

Yes, yes, but why is this so? Why are the tides so large along the Maine coast, and why does the tidal range increase so dramatically northeastward?

Well, my friend, before we address these important questions, we should review some basic facts about the tides. Here, let me sketch a few things that will remind you about our place in the sky.

A quiet rumble, as if a dark cloud had suddenly passed overhead.

Didn’t expect a physics lesson on this beautiful day.

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The only physics needed, my friend, you learned as a child, so not to worry. The sketch is a top view, looking down on the ’s north pole. You see the moon in its monthly orbit, moving in the same direction as the earth’s rotation. And while this is going on, the earth and moon together orbit the distant once a year, in about twelve , right?

Got it skippah. And I see the new and positions in the monthly orbit. But why do we get two tides each day, more or less, since the moon passes by only once each day as we rotate under it? And why does the time of high water get later every day?

Let me remind you of our own experience. Growing up on the Maine coast, surrounded by big tides, we soon learn to regulate our lives by two clocks. We awaken mornings, go to school, and more or less carry out our expected duties like normal folks, following the solar clock, the one hanging on the wall. But for us there is another persistent ticking, an insistent lunar synchrony that drifts in and out of step with the wall clock. Sometimes the lunar beat gets the upper hand and at three in the morning, under a bright moon, we find ourselves chasing a run of smelt in a tidal creek choked with flashing fish.

But back to the story. The moon's obvious westward motion on a starry night is due to the earth's rotation, which carries us eastward under the celestial sphere at a rate of 15 degrees of longitude each hour. This is simple enough by itself to explain the regular motion of the stars, but the moon's position in the sky is influenced by its own eastward movement in a roughly 29 day orbit. Because of this, each successive day the earth's rotation must carry us a bit farther around before the moon passes our longitude again. For the same reason, at a particular location are delayed each day by the time it takes for the earth to "catch up" with the moon. 3

And how long is this delay? Well, in the 24 hours required for the earth to turn once on its axis, you see that the moon advances about 1/29th of its orbit, so the earth must turn an extra 1/29 rotation to bring the moon back in line with a particular location. Thus the extra time required is 24/29 hours, or about 50 minutes, and this is the fundamental reason why the tides are later each day at a given port.

Hold on, I can read a table! The time between successive highs right here at this dock is about 12 hours, 25 minutes, not 12 hours, 50 minutes, and there's usually two tides a day. And if you're going to tell me the moon's gravity is the reason, how come we get high tides when the moon is long since set, clear around on the other side of the earth – what am I missing?

It’s the moon’s gravity all right, but to answer your question we must realize that each the earth and the moon orbit each other around their common center of mass. The earth is about 80 times more massive than the moon, so this balance point actually is inside the earth, about three-fourths of the way out from the center. As a result, every month all points on the earth travel around that balance point, known as the barycenter, following circular paths with the same radius.

This may be difficult to visualize, so let me offer a couple more sketches:

This is a side view, showing the moon and the earth connected by an imaginary thin stick. Because the earth is much more massive than the moon, the balance point on the stick is inside the earth, about 4700 km out from the rotation axis (distance “r” in the sketch). Now flip the picture so you are looking down on the North Pole…

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…and you see the earth and moon together orbiting the barycenter once each month. The thin stick is gone, replaced by the gravitational attraction between the two bodies. To see what happens next, it helps to turn off the earth’s daily rotation and focus on the monthly orbital motion. Choose any points you like on or in the earth, for example points a, b and c shown in the sketch. Follow them over the course of the month, and you see that they all make circles with the same radius, r.

Now recall the first time you learned how to whirl a stone or an apple on a string. To keep it in a circular path, you must provide an inward pull known as centripetal force. If the string breaks (or you just let go) the object continues in the tangential direction it is moving when the inward force vanishes. Maybe you also learned about centripetal force on a spinning carousel in the park, where that inward pull is necessary to avoid being launched into the dirt.

Right, my sister taught me that lesson at recess in grammar school.

So here’s the basic story: The moon’s gravity provides the inward pull, the centripetal force, the invisible “string,” needed to keep the earth and moon in a stable orbit. But the gravitational attraction between objects in space sensitively depends on their separation distance (the inverse square, actually - thank you, Isaac), so the attractive force is stronger on the side of the earth under the moon, at zenith, and weaker on the opposite side, at nadir. In contrast, all points on the earth, including those in the , experience the same centripetal force because in their monthly orbit they all travel in circles with the same radius, as illustrated in the sketch. Here’s the key: At the center of the earth, the moon’s gravitational attraction provides exactly the centripetal force necessary to maintain the stable orbit. Therefore, on the side of the earth closer to the moon, the gravity force is larger than the centripetal force, and the reverse is true on the side away from the moon.

The result is a tidal pull of the water toward the zenith point under the moon, where the gravitational force is stronger, and a second pull directed away from the moon on the opposite side of the earth, where the centripetal force wins out. The actual forces are tiny, but it’s the difference between them that matters. In the simplest interpretation, the 5 combination produces an egg-shaped distortion of the ocean surface, with the long axis of the egg pointing at the moon and following it in its orbit.

Maybe another sketch would help, this time a side view showing the moon’s orbital plane and the tidal “egg,” tilted relative to the earth’s equator:

You can see that an observer carried around under the tidal egg by the earth's daily rotation will experience two highs, one under each lobe of the egg, and likewise two lows separating them. You will also understand that the time separating successive highs or lows is therefore 12 hours plus about one-half of the "catch-up" time mentioned earlier. This is close to 12 hours, 25 minutes, comfortingly in agreement with tables and experience.

An apprehensive sideways glance, and I suspect my trapped companion silently wishes he were with the flashing fish.

And I suppose this artful sketch also explains the unequal highs that we often see on a particular day, and the unequal lows as well?

Ah, yes, as you point out, the afternoon high may be higher than the morning one, or vice- versa, and the evening low correspondingly lower. To explain this diurnal inequality, note that the plane of the moon's orbit is tilted relative to the the plane of the earth's equator. The tilt angle, known as declination, is about 28.5 degrees. Thus in a month the moon swings above and below the equator, and the amount above or below on a given day depends on where the moon is in its orbit. And keep in mind that the long axis of the tidal egg, shown greatly exaggerated by the dashed oval, always points to the moon in its orbit.

Let’s choose a time when the moon is at its maximum northern declination, as shown in 6 the sketch. As fixed observers on the rotating earth, we travel parallel to the equator at constant latitude under the inclined tidal egg. The sketch shows that the rotation carries us, here in the , under a higher high when we pass under the moon, relatively close to the axis of the egg, and a lower high on the opposite side of the earth, when we pass farthest from the axis. A little more thought shows that when the moon is over the equator twice a month in its orbit, we should see equal highs and equal lows. Thus in the course of a lunar month, we observe fortnighly variations in the strength of the diurnal inequality.

Well and good, but I know a pelagic boy from downeast Maine who grew up to be a sea captain, and he reports from Singapore that only one tide per day disturbs the waters there. From other ports around the world he sends word of mixed tides, with large inequalities between successive highs and lows. What says your crystal egg now?

Yes, as these observations point out, there are many complications that lie beyond our reach here on the dock. To name a few we have conveniently overlooked, the location of and the variable ocean depth must be considered to accurately predict the details of the tide at a particular location. One of those details is the amount of the diurnal inequality, which can be so large that you see only one high and one low each lunar day. Nevertheless, the tidal egg provides a fundamental, if simplistic, explanation for the tides.

Maybe so, but what about springs and neaps? The words themselves are secret chantings of tidal brotherhoods! Yet I clearly see the extreme ranges of spring tides at full , and in between the more moderate neaps. How speaks the egg to this?

Well, my friend, actually there are two eggs involved. Come back to the first sketch, here, and you will realize that the sun also causes an egg-shaped tidal distortion in the ocean. The solar egg is only about half as strong as the lunar one, but to get this right we must keep track of both. As the sketch shows, once each lunar month, the moon passes between the sun and the earth, and the grazing angle of incidence of sunlight illuminates for us only the thin crescent of a . A fortnight later, the moon is on the opposite side of the earth from the sun, so that we see its fully illuminated disk. At intermediate times we see a partially illuminated lunar disk as the moon waxes toward full or wanes toward new.

Here is the secret rite of admission to the tidal brotherhood: At both full and new moons, the lunar and solar tidal eggs are oriented with their long axes closely aligned, and their combined influences act in harmony to produce maximum effect. Thus at full and new moons, separated by a fortnight, we see spring tides. When the moon is midway between new and full, with half its disk visible, the lunar and solar tidal eggs are positioned with their long axes crossed almost at right angles. At those times, the lunar high closely coincides with the solar low, and the resulting diminished tides are called neaps. Spring tides are often called "moon" tides, in reference to the usually obvious full moon, but it is important to know, for admission to the innermost circle, that new moons are just as effective at producing spring tides.

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And while you’re at it, what’s this about ? I see that the full moon is bigger at those times, but why does that happen?

Ah, supermoons. The popular press loves them because the full moon’s disk is visibly enlarged at those times. Have another look at that first sketch and you will see that the moon’s orbit actually is slightly elliptical, not circular. Each month the moon passes closest to the earth at perigee, and a fortnight later it is most distant at apogee. When a full or new moon happens near perigee, the tidal influence is enhanced because of the stronger gravity during the closer approach, and the resulting spring tide is even larger than usual. Note that super-new-moons, as shown in the sketch, are just as effective as super-full-moons in this regard, but only the latter capture much attention because of the visual spectacle. The perigees drift in and out of sync with new or full moons as the earth-moon system makes its annual orbit around the sun, so we typically see only two or three supermoons each year.

So why don’t we have a of one flavor or the other at perigee every month? Why only two or three each year?

Well, it’s getting late and I was going to spare you the details, but since you asked, take a look at this figure I just happen to have on my iPhone:

In earlier sketches, I indicated that the lunar orbit is “about” 29 days. Well, we have to take a more careful look at that. The familiar time between full moons is about 29.5 days, 8 known as the synodic month. However, the actual time required for the moon to complete one orbit relative to the fixed stars is only about 27.3 days, approximately the time between perigees called the sidereal month, as shown in note 1. The figure also places the full moon at perigee, directly opposite the sun; i.e., a super full moon. But in the time required to complete one sidereal orbit, the earth and moon move together in their solar circuit, advancing about 27° of the 360° annual orbit, as shown in note 2. Because of that advance, an additional two days or so is required for the moon to reach its next opposition from the sun, so the next full moon occurs about 29.5 days later, well past the perigee and supermoon status (notes 3 and 4). Each succeeding month the full moon lags about another two days later than perigee, and close to 14 months must elapse before the two occur in close synchrony again. But recall that new moons can also happen at perigees, so one or the other occurs roughly every 6 or 7 months.

So, my friend, I suspect that is more than you wanted to know. But with Tides 101 firmly in hand (and no final exam), let’s come back to the original question. How is it that the tides in the Gulf of Maine, especially toward the east and in the , are so greatly amplified, compared to most other places? These are especially puzzling questions when we realize that the typical open ocean tidal range is about three feet - hardly noticeable by Maine standards.

Thought we’d nevah get heah, my friend sighs.

OK, first, it is important to realize that the Gulf of Maine, which includes the Bay of Fundy as an appendage, is nearly cut off from the open waters of the by the shallow Georges and Browns Banks. Here’s another figure from my phone:

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For a time after the last great glaciation, these banks, which extend northeastward from Cape toward , were above , and the gulf was essentially an inland sea cut off from the ocean. Today, the water barely covers the banks, and a satellite view of the gulf suggests an unfettered open connection with the Atlantic.

But we must look beneath the surface. When we do, we see that the principal connection with the Atlantic is a narrow, deep channel that slices across the banks, dividing Georges from Browns. Most of the tidal impetus for the Gulf enters through this old glacial river valley, now known as the Northeast Channel. From the point of view of the tides of the world ocean, the Gulf of Maine looks much like an inland sea, connected to the rest of the ocean by a narrow neck. The twice-daily Atlantic tidal wave sweeps down from the north, generally following the of , and as the wave passes the entrance to the Northeast Channel, the water is forced in and out in step with the tidal rhythm. It’s like a watery jug band, with Neptune himself blowing a tidal backbeat across the mouth of a colossal bottle.

The question brings us to a quirk of nature, a consequence of glacial geology and continental drift. It turns out that the dimensions and depth of the Gulf and Bay are just right to produce a near-perfect match between the natural response of the Gulf waters and the tidal wave in the Atlantic Ocean. Visualize the twice-daily tidal wave, sweeping past the entrance to the Northeast Channel. The waters slosh back and forth between the Gulf and the Atlantic Ocean with a period that is set precisely by the - the prime tidal interval, the semi-diurnal period. The tidal wave spreads inward and northeastward, sweeping into the Bay of Fundy, which becomes narrow and shallow at its upper end. But it is not just the constriction that is responsibile for the extraordinarily large tidal ranges there; were this the entire reason, or even the principal one, the tides would be much smaller than they are throughout the rest of the Gulf.

Here is the principal reason. When the tidal wave inside the Gulf ebbs and flows back to the Atlantic to begin another cycle, it arrives at the Northeast Channel and the offing of the banks almost exactly in step with the next Atlantic tidal impulse, which sweeps past the channel entrance at the propitious moment when the waters inside can most easily accept the next inrush. This is a physical phenomenon called resonance, which happens when the driving period closely matches the natural oscillation period of the driven system. The result is a very large amplitude of the response, compared to the driving amplitude.

Here on our sunny dockside retreat, my patient companion, long an observer of the tides and ardent explorer of the ledges and clam flats, turns to me with a startled look.

I know what you mean.

Equally surprised, I descend from the podium and return the expression. Huh?

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I understand what this is all about.

Now this sounds like an epiphany, so I ask would he please enlighten the rest of the world with his insight? A bit perplexed by the talk about resonance, he offers his own explanation.

You’re a Maine boy, like me, so I suspect as a youngster you had to endure your Saturday night bath, whether you needed it or not. And like me, I presume you would have preferred to be elsewhere at those times…

The tale has a sterling ring of honesty, the sound of a lightly-struck churchbell. Here is his story:

The experiment is a simple one, easily repeated, with results that can be corroborated by the most inexperienced investigator. Expensive apparatus is not required, nor fancy letters after one's name. The boy finds himself in his Saturday bath, an event neither enjoyed nor requested but nonetheless required, and therefore susceptible to disruption in search of an exit strategy. Sitting in the center of the half-filled tub, the despondent bather soon finds, by sloshing the water back and forth, that a particular sloshing rate brings spectacular effects at the end of the tub, including big waves that splash over on the floor, hopefully leading to evacuation orders. The heart of the experiment is to discover that, for given depth of water, size of tub, and beam of bather, there is a specific sloshing period that brings the desired effect; either a faster or a slower rate produces uninteresting results and prolonged immersion.

The boy's experiment is a classic resonance demonstration in which the amplitude of the response - the wave at the end of the tub - depends critically on the match between the sloshing period and the natural period of the contained . In and gulfs, the tidal responses are complicated by many details, but the principle of resonance is the same. For the case at hand, the in-and-out "sloshing" of the Atlantic tidal wave very closely matches the natural period of the Gulf of Maine and Bay of Fundy. And, as in the experiment, the largest height excursions occur at the far end of the “tub;” i.e., the head of the Bay of Fundy, and amplified tides are found throughout the basin.

So my friend, the sun is over the yardarm, and we have spent an afternoon contemplating the tides instead of sailing in them. Perhaps we could have better used this time slipping eastward along the coast, following the flood down to Lubec Narrows, where we could shoot under the bridge into the icy waters of Cobscook Bay. That's how you really learn about the tides. On the other hand, it's worthwhile now and then to dry out on the dock and think about what we've got here on the Maine coast, and how to keep it that way. It seems to me that the tide is a good place to begin.

Ayuh, cahn’t ahgue with that. ______

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David A. Brooks, originally from Eastport, Maine, is a professor emeritus of at Texas A&M University. He spends summers in Boothbay Harbor, working with scientists, students and friends at the Bigelow Laboratory and the University of Maine.

Source for Gulf of Maine map https://www.google.com/search?q=gulf+of+maine+boundary+map&tbm=isch&tbo=u&sourc e=univ&sa=X&ved=0ahUKEwjSuNLB9dDYAhUX9WMKHTnNBT8Q7AkISQ&biw=1161&bih=895