I'm world-building for a SF-story and need some help figuring out what the ocean tides would look like.
My planet orbits a close binary star system; it does not have any satellites itself. The mass of the binary is 5/3 MSun. The orbit is closer than that of Earth and is highly eccentric (a ~ 1/2 AU, e ~ 4/5), such that the planet orbits at about 0.1 AU at perihelion and at about 0.9 AU at aphelion. The value of e was chosen for plot purposes, while the value of a is simply a result of the requirement that the planetary insolation, averaged over the year, must be similar to that of Earth. The planet rotates once every 60 (Earth-)hours.
Originally, I simply assumed that lack of moons meant that the only aspect of tidal effects I needed to worry about was long-term, namely tidal resonance. According to the 'pedia article, the characteristic time-span for tidal locking scales as a^6, meaning that my planet would be locked to its binary 64 times more rapidly than Earth to Sun*. Given that Earth is nowhere near locked, and that I'm free to choose other parameters which come into play, such as the planet's angular momentum upon formation, in whichever way delays locking, I should be fine in that regard: It's not implausible for my planet to have remained unlocked for long enough for my protagonists, a human-like species native to the planet, do have evolved.
But that initial assumption was nonsense, of course - short-term tidal effects such as ocean tides do have to be carefully considered, moons or no moons. On Earth, solar tides are only slightly (less than an order of magnitude) weaker than lunar tides. The only reason we don't ordinarily notice the former is that they manifest as modulations of the latter, rather than as effects in their own right. So, even around aphelion, my planet would experience ocean tides of a magnitude comparable to those on Earth.
Where things get... interesting, let's say, is around perihelion, however. Tidal forces scale as M/d^3, I believe, where M is the mass of the force-exerting body and d the distance between it and the force-subjected body. Scaling my case to the Earth-Moon one, that gives
Ftidal ~ (Mbinary/MMoon) / (dperihelion/dMoon)^3 * Ftidal|Earth ~ ((5/3 * 2*10^30 kg)/(7*10^22 kg)) / ((0.1 * 1.5*10^11 m)/(4*10^8 m))^3 * Ftidal|Earth ~ 10^3 * Ftidal|Earth
I'm not certain, but I think an increase in tidal force by a factor of one thousand means an increase in the height of the tidal bulge by a factor of one thousand. On Earth, the characteristic amplitude of the tides is on the order of a metre ('pedia), so on my planet, that would mean a characteristic amplitude of a kilometre. Not what one would call negligible.
Okay, that's as far as I've progressed. If someone could check my work and point out any flaws, that would be appreciated. Mainly, though, I need help getting a handle on the final step - translating the abstract idea of "kilometre-high tides" into a mental image of what those would actually do to a planet like Earth. For starters, I'm looking for answers to questions like the following:
- On Earth, tidal amplitudes vary considerably from place to place, by as much as an order of magnitude. Would the same apply in my case, i.e. would there be some coastlines where the Fearsome Flood (Dreaded Deluge? Terrible Tide?) would "only" reach a few hundred metres above normal, and others where it would be not just one but several kilometres? Or would the much greater base amplitude swamp out those contributions which give rise to the local effects observed on Earth, so that there'd be little noticeable difference in my case?
- On Earth, it doesn't seem to be particularly relevant how a coastline is oriented with respect to the planet's rotation. The tides experienced on East-facing coasts aren't noticeably dissimilar to those experienced by West-facing coasts, nor to those experienced by North- and South-facing coasts. Rather, what matters is the size and shape of the body of water bounded by the coast in question. Would this be the same in my case, or would the question of whether a given coastline represents a "leading edge" or a "trailing edge", in terms of planetary rotation, result in significantly different types of tides?
- Would a kilometre-high bulge basically behave like a metre-high bulge, i.e. would it simply flood the land which is less than its height above normal sea-level, and then recede? Or would it be more like a wave on a beach, which has the ability to "climb" a shallow slope quite a long way above its own height, due to inertia? In the former case, highlands should be habitable for land-dwellers, while in the latter, the bulge could conceivably simply keep going across an entire continent and re-join the ocean on the other side - so land-dwellers, if they'd exist at all, would have to have a way to deal with flooding no matter where they lived.
- How violent would the impact of the bulge on a coastline be? Should one be thinking Earth-like flood, scaled up, or rather mega-tsunami? On the one hand, a vertical increase in sea-level by a kilometre over 15 hours (a quarter of one of my days) translates into a rate of a few centimetres per second, which sounds quite benign. On the other hand, the horizontal speed of the bulge with respect to the surface is the same as the rotation speed of the planet, which is on the order of a thousand kilometres per hour, which doesn't sound benign at all. I suspect neither of those two figures is particularly useful, though, except as maybe some manner of upper and lower bound for one's mental image of the process.
- Would it make a significant difference whether the geography of my planet is water-dominated (i.e. has a number of isolated landmasses emerging from one contiguous ocean, as is the case on Earth) or land-dominated (i.e. has one contiguous landmass containing a number of isolated oceans, rather like really big lakes)? I'm thinking that the latter should make the tides somewhat less extreme, as any one body of water would never experience the planet's full tidal differential.
Any pointers would be appreciated. Needless to say, seismic effects should probably also be taken into consideration in all this, but I ultimately feel more comfortable ignoring those for the sake of plot development, if it comes to that. In that sense, the ocean tides are the primary concern, for the time being.
* That's ignoring tidal resonances between Earth and Moon, which is silly in general but should hold for this line of argument specifically, I think.