Tidal implications of eccentric planetary orbit

[onomatomanic]

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 M_Sun. 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.

[Hornblower]

What is the separation of the two stars of the binary system? That is critical in determining whether or not the planet's orbit will be stable.

With a highly eccentric orbit, I would not expect the planet to ever reach a 1:1 tidal lock. I would expect some sort of modified lock that has the planet's rotation nearly synchronous at perihelion, as in the case of Mercury. With such a close perihelion I think that is a foregone conclusion in a relatively short time.

The insolation is going to vary by a factor of 81 over the course of one orbit. That just might be more of an obstacle to life than the extreme tides.

[onomatomanic]

The binary consists of an orange dwarf (3/5 M_Sun, ~1/10 L_Sun) and a white dwarf (16/15 M_Sun, <1/100 L_Sun). Their separation is ~5/3 R_Sun, which corresponds to an orbital period of a few (Earth-)hours, IIRC. The planet is at a distance of ~18 R_Sun from the binary's centre of mass, at perihelion, so that's a bit more than an order of magnitude higher than the stars' separation.

I hadn't considered tidal resonance in the form of perihelion-synchronous rotation, but that makes a lot of sense, now that you mention it. And I think it should pretty much work out with the parameters I came up with independently, as well. Let's see. If I assume the planet's kinetic energy is negligible at aphelion, I can get the orbital speed at perihelion via conservation of energy:

1/2 m v_perihelion^2 - G m M_binary / d_perihelion ~ - G m M_binary / d_aphelion
v_perihelion^2 ~ 2 G M_binary (1/d_perihelion - 1/d_aphelion)
v_perihelion^2 ~ 2 * 7*10^-11 m^3/kg/s^2 * 5/3 * 2*10^30 kg * (1/0.1 - 1/0.9) * 1/(1.5*10^11 m)
v_perihelion^2 ~ 4*10^10 m^2/s^2
v_perihelion ~ 2*10^5 m/s

w_perihelion = v_perihelion/d_perihelion ~ (2*10^5 m/s) / (0.1 * 1.5*10^11 m) ~ 1.5*10^-5 1/s

That's the angular speed of the suns in the sky due to orbital motion. The angular speed due to planetary rotation is simply w_rotation ~ 2 pi / (60 h * 3600 s/h) ~ 3*10^-5 1/s, double the orbital value. So, I'm in the ballpark, but still a bit off. I can either fiddle with the parameters to make the two coincide, or posit that the planet is well on its way to the resonant state but not quite there yet. Hmmm.

If I go with the first option (full resonance), what does that mean for the perihelion tide? There'd still be a huge tidal bulge, of course, but since the planet wouldn't be rotating at all with respect to the binary, that bulge wouldn't be going anywhere. Thus, the water level should remain constant during perihelion, and the tides before and after that are bound to be rather complicated, as the increase and decrease in the vertical height of the bulge itself might be as much of a factor as its horizontal motion due to the diminished planetary rotation. Argh. Even so, this does sound like it'd make things a little less extreme, at the very least. Is that about right?

---

The insolation is briefly close to ten times the terrestrial value near perihelion and then quickly drops down to little more than a tenth of the terrestrial value, where it remains for most of the three-Earth-month-long year. The annual average insolation is more or less identical to the terrestrial value. As long as the planet's surface can absorb a reasonable fraction of the energy boost it receives during the short summer, that should be sufficient to keep the relatively long (but absolutely still short) winter from becoming too bitter. It requires a more resilient biosphere, admittedly, but it doesn't sound insurmountable, based on what I've read.

[onomatomanic]

I made a little progress on this front in the past week.

Namely, I calculated the tidal power dissipation, via the expression for the tidal locking timescale given in the wikipedia article linked in the OP, as on the order of 10^18 Watts, aka 1 Exawatt.

Then, I calculated the height at which a) ordinary surface waves and b) tsunami waves would carry a similar amount of power density. Obviously, this is far from ideal as a comparison, since tides constitute a flow of the body of water itself, whereas waves constitute merely a flow of energy, for the most part. But it's the best comparison I could come up with even so. My results were 10 metres in the former case and 50 metres in the latter case. That's obviously at odds with each other; however, the practical implications are sufficiently similar to frame a mental image for the impact of the perihelion tides, IMO.

Such waves would have sufficient force to thoroughly devastate the flooded area. Practically, since the same area is flooded every year, it would remain a wasteland with nothing to devastate. I imagine it'd be completely flat, and there may (or may not) be some low and hardy vegetation like grasses or shrubs with a very tough and interwoven root system, and that'd be about it.

On the other hand, such waves would not have sufficient inertia to propagate far inland beyond the equilibrium high-water level. For tsunamis, the limit typically to be on the order of tens of kilometres, depending on the height of the wave and the terrain. The most spectacular thing that could happen is that successive floods eat away at a chain of hills shielding a valley which is just below the high-water level, and eventually one breaks through and the valley gets deluged. That's entirely within human experience though, just perhaps not at that scale, thus, not a problem from the author's perspective.

Further comments are invited.

[grapes]

Further comments are invited.

The solid ground also participates in the tidal adjustment. On earth, now, it's about half the total tide--it reduces the shoreline effect by about that much. If the solid ground has enough time to adjust, it will adjust completely, and there will be almost no shoreline effect. The immense stress associated with that adjustment, through friction, produces much of tidal heating.

[cran]

[oops - accidental double post]

[cran]

I'd be more concerned about the unstable land surfaces; not sure how complex life could evolve there, let alone a civilisation. Between the rapid thermal extremes and its effect on weathering (which in turn makes the land more vulnerable to strong ocean tides and all types of floods), and the seismic disturbances due to tidal stresses, it would make for a very happening place to try and settle down.

Average insolation doesn't really come into it: even daily extremes on Earth can make it uncomfortable for human life. When it's too hot, it's too hot; and when it's too cold, it's too cold - in either case, being on the surface of that planet is more than just a health hazard.

[onomatomanic]

The solid ground also participates in the tidal adjustment.

Yes, I guess it's time to revisit that point. As I said in the OP, I'm prepared to simply ignore that aspect if it turns out that the effect of the body tide would be to render the land uninhabitable due to excessively violent seismic and volcanic activity.

If the solid ground has enough time to adjust, it will adjust completely, and there will be almost no shoreline effect.

From what I've read, this is not really so. In this context (though this is certainly not true in general), Earth responds pretty much as an elastic body, rather than a liquid one, regardless of the fact that the elastic (solid) surface is relatively thin compared to the size of the mostly liquid interior. A (necessarily imperfect) analogy might be a water-filled balloon, which behaves quite differently from a blob of water of the same size, even though the rubber skin accounts only for a tiny portion of the body as a whole. As long as it holds, of course.

In the absence of deformation forces such as centrifugal and tidal effects, self-gravity and surface elasticity will act together to produce a spherical planet, since for a given volume, a sphere both minimizes gravitational potential and the surface-to-volume ratio. In the presence of deformation forces, the two act against each other, as the liquid interior tries to assume an ellipsoid shape which conforms to the modified potential field, while the surface tries to resist this change due to the strains resulting from the increased surface-to-volume ratio.

As usual, the result of these two counteracting forces is an equilibrium state between the two extremes. In this case, this state is described by the Love numbers, e.g. "h is defined as the ratio of the body tide to the height of the static equilibrium tide; also defined as the vertical (radial) displacement or variation of the planet's elastic properties. In terms of the tide generating potential V(θ, φ)/g, the displacement is h V(θ, φ)/g where θ is latitude, φ is east longitude and g is acceleration to gravity. For a hypothetical solid Earth h = 0 and h = 1 for a liquid Earth. [...] For elastic Earth the Love numbers lie in the range: 0.616 ≤ h2 ≤ 0.624 [...]"

If I understand this right, this number depends only on the composition of the body, and not on its rotational period. That said, your claim of course does apply in the limit of very fast and very slow rotation: In the former case, there will come a point at which the interior can no longer fully respond to the quickly varying potential field, which will decrease the amplitude of the tidal response. There will also come a point at which the body tides begin to excite internal resonances (for Earth, the order of magnitude of these is given by the ratio of its size to the typical propagation speed of seismic waves, which works out to be between tens of minutes and a few hours). Not sure which one kicks in first. In the latter case, there will come a point at which the surface has enough time to deform viscously (irreversibly) rather than elastically, which will increase the response amplitude.

However, all this happens because the model which describes the actual Earth tides exceedingly well no longer holds at those extremes, not because the model itself predicts such a dependence.

The immense stress associated with that adjustment, through friction, produces much of tidal heating.

I don't know of this is true, for Earth. Several of the materials I've read assert this sort of thing (pdf, emphasis mine):

3.06.3.2.3 - Anelastic effects

All modifications to the Love numbers discussed so
far apply to an Earth model that is perfectly elastic.
However, the materials of the real Earth are slightly
dissipative (anelastic), with a finite Q. Measurements
of the Q of Earth tides were long of interest because
of their possible relevance to the problem of tidal
evolution of the Earth–Moon system (Cartwright,
1999); though it is now clear that almost all of the
dissipation of tidal energy occurs in the oceans (Ray
et al., 2001), anelastic effects on tides remain of interest
because tidal data (along with the Chandler
wobble) provide the only information on Q at frequencies
below about 10^-3 Hz.

On the other hand, there is at least one well-known example of non-negligible power output from body tides - Io. The article mentions that the tidal deformation varies by on the order or 100 metres there, so naively one should expect my planet, with ten times that value, to undergo even more internal heating from that source and consequently be even more geologically active. However, there are so many potentially relevant differences between the two cases (oceans, tidal lock to the orbited body, tidal resonance with other satellites) that I'm not at all sure that that naive expectation would actually be justified.

[onomatomanic]

I'd be more concerned about the unstable land surfaces; not sure how complex life could evolve there, let alone a civilisation. Between the rapid thermal extremes and its effect on weathering (which in turn makes the land more vulnerable to strong ocean tides and all types of floods), and the seismic disturbances due to tidal stresses, it would make for a very happening place to try and settle down.

I'm imagining most of the planet to be uninhabitable to (Earth-like) life. I stuck in the qualification because the option of having the remainder populated by some sort of extremophile higher organisms has a certain appeal.

The primary habitable zones would be places like Chile, i.e. long and narrow stretches of land with ocean on one side and a mountain chain on the other, by virtue of plate subduction (actually, my geology isn't entirely Earth-like, so the term fits only partially, but the effect is at any rate the same). In my mind, that seems to solve several of the problems you touch on: Steep gradients between sea-level coastline and high altitudes, keeping the perihelion floods from propagating far inland. Relatively milder sea climate, and even a possibility of taking refuge at higher (cooler) elevations if the summer gets too hot. Erosion balanced by subductive raising.

I'm basing my protagonist culture partly on the Incas, for this reason, among others.

Average insolation doesn't really come into it: even daily extremes on Earth can make it uncomfortable for human life. When it's too hot, it's too hot; and when it's too cold, it's too cold - in either case, being on the surface of that planet is more than just a health hazard.

Yes, this is true. Bear in mind, though, that the heat capacity of Earth's surface is quite significant, especially that of the oceans (see above). That's why our seasonal temperature variations lag by something like six weeks behind the variations in insolation. The effect of my planet's greater fluctuations and shorter year should be that this effect becomes even more significant.

The summer is certainly extreme, but it only lasts for a few days, and at its start, land and sea are still barely above their winter temperatures. So most of the heat will be quickly absorbed, I'm thinking. The biggest danger I see during this time is direct solar heating of the ecosphere, leading to things like heat-stroke in animals and wildfires in plants. The former cope with that by shifting their daily cycles - active during the morning and evening, while remaining in their shelters for most of the day. Generally, my animals will be (even) more reliant on both shelters and seasonal physical adaptations like fat layers and winter coats then Earth's. The latter cope with it by being more hardy and less flammable. That last part is well-covered by creative licence, IMO.

Similarly, the winter, while being potentially more extreme than ours, is also shorter, so the thermal buffers make more of a contribution to keeping the temperatures from dropping too precipitously. According to my calculations, the change in insolation is about double that on Earth, at temperate latitudes, which would correspond to a temperature drop about 25% greater during a three-month winter. But the winter only lasts half that long, so it ought to turn out a little milder than ours, after buffering is accounted for.

[grapes]

In this context (though this is certainly not true in general), Earth responds pretty much as an elastic body, rather than a liquid one, regardless of the fact that the elastic (solid) surface is relatively thin compared to the size of the mostly liquid interior. A (necessarily imperfect) analogy might be a water-filled balloon, which behaves quite differently from a blob of water of the same size, even though the rubber skin accounts only for a tiny portion of the body as a whole.

Not for the earth--the earth is over 7/8 mantle, which is solid.

On the other hand, there is at least one well-known example of non-negligible power output from body tides - Io. The article mentions that the tidal deformation varies by on the order or 100 metres there, so naively one should expect my planet, with ten times that value, to undergo even more internal heating from that source and consequently be even more geologically active. However, there are so many potentially relevant differences between the two cases (oceans, tidal lock to the orbited body, tidal resonance with other satellites) that I'm not at all sure that that naive expectation would actually be justified.

Io was certainly the example that I was thinking of--but the tidal lock minimizes the tidal heating I think--the perturbations by the other satellites away from lock are what allow the tidal heating to occur.

[onomatomanic]

[T]he earth is over 7/8 mantle, which is solid.

*blushes* Okay, now I feel stupid. I guess I've always assumed that since it's more viscous than rigid, it should count as liquid. But that's not really how it works, is it.

[cran]

Well, it's more like 3/4; the inner and outer core make up roughly 1/4 of the volume (and roughly 1/3 of the mass); and the crust represents an even smaller fraction than your water-filled balloon skin. There is a thin viscous layer - the Asthenosphere - near the outer margin of the mantle; it is upon this layer that the plates rest and move. The outer core is, to all intents and purposes, a hot dense liquid. And there are fluids that circulate within the solid mantle; the fluids are partial melts and the mechanism for what we call mantle convection. The mantle itself is a collection of hot, dense, metal-rich crystalline minerals - if one could distinguish individual rocks in the mantle, they would be many hundreds of times larger than our continents.

A world like Chile would not support much in the way of population.
It would probably be a world more like Indonesia on speed, anyway.

So most of the heat will be quickly absorbed, I'm thinking.

Not quite. The reason for the lag you mention is that water is much more of an insulator than land; heat absorption is much slower, and so is the release. Whilst the oceans will remain fairly stable, surface evaporation will increase to many times that of our tropics, although cloud formation will be delayed. Why? Thermal conductivity is even lower for water vapour than it is for liquid water. Most of the incoming heat will stay in the atmosphere.

Rocks heat up relatively quickly, and release that heat just as quickly - go and sit on a sunlit rock ledge on a hot summer's day; you'll see what I mean. On Earth, in the sub-tropics and the lower mid-lats - where our biggest deserts tend to be - the heat gained during the day is completely lost overnight; any residual heat on the surface is rising heat from underneath. This doesn't happen in the tropics, and it won't happen on your world - daytime humidity and nighttime cloud formation will trap much more of the OLR (heat).

The shift from hot to cool will bring rains - not gentle rains, heavy flooding rains; the sort of rains that suggest ark-building is a good idea. The sort of rains that lead to avalanches and mud slides; mass wasting events that will reduce your young volcanic mountain chains.

When cool gets to cold, the water that has seeped into the rocks will freeze, and expand, breaking new ground for the next cycle. It's not the length of the cold season, but the number of freezes, that determines the rate of erosion from ice expansion. Ice and snow avalanches are much more common where steep, young, active mountains are involved.

Isostatic adjustment and subduction tectonics may well maintain the overall elevation of the mountains, but with the outer layers of the mountains being eroded and deposited downstream, neither the heights nor the plains have a high probability of retaining the same surface over anything like a human lifetime. Not only would settlements have to move, they would have to know where to move to in a given situation. Forests would have a tough time of it.

With increased erosion of volcanic rocks is an increase of acidity in the water cycle. Increasing volcanic activity also contributes to acidity in the atmosphere.

As I said before, what you have is a very happening place.

[grapes]

Well, it's more like 3/4; the inner and outer core make up roughly 1/4 of the volume (and roughly 1/3 of the mass); and the crust represents an even smaller fraction than your water-filled balloon skin.

I meant to say "almost 7/8" instead of "over 7/8", but I don't think I can blame that one on spellcheck, this time. :)

I was using the approximation that the core-mantle boundary is roughly halfway down, which would mean the core is roughly (1/2)^3, or 1/8, the volume of the earth--and the rest about 7/8 (.875). I knew the mantle didn't extend quite halfway down, but said "over" instead of "almost". The mantle is more like .84 the volume of the earth.
http://en.wikipedia.org/wiki/Mantle_(geology)
http://pubs.usgs.gov/gip/interior/

There is a thin viscous layer - the Asthenosphere - near the outer margin of the mantle; it is upon this layer that the plates rest and move. The outer core is, to all intents and purposes, a hot dense liquid. And there are fluids that circulate within the solid mantle; the fluids are partial melts and the mechanism for what we call mantle convection. The mantle itself is a collection of hot, dense, metal-rich crystalline minerals - if one could distinguish individual rocks in the mantle, they would be many hundreds of times larger than our continents.

The idea of partial melts circulating *within* the mantle is new to me, I'd like to hear more about it. Some of the hotspot material has been hypothesized to erupt from the core-mantle boundary, is that what you're referring to?

The more a body behaves like a fluid, the more readily it would adjust to the tidal forces, of course.

[onomatomanic]

A world like Chile would not support much in the way of population.

My humanoids are significantly smaller than we are, so a given area can support a significantly higher population density. Even after accounting for that, though, the habitable area is a relatively small fraction of the total surface - that's intentional.

The reason for the lag you mention is that water is much more of an insulator than land; heat absorption is much slower, and so is the release.

My understanding is completely different: Water is effectively much less of an insulator than land, because it can carry heat by bulk motion and not just by conduction. I do not know if heat absorption is slower or not, all else being equal. Rather, the water surface heats up much more slowly than the land surface (the absorbed heat doesn't stay at the water surface but propagates downwards relatively quickly), and consequently heat absorption rates remain relatively high during the whole day/season for water; land, on the other hand, quickly reaches thermal near-equilibrium between a thin surface layer and the incident energy, and consequently heat absorption rates drop rapidly to almost nothing.

Similarly, heat release from water is indeed much slower, but not because water is a better insulator. It's because the absorbed heat is distributed throughout a much thicker layer than is the case for land. Thus, the gradient between the surface of the body of water and the heat sink (air) is much smaller. Thus, the release rate is much lower. Indeed, the observed fact of milder coastal climates can't really be explained with your assumptions, it seems to me. If it was a question of water absorbing heat at lower rates during the day/summer, rather than one of having a greater heat capacity, then even at correspondingly lower release rates, there should be no substantial difference in the periods over which water and land can release heat.

Maybe I just misunderstood what you were trying to say?

As I said before, what you have is a very happening place.

Yes, that's the intention. Good old-fashioned man-versus-nature (well, not "man", strictly speaking) is a significant source of conflict and drama in the plot. I made the planet more hostile than Earth to increase that potential. I appreciate the remainder of your points and will try to read up on those lines of reasoning I can't follow directly. In the end, anything too excessive will simply fall prey to creative licence, though.

[onomatomanic]

The idea of partial melts circulating *within* the mantle is new to me, I'd like to hear more about it.

The wikipedia article you just linked to does mention "partial melts" on several occasions. ;)

I have a very dim recollection of a past flatmate of mine, who studied geology, telling me about the importance of water being carried down into the mantle by the subduction of the "water-logged" oceanic plates - both because water acts as a lubricant, and because it affects the melting point of the mineral it suffuses.

"Very dim", mind you.

[cran]

I meant to say "almost 7/8" instead of "over 7/8", but I don't think I can blame that one on spellcheck, this time. :)

I was using the approximation that the core-mantle boundary is roughly halfway down, which would mean the core is roughly (1/2)^3, or 1/8, the volume of the earth--and the rest about 7/8 (.875). I knew the mantle didn't extend quite halfway down, but said "over" instead of "almost". The mantle is more like .84 the volume of the earth.
http://en.wikipedia.org/wiki/Mantle_(geology)
http://pubs.usgs.gov/gip/interior/

yeah, you're right - I lost a dimension in my unchecked mental calculations. half the radius; quarter of the surface area; eighth the volume. doh.

The idea of partial melts circulating *within* the mantle is new to me, I'd like to hear more about it. Some of the hotspot material has been hypothesized to erupt from the core-mantle boundary, is that what you're referring to?

The more a body behaves like a fluid, the more readily it would adjust to the tidal forces, of course.

That's right, and that's why the bulk mantle must be treated as a solid, or as a seriously viscous plastic.

Leaving aside decompressional melt in the upper mantle, and mantle plumes, just for the moment, fluid movement in the mantle can be compared with fluid (groundwater) movement within the solid crust, or even in fired clay; it occurs between the grains (or crystals) and its rate is independent of the motion of the material in which it moves; driven instead by density and pressure differences; temperature and gravity are also factors. Unless one wants to argue that the bulk Earth is in chemical equilibrium, then some remnant of of the processes which led to fractionation and differentiation is still in effect - partial melts which are less dense than the residuum tend to rise; and those which are more dense tend to sink. Convergent flows lead to accumulations; in the upper mantle, we see the result in decompressional upwelling partial melts along divergent crustal boundaries; in the lower mantle, we argue that they form mantle plumes.

This paper is not the one I was looking for, but it does provide the basic components, whilst considering deep mantle partial melts, the Ultra Low Velocity Zone, and deep mantle plumes, and the pros and cons of percolation above and below the CMB. In amongst it all, it mentions that bulk (solid) mantle convection does not (can not) occur near the lower mantle boundary, elsewhere arguing that heat transfer must therefore be via conduction or fluid transport; one assumes that the bulk of this fluid transport is via plumes, however it also shows that not all plumes can or should rise to the surface.
http://jupiter.ethz.ch/~pjt/papers/H...eepMelting.pdf

[cran]

My understanding is completely different: Water is effectively much less of an insulator than land, because it can carry heat by bulk motion and not just by conduction. I do not know if heat absorption is slower or not, all else being equal. Rather, the water surface heats up much more slowly than the land surface (the absorbed heat doesn't stay at the water surface but propagates downwards relatively quickly), and consequently heat absorption rates remain relatively high during the whole day/season for water; land, on the other hand, quickly reaches thermal near-equilibrium between a thin surface layer and the incident energy, and consequently heat absorption rates drop rapidly to almost nothing.

Similarly, heat release from water is indeed much slower, but not because water is a better insulator. It's because the absorbed heat is distributed throughout a much thicker layer than is the case for land. Thus, the gradient between the surface of the body of water and the heat sink (air) is much smaller. Thus, the release rate is much lower. Indeed, the observed fact of milder coastal climates can't really be explained with your assumptions, it seems to me. If it was a question of water absorbing heat at lower rates during the day/summer, rather than one of having a greater heat capacity, then even at correspondingly lower release rates, there should be no substantial difference in the periods over which water and land can release heat.

Maybe I just misunderstood what you were trying to say?

Thermal Conductivity - k - W/(m.K)
T=25C (except where noted)
Air, athmosphere (gas) 0.024
Earth, dry 1.5
Quartz mineral 3
Rock, solid 2 - 7
Water 0.58
Water, vapor (steam) (T=125C) 0.016

Conclusion: water is a better insulator (poorer conductor) than the solid Earth;
steam is a better insulator than air.

Specific heat, or heat capacity, is its corollary - the amount of energy required to raise a given mass -
usually expressed as calories per gram or joules per kilogram - by 1C.

Substance (qualifier) (cal/gC) (J/kgC)
Air, dry (sea level) 0.24 1005
Granite 0.19 790
Sandy clay 0.33 1381
Quartz sand 0.19 830
Ice (0oC) 0.50 2093
Water, pure 1.00 4186

Conclusion: substantially more energy is required to raise the temperature of water by 1 degree C

I'll use the simple source here; I can easily find others.

Most of the heat energy of sunlight is absorbed in the first few centimeters at the ocean's surface, which heats during the day and cools at night as heat energy is lost to space by radiation. Waves mix the water near the surface layer and distribute heat to deeper water, such that the temperature may be relatively uniform in the upper 100 m (300 ft), depending on wave strength and the existence of surface turbulence caused by currents. Below this mixed layer, the temperature remains relatively stable over day/night cycles. The temperature of the deep ocean drops gradually with depth. As saline water does not freeze until it reaches −2.3 °C (colder as depth and pressure increase) the temperature well below the surface is usually not far from zero degrees. [1]

http://en.wikipedia.org/wiki/Thermocline

Conclusion: water is a poor conductor of heat.
The upper mixed layer is relatively thin.

In contrast, the temperature on land increases with depth due to thermal conduction from the deep Earth.

[onomatomanic]

Thermal Conductivity - k - W/(m.K)
T=25C (except where noted)
Air, athmosphere (gas) 0.024
Earth, dry 1.5
Quartz mineral 3
Rock, solid 2 - 7
Water 0.58
Water, vapor (steam) (T=125C) 0.016

Conclusion: water is a better insulator (poorer conductor) than the solid Earth;
steam is a better insulator than air.

Bear with me here; I'm the first to admit that thermal physics has never been my strong suit.

What do these scalar quantities physically mean for fluids? Obviously, their ability to macroscopically transport heat energy is generally dependent on direction (with respect to the gravitational field), because heat transport will often be dominated by convection currents. Thus, if thermal conductivity were directly related to heat transport, it should be a higher-dimensional quantity for these.

Is this some sort of theoretical measure describing a state in which bulk motion is somehow prevented from occurring, as is the case in solids? Or am I completely missing the point?

[cran]

Bear with me here; I'm the first to admit that thermal physics has never been my strong suit.

What do these scalar quantities physically mean for fluids? Obviously, their ability to macroscopically transport heat energy is generally dependent on direction (with respect to the gravitational field), because heat transport will often be dominated by convection currents. Thus, if thermal conductivity were directly related to heat transport, it should be a higher-dimensional quantity for these.

Is this some sort of theoretical measure describing a state in which bulk motion is somehow prevented from occurring, as is the case in solids? Or am I completely missing the point?

It's the difference between conduction and convection; conduction is not dependent upon gravity nor upon density gradients nor even upon turbulence. Conduction is the in-contact transfer of heat from one particle to another; convection is the (upward) transport of a particle. Apart from submarine sources of heat, warm water masses tend not to transfer heat below the thermocline before most of that heat is given up as OLR (outgoing longwave radiation - infrared radiation, or heat).

No, it's not theoretical. Measuring thermal conductivity in fluids is done in laboratories. Convection and mixing can be ruled out by beginning with a known volume of fluid of equal temperature and density. The rate of heat loss to equilibration can be directly compared with that of other materials (such as clay or rock, metal or glass).

The corollary - heat gain (specific heat) - is even easier to measure against time with a consistent heat source.

[onomatomanic]

No, it's not theoretical. Measuring thermal conductivity in fluids is done in laboratories. Convection and mixing can be ruled out by beginning with a known volume of fluid of equal temperature and density. The rate of heat loss to equilibration can be directly compared with that of other materials (such as clay or rock, metal or glass).

I still don't get it. Either there is a temperature gradient within the fluid, in which case it will under ordinary conditions begin to convect as well as conduct, or there is no gradient, in which case there is no heat flow at all and there is nothing to be measured. I'm sure whatever I'm missing will seem obvious in retrospect, but I'm definitely missing it at the moment.

[ctcoker]

Not all temperature gradients are created equal. Basically, if heat transfer via conduction or radiation is significantly more efficient than convection in a given material under given conditions, large scale convection will be suppressed. Another way of saying this is that if the temperature gradients from conduction or radiation are very much shallower than that from convection, large scale convection will not occur. In most situations with fluids we encounter in everyday life, convection is the most efficient (like in a boiling pot of water on the stove), so it naturally dominates.

[onomatomanic]

So... how does one measure the thermal conductivity of water under normal conditions? Maybe putting it in something like a really thin tube might be sufficient to suppress convection?

[cran]

I still don't get it. Either there is a temperature gradient within the fluid, in which case it will under ordinary conditions begin to convect as well as conduct, or there is no gradient, in which case there is no heat flow at all and there is nothing to be measured. I'm sure whatever I'm missing will seem obvious in retrospect, but I'm definitely missing it at the moment.

Thermal conductivity can be measured between particles of different kinds - water and metal, for instance, or water and glass; convection and mixing play no part in heat transfer between liquids (or gases) and solids; it's all conduction. Where the specific heat and thermal conductivity of the containing material is known, and the volume of fluid contained and its temperature at the beginning of the trial, the time to equilibrate remains the one variable to be measured, and from that measurement, both the specific heat and the thermal conductivity can be determined.

You can use thin tubes, porous plates, or large containers of known volume; using the latter, the thermometer(s) are measuring the top of the body of fluid (and of the container) - big fancy ones can have more thermometers measuring at various depths; these are used to measure convection rates.

[eburacum45]

I've got one planet with a similar eccentricity to this one in OA; Locus, with an eccenticity of 0.73 (slightly less than yours).
http://www.orionsarm.com/eg-article/4eb9314768886
This world is tidally locked, but it does not display the same face all the time to its star; based on information gathered from this forum, I've emphasised the fact that the planet constantly faces in the rough direction of the empty focus in the ellipse.

What that would mean for the tides I haven't considered; I think that means that the tides would be very slow, occuring only twice every 74 days (but they might be much higher than I expected).

[chornedsnorkack]

So... how does one measure the thermal conductivity of water under normal conditions? Maybe putting it in something like a really thin tube might be sufficient to suppress convection?

Easier!

If measuring the conductivity above maximum density temperature (+4) consider that convection means warm water rising up.
Therefore, simply heat the water from top. No convection possible.

[grapes]

The wikipedia article you just linked to does mention "partial melts" on several occasions. ;)

As near as I can tell, only in this passage:

The distinction between crust and mantle is based on chemistry, rock types, rheology and seismic characteristics. The crust is a solidification product of mantle derived melts, expressed as various degrees of partial melting products during geologic time. Partial melting of mantle material is believed to cause incompatible elements to separate from the mantle, with less dense material floating upward through pore spaces, cracks, or fissures, that would subsequently cool and solidify at the surface.

I would think that those cracks and spaces are very close to the surface, producing crust, rather than within the mantle.

I have a very dim recollection of a past flatmate of mine, who studied geology, telling me about the importance of water being carried down into the mantle by the subduction of the "water-logged" oceanic plates - both because water acts as a lubricant, and because it affects the melting point of the mineral it suffuses.

Definitely affects the melt at subduction zones, near the surface, where the product rises to form the "ring of fire" volcanoes. That mixing occurs within about 250km of the surface though.

This paper is not the one I was looking for, but it does provide the basic components,
::snip::
http://jupiter.ethz.ch/~pjt/papers/H...eepMelting.pdf

Thanks for the link, interesting reading...and, uh, I'm not done yet. :)

We can probably continue the discussion without it, though. :)

[eburacum45]

Can't some of these anomalous deep features be explained by segments of subducted crust floating about in the mantle?

[cran]

As near as I can tell, only in this passage:

I would think that those cracks and spaces are very close to the surface, producing crust, rather than within the mantle.
Definitely affects the melt at subduction zones, near the surface, where the product rises to form the "ring of fire" volcanoes. That mixing occurs within about 250km of the surface though.

Thanks for the link, interesting reading...and, uh, I'm not done yet. :)

We can probably continue the discussion without it, though. :)

"pore spaces" is probably not the right term when considering partial melts - it's more commonly associated with groundwater and sedimentary rocks. Intercrystalline and intergranular porosity is also generally limited to crustal and upper mantle-derived rocks, outside of purely theoretical discussions, although (mea culpa) I often use the terms in preference to something like inter-atomic boundary dislocations and the other fun phrases that apply to deep mantle matrix crystal or melt mobility.

Microcracks and heterogenous boundaries were discussed in uni, in relation to deep subducting slabs and crystal phase transitions, but I can't I can't point to anything definitive. Known cracks and fissures are limited to the uppermost layers, and mostly crustal.

Another bit of bedside reading from 1967, discussing how little we then knew, but interesting insights into probable causes of wave attenuation in the mantle. Much of it appears to still be valid, despite the leaps made in the 1990s.
www.gps.caltech.edu/uploads/File/People/dla/DLAgjras67.pdf