Tidal implications of eccentric planetary orbit

onomatomanic

Lots and lots of fiddling payed off at last: Proof of concept! (warning - takes a bit of patience)

onomatomanic

(continued from post #7)

Tsunamis: Tsunamis are a means of carrying away the bulk of the energy liberated by landslides into (or underneath) the sea. A popular worst-case scenario for such a landslide is the sudden and total failure of one flank of the Cumbre Vieja volcanic ridge in the Canary Islands. The article gives estimates of the physical quantities involved, which allows us to calculate the gravitational potential energy available to fuel the tsunami:

E_tsunami ~ E_grav|initial - E_grav|final
E_tsunami ~ G M_earth M_landslide (1/(R_earth-H_sea) - 1/(R_earth+H_mountain))
E_tsunami ~ G M_earth M_landslide ((H_mountain+H_sea) / ((R_earth-H_sea) (R_earth+H_mountain)))
E_tsunami ~ G M_earth M_landslide ((H_mountain+H_sea) / R_earth^2)
E_tsunami ~ (7*10^-11 m^3/kg/s^2) * (6*10^24 kg) * (10^15 kg) * (1 km + 2 km) / (6*10^6 m)^2
E_tsunami ~ 3*10^19 J

where the H are estimates of the characteristic height of the pre-slide mountain and depth of the off-shore oceanic basin, respectively. According to one of the scientific publications linked from the article, this tsunami would expend most of its energy on the Eastern shores of North America and Northern South America. There, it would cause ~15 metre waves for a duration of ~15 minutes, which corresponds to a power density (power per unit length of coastline) of

L_tsunami ~ (3*10^19 J) / ((15 minutes) * (10,000 km)) ~ 3 GW/m

Correspondingly, the mean power density of my tides is given by

L_tidal ~ (10^18 W) / (40,000 km) ~ 30 GW/m

So, by this comparison, the impact of the perihelion tide is comparable to that of ten tsunamis of ~15 m, or, assuming the dependence of wave power on the square of the wave height applies to these as well as to surface waves, a single tsunami of something like ~50 m. That seems a little bit at odds with the previous result of ~10 m ordinary waves - but not grossly so, as those have a frequency an order of magnitude higher. Anyway, the important implication is the same - at this energy content, the tide should be able to devastate everything below the high-water mark, but should not be able to propagate significantly farther inland than that high-water mark on sheer inertia. For tsunamis, the limit seems to be some tens of kilometres, depending on the height of the waves and the steepness of the coast.

JohnRC

I have been thinking about the influence of "huge tides". I am absolutely no expert (physical chemist with a minor professional interest in Geochemistry and a fairly peripheral interest in physical geography). I was a little surprised by the account of tidal locking in the original post, but it certainly seems to be in accord with the wiki article. I have three remaining reservations though:

(1) What is the connection between tidal locking -- i year = 1 day, same face towards sun, ant the "resonant rotations" of venus (1 year = –1 day) and mercury (2 years = 3 days)?

(2) There are two large "fiddle factors" in the equation brought forward for tidal locking in the wiki article. I note that apart from Io and Europa (largely liquid interiors, but unarguably tide-locked under any conceivable model) the equations have only been applied to solid bodies. I wonder how much the presence of significant liquid regions, where liquids could actually flow with the tidal bulge and dissipate huge amounts of energy as friction, might lead to totally different values for these two parameters, or even invalidate the model altogether.

(3) Is the reservation that I think the OP has already picked up on. Tidal friction is a bit like a gently applied drum brake. But a very eccentric orbit amounts to a drum brake that is applied quite hard on the rotation for a short period once each revolution. I would be amazed if it did not lead to a very long year in a relatively short time (whether tide-locked or resonance-locked I would have no idea). I would also ask those more in touch with the detail of the dynamics: if a brake is applied for a short time each revolution at perihelion, kinetic energy must be reduced while angular momentum is conserved. Kinetic energy can notionally be broken down into radial and angular components. Am I right in imagining that the radial kinetic energy would be most affected (thus lowering the eccentricity) because the linear momentum would, in first order, be conserved?

Now to proceed to the detailed effects of "huge tides". When people generally consider tides, they are only thinking of ocean tides. In this case the tides are scaled up by a factor of about 1000, and we need to think of tides in all three realms.

AIR
On Earth, tidal effects exert a strong secondary influence on atmospheric circulation. If they were 1000 times stronger, the effects would be dominant. I would expect
• huge wind and storm systems that encircle the whole planet
• twice daily pressure changes that would span at least a factor of 2 in local atmospheric pressure, and possibly much more.

OCEANS
There would be immediate effects, including tsunami like effects in some places (Imagine the Severn "bore", a completely tidal effect, multiplied by 1000!). Accommodation of large tidal effects would involve both horizontal and vertical motions of water. Effects would depend on the fine detail of ocean floor topography and ocean depth, but because of the way that the wave equation works they are likely to be at their greatest close to shorelines. Local variations would be considerable! If we take the factor of 1000 as representative, then the 8 m tides that occur in parts of Northern Australia could wash over a range as high as the Himalayas! (8 km) Water erosion would be very rapid. In the immortal words of Handel "Every valley shall be exalted, and every mountain and hill made low". (Or was it Isaiah?). -- but wait for the next exciting episode!

CRUST
At present on Earth, tidal flexion produces an amount of heating that contributes to total geothermal heating of the planet. Although its absolute size is not accurately known, or at least not known without controversy, it is generally reckoned to be somewhere between 10% of heating through radioactive decay, and a figure slightly larger than that for radioactive decay. So if tides are going to be 1000 times larger than on Earth, we have to imagine a geothermal effect at least 100 times greater than that operating at present on Earth. As far as general heat balance is concerned, this would not be a problem for surface conditions, But below the surface it would surely mean greatly increased plate tectonics, and associated seismic and volcanic effects. This would counteract the greatly increased surface weathering, but ocean tides and land tides between them would surely make existence very precarious for any sentient beings on such a planet!

I cannot imagine the inhabitants of this planet being able to maintain permanent settlements. Even if they were able to survive and build up a coherent society, I do not see how they could get past the nomadic hunter-gatherer stage.

onomatomanic

Thanks for that! I'm going to wait and see if others can shed some light on the various questions you raised before replying in detail, except for the two points below:

I've more or less adopted mfb's suggestion from post #14 regarding the white dwarf, i.e. that it only recently became part of the solar system by ejecting one of the components of the original binary and usurping its place, and that the planet's orbit only became eccentric as a consequence of that encounter. Positing that that transition was (just) survivable means that the orbit only has to have undergone tidal resonance effects for as long as it would take the biosphere to recover from that upheaval, which reduces the timescale by maybe two orders of magnitude. That makes things more plausible in that regard, surely.

I wondered about that initially, but something I read in the meantime (can't remember what, unfortunately) gave me the impression that the pressure would remain constant, to first order, because the atmospheric tides, like the ocean ones, are primarily flows towards an equipotential state. Thus, the increased height of the air column overhead during "high tide" is exactly (again, that's to first order) counteracted by the reduced weight of that air. Does that make sense to you, or did I misunderstand something there?

JohnRC

Sorry, but I have just realised that to get 1000 times the energy into a wave, the wave would only have to be √1000 = 30 times as high, not 1000 times. So the effects of water tides would not be nearly so drastic as in my last post. But tidal effects on the oceans would still be quite severe enough to lead to some catastrophic problems.

It would be beyond my knowledge of fluid dynamics to work out how a global tidal bulge which scaled directly with height onto energy would interact with local-ish wave effects that would scale as height with √energy

onomatomanic

^ Yeah, that's what the first bullet point in my OP was asking as well. Unless someone tells me otherwise, I'm just going to assume that local variations in tide amplitude can be ignored. To increase it by an appreciable amount somewhere other than in a narrow fjord or some such, you'd have to move a hell of a lot of extra water to the place in question from somewhere else, and it doesn't seem reasonable to assume that fairly shallow coastlines could cause that amount of flow, it seems to me.