TIDE SIMULATION Bryce M. Hand Emeritus Professor of Geology Syracuse University Bryce M. Hand Emeritus Professor of Geology Syracuse University January, 2010

Time when Moon is at its highest point in the sky and tidal-bulge model predicts High Tide Tides are commonly depicted as twice-daily rise-and-fall of sea level produced by a locality’s passing through oceanic tidal bulges directed towards and away-from the Moon. While it’s true that the gravitational pull of the Moon (and to a lesser extent, the Sun) causes our tides as the Earth rotates, those ocean tidal bulges don’t exist. One can confirm this by noting that high tides don’t necessarily happen when the Moon is at its highest position in the sky (or directly underfoot, on the far side of the Earth)…as would be predicted by the tidal-bulge model. In fact, almost anywhere along our east coast, low tide occurs when the tidal-bulge model calls for high tide! For example, here are tides for Coney Island (NY) on January 15, 2010: Tides are not as usually represented!

Actual Tides As Earth rotates, the gravitational attraction of the Moon (and Sun) do disturb the oceans. But instead of producing simple bulges that follow the Moon from east to west, the result is a complex system of waves that travel in circles around centers known as amphidromic points. In the Atlantic Ocean, there are two such basin-wide rotational (amphidromic) systems, one in the South Atlantic, the other in the North Atlantic. Each of these is like a wave sloshing around the outside of a washbasin that you move with a circular motion: At any instant, the water will be high (“high tide”) on one side of the basin, and low (“low tide”) on the opposite side. In the center of the basin, as in real-world amphidromic systems, there’s little or no vertical motion of the water surface as the tides race around the perimeter. The Simulation presented here will show the behavior of the two main Atlantic systems.

How the Simulation was Constructed The maps in this Simulation are based on the world tides map posted in 2007 on NASA’s Global Geophysical Fluids Center website ( I assigned spectral colors to different stages in the tidal cycle, then colored segments defined by the (white) cotidal lines of the NASA map to show how sea-surface height would appear at any particular time. NOTE: The colors in my Simulation maps have nothing to do with the colors on the NASA map, which show tidal range, not instantaneous heights.

Running the Simulation The Simulation begins (“0 Hours”) when it’s high tide along our east coast. Subsequent slides show conditions hour-by-hour, through slightly more than one day. By the time you reach “24 Hours,” tides will have performed two complete counterclockwise circuits around each amphidromic center.* I suggest running the Simulation multiple times and at different speeds, focusing on one part or another of the Atlantic, to see how the northern and southern systems behave individually and how they interact. *Strictly speaking, each sector defined by cotidal lines represents a time interval a bit longer than an hour, because the Moon advances in its orbit around Earth by about 13° each day and tidal period is determined by Earth’s rotation with respect to the Moon. This change in the Moon’s position explains why high tide (or any other particular tidal phase) occurs an hour (actually, 50 minutes) later each day. But to be a stickler about this, I’d have had to label successive maps “One Hour and Two Minutes,” “Two Hours and Five Minutes,” etc. Living with the 4 percent discrepancy seemed worth it!

0 Hours (Begin first cycle) H H Tide at New York

H H H 1 Hour Tide at New York

H H 2 Hours Tide at New York

H H 3 Hours Tide at New York

H H 4 Hours Tide at New York

H H 5 Hours Tide at New York

H H 6 Hours Tide at New York

H H 7 Hours Tide at New York

H H H 8 Hours Tide at New York

H H H 9 Hours Tide at New York

H H H H 10 Hours Tide at New York

H H H H 11 Hours Tide at New York

12 Hours H H Tide at New York

H H H 13 Hours Tide at New York

H H 14 Hours Tide at New York

H H 15 Hours Tide at New York

H H 16 Hours Tide at New York

H H 17 Hours Tide at New York

H H 18 Hours Tide at New York

H H 19 Hours Tide at New York

H H H 20 Hours Tide at New York

H H H 21 Hours Tide at New York

H H H H 22 Hours Tide at New York

H H H H 23 Hours Tide at New York

24 Hours H H Tide at New York

H H H 25 Hours (New cycle) Tide at New York

H H 26 Hours Tide at New York

H H 27 Hours Tide at New York

End of Simulation