diurnal tides: why?

[eub]

You know, the diagram to explain tides is the earth turning inside the hydrosphere that's an ellipse from tidal strain. That gives two high and two low tides per full rotation, semidiurnal tides.

Kayaking class today pointed out that the East Coast gets that, but some places get diurnal tides, one high and one low per day. (And we, for example, get a complicated tangle, but that's for later.) Where does that low-frequency 1/day component come from?

Wikipedia is not satisfying. (It does note that the peak resonance of ocean slosh is at about 1/(30 hours), which is interesting, but not to the purpose here.)

This page notes that

The dynamical theory of Laplace and Airy considered the tides as the effect of the excitation of normal modes of oscillation of the ocean's surface. This explained the phase problem, as well as the extremely various nature of the tidal signatures. Although this was a complete and satisfactory explanation, it is very difficult to calculate tides a priori because of the complex nature of the oceans.

Nod nod nod that's elegant... wait, but what's the excitation? Isn't the excitation something handwavily related to the sinusoid of frequency 2/day that comes from the tidal-strain ellipse? Where's that huge (and sometimes quite clean) subharmonic coming from? It doesn't sound from this description as if Laplace and Airy were invoking nonlinearity.

Comments

[eub.livejournal.com]

Ooh, how about this. The hydrosphere is not actually an ellipse, it's a prolate ellipsoid. If you're on the earth's equator, you're tracing a ""great-circle"" route along the hydroellipsoid, which is semidiurnal. But if you're up near the pole -- which is not generally on the "waist" of the ellipsoid, it's canted 0 to 23° off -- let's say it's 23° off today -- then the tide is shallower on one side of the pole, the side that's closer to the waist, and deeper on the other, towards that tip of the ellipsoid. Once a day you're carried through the deep water.

That gives me the 1/day energy to ring the oceans with, so I'm happy. I don't need for us to get more diurnal tides away from the equator; the oceans are hairy.

[hattifattener]

That's a good thought. I was going to skept at the idea of a nonlinearity generating subharmonics. But it seems perfectly reasonable that the axial tilt would generate enough 1/day energy to get filtered into a 1/day tide by the local seafloor. (As an extreme case, consider a point at latitude 77 on the solstice.)

I wonder how much energy is tied up in tidal resonances, or what the Q is? If the sun and moon disappeared, how quickly would the tides die down?

[cheesepuppet.livejournal.com]

You two make me smile.

[eub.livejournal.com]

We have fun, too.

[eub.livejournal.com]

Tidal amplitude is all over a lot higher than the ~1 meter I see people computing from spherical cows, so I guess there must be hefty resonance gain. Let's see, we're at, uh, about log_2 6/5 = a quarter-octave off Wikipedia's 1/(30 hr) resonant peak, which, uh, can some licensed EE figure the max gain we can get there by twiddling that peak's Q?

We're also seeing a lot of gain at the semidiurnal frequency, so there must be poles somewhere up there... maybe that'd be the Atlantic and the Pacific basins each sloshing, something like that.

[bhudson.livejournal.com]

I always wondered about the spherical cow assumptions for tides. There's these huge continent thingies that get in the way of the water. The explanation for no tides in lakes is that the moon can't "draw" water from elsewhere or to elsewhere. But then I'd expect Atlantic tides to be far weaker than in the Pacific, yet they aren't (in fact, I was kind of surprised at the general wimpiness of pacific tides, but that's just compared to the 30m peak-to-trough amplitudes I grew up with on one coast, and the deceptive size of 1m tides on a 2km-wide beach on our other coast).