In viewing the thread about the Panama Canal there was a reference to a website with the maximum tides being +/- 11 feet on the Pacific Ocean and +/- 1.5 feet on the Atlantic Ocean at the openings of the canal. Obviously the geography plays an enormous part here, but how exactly? Or more simply, what is the major factor that moderates or amplifies each of these tides?
Wikipedia says that 21" is the theoretical tide due simply to gravitational pull, but what would be the maximum tide (or more interestingly, tidal bore) that one could design?
I was made to understand that in the Bay of Fundy (where tides are substantial) the increase is due to the fact that the time it takes a wave to go from the tip of the bay back out to the edge of the continental shelf (where the depth change would make it reflect) is close to exactly the time between tides. So the reflected wave created by the last tide gets combined with the new tide, making it bigger, meaning a bigger wave coming back later to meet the tide after that, &c, &c.
So based on that, I guess the ideal geography for tides is a narrow inlet, which drops off steeply at its mouth, and is exactly (speed of waves) * (time between tides) long.
If I understand you correctly, you’re thinking of a Helmholtz resonator. Electrical engineers might think instead of an RLC circuit. In all of these things (including the Bay of Fundy), you’ve got a forcing function (the tide, an AC voltage input, or an acoustic tone), and when the frequency of the forcing function matches the natural frequency of the oscillator, you’ll see very high-magnitude oscillations.
The average depth (and variations of depth) within the bay matter, but the biggest factors that define a Helmholtz resonator are the volume of the enclosed chamber (i.e. the bay), and the volume and length of the neck (i.e. the channel between the bay and the open ocean).
Re: maximum tide, it would be a resonator in which the chamber volume and neck volume/length create a resonant frequency that matches that of the tides AND produces minimal resistance losses. I’m imagining a very large bay and channel that have smooth, steep sides and a low surface-area-to-volume ratio so that the least possible tidal energy is lost to flow resistance and breaking waves.
Interesting leahcim and Machine Elf! Does the “backward” orientation, with regard to the moon movement, of the Bay of Fundy help or hurt the tidal bore? I would imagine one could idealize the bore by moving the bay to be straight east-west and a perfect north-south continental shelf- but would the opening of the bay be east or west?
A tidal bore is something distinct from the rising tide itself; a bore usually happens at the mouth and/or lower end of a river or a very narrow bay. There are tidal bores at the mouths of several rivers that empty into the Bay of Fundy, but there isn’t a tidal bore traversing up the Bay of Fundy from the open ocean.
As for whether the orientation of the bay matters much with respect to the spatial variation in lunar gravitational attraction, I would guess not. The bay is only about 170 miles long, about one percent of the earth’s circumference at that latitude. Even if it were oriented in a perfectly east-west manner, the time of peak tide would vary from one end of the bay to the other by only thirteen minutes.