Thermodynamics and ice melt flows

From Dr. Judith Curry’s Climate Etc.

by Dan Hughes

I recently ran across the paper by Isenko et al. [2005] listed below. The second paragraph of the introduction states:

“According to the conservation of energy, the loss of potential energy for a volume of water is sufficient to warm it by 0.2 C for each 100 m of lowering.”

The described process corresponds to isentropic compression of liquid water by increasing the pressure by about 1 MPa, through a change in elevation of 100.0 m. Note that the temperature change is given independent of any other information relating to flow velocity, kinetic energy, viscosity, dissipation, or any details of the flow channel that might affect conversion to thermal energy by viscous dissipation of kinetic energy. Especially note that for the case of flows in horizontal channels, for which the potential energy change is zero, apparently there would not be any temperature changes. The same can be said relative to flows upward against gravity.

The calculation by the authors is related the same concept that is the subject of this previous post. That is, the total potential energy at the top of a column of water is converted to thermal energy content by the action of viscous dissipation. As in the subject papers of the previous post, the temperature increase is too high.

When the process is considered to be compression of subcooled liquid water isolated from interactions with its surroundings, the temperature increase is estimated to be about 0.01 K per 100 m.

In general, textbooks recommend that temperature increase due to viscous dissipation can be neglected for all but a few special situations. The recommendation is particularly valid whenever thermal interactions between the fluid and channel walls, i.e. heat transfer, is the focus of the application.

The temperature increase for compression of subcooled liquid water is estimated in the attached PDF FILE. [WorkPost03]

Reference

Evgeni Isenko, Renji Naruse, and Bulat Mavlyudov, “Water temperature in englacial and supraglacial channels: Change along the flow and contribution to ice melting on the channel wall,” Cold Regions Science and Technology, Vol. 42, pp. 53– 62, 2005.

Herbert B. Callen, Thermodynamics: An Introduction to the Physical Theories of Equilibrium Thermostatistics and Irreversible Thermodynamics, John Wiley & Sons, Incorporated, New York, (1960).

W. Bridgman, “A Complete Collection of Thermodynamic Formulas,” Physical Review, Vol. 3, No. 4, pp. 273–281, (1914). doi:10.1103/PhysRev.3.273.

W. Bridgman, The Thermodynamics of Electrical Phenomena in Metals and a Condensed Collection of Thermodynamic Formulas, Dover Publications, Inc. New York. (1961).

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Steve Case
April 2, 2022 10:46 pm

 As in the subject papers of the previous post, the temperature increase is too high.
___________________________________________________________

Every climate metric is hyped and inflated. It’s part of the landscape.

Duane
Reply to  Steve Case
April 3, 2022 5:38 am

It’s not merely hyped, in this case the claimed conversion of all potential energy to thermal energy is simply fundamentally wrong and reveals complete ignorance of the physics of flowing semi-solid ice masses. Nearly all of the potential energy of a glacier is converted instead to kinetic energy of the vast flowing ice mass.

Loren C. Wilson
Reply to  Steve Case
April 3, 2022 6:36 pm

The 0.2 K of heating is for the case of water flowing down hill. This value is correct. The potential energy is converted into heat via friction. Ice sliding down a glacial valley should do the same thing. This happens on every stream and river in the world and has been since rivers formed several billion years ago.

April 3, 2022 12:09 am

“The calculation by the authors is related the same concept that is the subject of this previous post. That is, the total potential energy at the top of a column of water is converted to thermal energy content by the action of viscous dissipation. As in the subject papers of the previous post, the temperature increase is too high.”

Their calculation is correct. What you never explained, in last post or this, is where else the energy could have gone. Energy is conserved, you know.

lee
Reply to  Nick Stokes
April 3, 2022 1:54 am

In the land of “we don’t know”?

M Courtney
Reply to  Nick Stokes
April 3, 2022 2:00 am

Water is not H20. It is (H20)n.
The high thermal heat capacity of water comes from n changing. Effectively there are mini-phase changes for liquid water.
You’re talking physics. But you need to look at the chemistry.

Reply to  M Courtney
April 3, 2022 2:03 am

How about some numbers?

M Courtney
Reply to  Nick Stokes
April 3, 2022 2:54 am

Not sure anyone can tell you the actual quantified energy changes of hydrogen bond formation in liquid water. It would be cutting edge if they could. I don’t know it.

But we know it’s of the order to account for this “missing” energy because of the high thermal capacity of water.

Reply to  M Courtney
April 3, 2022 2:59 am

No, energy is not missing because of high specific heat. The heat is just the product of cp and dT (or integral if cp varies with T). If cp is high, dT is low, but the heat energy still has to equal the PE lost.

Of course, the heat may be transferred to somewhere else (eg ice), but that is a different issue.

Duane
Reply to  Nick Stokes
April 3, 2022 5:18 am

You are ignoring the physics of flowing ice, which is the conversion of potential energy in the form of elevation head change (from change in elevation of the ice surface upstream to downstream) to kinetic energy of a flowing glacier. No different than the physics of liquid water in open channels, just a much higher viscosity of ice vs. liquid water.

Reply to  Duane
April 3, 2022 2:00 pm

There is no indication her that the ice is flowing. But even if it is, its KE is negligible. The PE loss of ice descending is 9.8 J/kg/m. The KE per kg is .5*v². At 1 m/day, or about 10⁻⁵m/s, that would be .5*10⁻¹¹. Equivalent to the PE from descending 0.5 picometres.

Duane
Reply to  Nick Stokes
April 3, 2022 5:04 pm

If the ice is not moving downhill then there is no reduction in potential energy, hence you whole stupid argument falls apart.

Gary Pearse
Reply to  Nick Stokes
April 4, 2022 8:51 am

This loss of KE is simply the same as that for dropping a rock one metre

Gary Pearse
Reply to  Gary Pearse
April 4, 2022 8:56 am

So when ice flows uphill for stretches, it cools.

mkelly
Reply to  Nick Stokes
April 3, 2022 6:15 am

Q = Cp * m * dT

Your post is missing the mass involved.

Reply to  mkelly
April 3, 2022 2:03 pm

I multiplied the mass of 1 m^3 water into the cₚ

Duane
Reply to  M Courtney
April 3, 2022 5:15 am

There are no significant changes in energy of an ice flow due to any phase changes. The only phase change is at the immediate interface between ice and rock, and thus there is no effect whatsoever on the vast majority (99.999…%) of the mass of ice in a large glacier that is thousands of feet thick and miles wide.

The overwhelming energy change is conversion of potential energy, in the form of elevation head, to kinetic energy of the flowing ice mass. A very small proportion of energy change feeds into frictional heat, but due to ice melt and reduced friction, that effect is extremely minor.

Gordon A. Dressler
Reply to  Duane
April 3, 2022 10:39 am

“The only phase change is at the immediate interface between ice and rock . . .”

You mean the underlaying rock must always be above a temperature of 0 °C?

Who knew?

BTW, the absolute pressure at the bottom of a half-mile thick glacier would be about 1040 psia, or about 72 bars. As can be seen in the attached phase diagram for water, there is NO depression or increase in the melting point of water at this pressure level.

In fact, the melting point of water would begin to decrease when the pressure reached about 300 bars, equivalent to an ice thickness of about 2.1 miles! . . . something not to be found on any glacier on Earth today.

Water_Phase_Diagram.gif
Duane
Reply to  Gordon A. Dressler
April 3, 2022 5:09 pm

No, the underlying rock need not have a surface temperature above 0 deg C. Friction between a moving ice mass and the underlying rock causes heat energy to be generated which in turn causes a phase change, ie ice melt, still at 0 deg C … which in turn causes a reduction in friction because liquid water is a lubricant … hence the phase change due to melting at the ice-rock interface provides a self limiting negative feedback to the frictional heating of the ice.

Gordon A. Dressler
Reply to  Duane
April 3, 2022 9:49 pm

Duane,

Friction between a moving ice mass and the underlying rock causes HOW MUCH heat energy to be generated? . . . and why do you assert that frictional heat remains at the interface of, oh, say -20 °C long enough to raise the interface to 0 °C whereupon phase change can occur, as opposed to being conducted away from the interface (either into underlying rock or into overlaying ice) well before the interface can be heated to 0 °C???

I seriously doubt that glacial ice, moving at typical glacial advance speeds of 25 cm/day, or .003 mm/sec (ref: https://lisbdnet.com/how-fast-does-a-glacier-move/ ) generates much heat flux (W/m^2 of contact area), especially if it were to be “lubricated” with liquid water as you assert.

I rather suspect that the ice at the rock interface plastically deforms in a continuous fashion, without melting, and by this process in able to move slowly downhill over a stationary rock surface.

However, I have seen studies suggesting that relatively small rocks and pebbles (the “till” left behind by glacial retreat) can act analogous to ball bearings to facilitate downhill glacial movement:
When glaciers retreat, they often deposit large mounds of till: gravel, small rocks, sand, and mud. It is made from the rock and soil that was ground up beneath the glacier as it moved.” —https://nsidc.org/cryosphere/glaciers/questions/land.html

Gary Pearse
Reply to  M Courtney
April 4, 2022 10:45 am

I’ve been arguing for years (with little response) that Le Châtelier’s Principal is an overlooked major restraint on Global Warming. In any interacting multi-component system a forced perturbation by one of the components (e.g. effecting a temperature rise by whatever agency), is resisted by responsive changes to all other components (P, V, concentration of compounds, in atmos and sea, bio responses, pH changes, evap, precip, KE, …). Increased CO2 is sequestered by plants and plankton and increased solution in seawater. The “expected” drop in pH in seawater from the dissolution of CO2 to form carbonic acid is, in turn, is buffered by changes in carbonate and bicarbonate concentrations:

“The redistributions among gaseous and dissolved carbon dioxide, carbonic acid, bicarbonate, and carbonate ions are governed by multiple co‐occurring equilibria with the result that approximately 19 out of the 20 molecules of carbon dioxide entering the ocean are converted into bicarbonate and carbonate ions.”

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7391262/

Calcium carbonate is even driven to precipitate into the deeper ocean.

In my experience, physicists seem unaware of the LCP. Climate is “The Chemistry” stupid!

LdB
Reply to  Nick Stokes
April 3, 2022 2:42 am

The calculation as stated is stupid beyond belief as a body of water will flow to replace any lowering and would have energy processes that would outscale all this bullshit. If you calculate for a closed system it has no relevance to the open system.

It’s one of those stupid calculations you may run that is meaningless a typical example is changes in mass of earth per year and the energy of that is way beyond the crap being discussed
https://www.sciencefocus.com/planet-earth/is-the-weight-of-the-earth-changing/

If you want to play in physics we need proper context and controls.

Reply to  LdB
April 3, 2022 3:06 am

Here is the calculation written spelt out for those who need it. It is really elementary:
PE lost in descent: ρgh=1000*9.8*100=980000J//m^3
Temperature gained by water from this energy converted to heat=980000/(cp=4200000)=0.233°C

Last edited 8 months ago by Nick Stokes
Duane
Reply to  Nick Stokes
April 3, 2022 5:24 am

Again, dummy you are ignoring what is actually by far the dominant energy conversion, which is potential energy to kinetic energy of the flowing ice, which fantastically exceeds any conversion of potential energy to thermal energy.

This is why “scientists” are never allowed to design anything in the real world outside the laboratory or your faked up grossly oversimplified models … because you guys have tunnel vision that enables you avoid acknowledging all relevant real world processes … while engineers must take all the science into account in order to design anything that actually works.

Scissor
Reply to  Duane
April 3, 2022 6:23 am

You are correct on the science (and engineering) Duane, and I appreciate your view regarding the difference between scientists and engineers.

It took me almost my entire career as a scientist to become somewhat fluent in communication with engineers, and your comment on design is most certainly true. I can do rudimentary engineering but I would rather leave it to a professional for the reasons you state.

I’m not sure about your “tunnel vision” comment as that implies scientists only seeing one thing out of ignorance. I think it’s more akin to scientists falling in love with an idea, consciously finding inspiration in it or in some problem that captures their imagination, albeit singularly focused but not from an inability to see other factors. Maybe our view is actually very similar on that.

In some respects, scientist are more artistic, seeing things from a different, maybe even distorted perspective, appreciated by different skill sets. Of course, there is overlap across something like a continuum. In general scientists throw better parties, but not from planning.

Phil R
Reply to  Scissor
April 3, 2022 8:49 am

Scissor,

Not an engineer but can confirm your empirical observation regarding scientists and parties. When i was working on my Geology degree last century, we would have great parties, which would continue on the field trips (good thing geology is a field science).

During field trips we would get the odd biologist (odd both figuratively in that only once in a while if they were taking a class to fill an elective credit, and literally in that biologists as a group were odd) and they would invariably comment on how great our field trips were compared to their boring biology field trips.

Now back to the regularly scheduled programming…

Scissor
Reply to  Phil R
April 3, 2022 8:57 am

I think biologists are better at throwing private parties, but I really wouldn’t know.

Dave Fair
Reply to  Scissor
April 3, 2022 10:39 am

Thank you, Scissor, you have made it all clear to me! Paleoclimatoligists are artists.

David More
Reply to  Duane
April 3, 2022 8:16 am

Another Overlooked problem being ignored.
0.2 C for each 100 m of lowering.
Glacial ice temperature profile runs from -30 to -60 to -30 top to bottom. What difference is 0.2 going to make? Will not create any melting.

Reply to  David More
April 3, 2022 1:29 pm

No, you have the situation wrong. The paper is titled
“Water temperature in englacial and supraglacial channels: Change along the flow and contribution to ice melting on the channel wall,”
They are writing about liquid water running down through channels. They are just trying to quantify the amount of heat generated. It’s true that it will mostly be transferred to the ice, with some possible melting. But it is added to the environment.

LdB
Reply to  Nick Stokes
April 3, 2022 6:11 am

Sure because viscous dissipation is 100% … please read the problem statement again 🙂

What is next classic physics calculations on a black hole event horizon.

Last edited 8 months ago by LdB
mkelly
Reply to  Nick Stokes
April 3, 2022 6:22 am

From Wiki:”…the specific heat capacity of water is 4184 J⋅kg−1⋅K−1.”

Where do you get rid of the m^3?

Reply to  mkelly
April 3, 2022 1:36 pm

OK, I said equivalently 4,200,200 J⋅m−3⋅K−1. The m-3 cancels out.

Or, if you want, put ρcₚ=1000*4184 in the denominator. Same arithmetic and result.

Kevin kilty
Reply to  Nick Stokes
April 3, 2022 9:34 am

Nick,

I can agree with your method, but if this is flow of ice, which is what I understand, then you can’t use the heat capacity of liquid water. Ice at 260K has a little less than one-half the heat capacity of water at 273K. So, I calculate about 0.49 C of temperture rise. However, the other complication is what process are we following?

Reply to  Kevin kilty
April 3, 2022 1:39 pm

Kevin,
They said the the PE of descending water would warm that same mass of water 0.2°C. Most of that heat ends up in the ice, but not the same mass of ice.

Ron Long
Reply to  Nick Stokes
April 3, 2022 3:34 am

Nick, how about a “real world” analysis of glacial melt water descending down topography under the influence of gravity? The dry air adiabatic lapse rate is 9.8 deg C per vertical kilometer difference. So, in a real world scenario, we have thermal heating due to viscous dissipation and additional ambient heating due to adiabatic lapse rate of atmosphere interacting with the water. Other factors? Almost certainly. The only useful measure of the physical state of H2O is sea level, and the variance of sea level is around 140 meters, which is a variance far greater than even the most rabid CAGW fanatic’s wet dreams.

Reply to  Ron Long
April 3, 2022 3:56 am

You can do that if you want. They did a simple and correctly stated calculation.

But the water won’t take in heat from its environment (lapse rate). It started out as liquid, and it’s ice all the way down. The heat flows the other way.

LdB
Reply to  Nick Stokes
April 3, 2022 6:13 am

Keep going it’s not even relevant and the calculation is stupid and meaningless. Here is us thinking we were trying to do real world calculations.

Last edited 8 months ago by LdB
Ron Long
Reply to  Nick Stokes
April 3, 2022 12:30 pm

Cold is absence of heat, so heat flows into icy glacial melt-water as it goes from generally higher elevations to lower elevations. My point is that trying to calculate the heat derived from internal friction is meaningless when compared tot he increasing temperature of the atmosphere due to the adiabatic lapse rate. No, I don’t heat my bathwater with a hair dryer, but the atmosphere does heat water.

LdB
Reply to  Ron Long
April 3, 2022 8:58 pm

Correct understanding +100

TimTheToolMan
Reply to  Nick Stokes
April 3, 2022 4:57 am

So for example a droplet of rain quickly reaches terminal velocity and the energy then goes into the droplet (increasing potential for re-evaporation) and heating the atmosphere it passes through.

Reply to  TimTheToolMan
April 3, 2022 1:40 pm

Yes

LdB
Reply to  Nick Stokes
April 3, 2022 9:01 pm

No because the droplet has surface area and it’s exchange based on movement thru the air is many many magnitudes larger. It’s called the real world 🙂

It is like E=MC2 and when something gets hotter it has more mass the challenge is to find a situation that means anything beyond a scientific calculation.

Last edited 8 months ago by LdB
TimTheToolMan
Reply to  LdB
April 4, 2022 12:46 am

No, what?

The droplet doesn’t “warm up” due to friction with the air and subsequently evaporate?
Or the droplet doesn’t warm the air due to friction with the air?

Or neither? Do you believe the energy goes elsewhere?

Duane
Reply to  Nick Stokes
April 3, 2022 5:06 am

No their fundamental misunderstanding is that the only change in energy is due to friction. The largest factor by far is converting potential energy of upstream ice accumulation or elevation head to kinetic energy. Friction loss is always minor in an open channel, and because any localized heating at the interface between ice and rock results in melting, such friction losses as occur actually result in liquid water lubrication and thus serves to limit friction losses as a negative feedback. It may seem counterintuitive that an ice flow has kinetic energy but it is certainly non-zero because glaciers most certainly do flow and thus convert potential energy to kinetic energy.

TimTheToolMan
Reply to  Duane
April 3, 2022 5:46 am

Your argument is not very convincing. If the meltwater in the channels was gaining kinetic energy as the primary factor for energy transfer then it would have to be continually increasing velocity. And it’d still lose that energy as heat whenever it pooled.

As Nick correctly states, energy is conserved.

Duane
Reply to  TimTheToolMan
April 3, 2022 5:22 pm

No – there is no need for linear acceleration .. a simple non-varying elevation head difference is all that is needed to keep ice or liquid water flowing at a constant velocity due to the acceleration of gravity. That is the fundamental science behind all hydraulic engineering and the flow of water or ice in an open channel. If there is any linear acceleration that can be due only to a change in the driving elevation head upstream.

Think of a river – it’s flow velocity is directly proportional to the depth of water upstream. The upstream depth increases only when the volumetric in-flow of water – from a rainstorm dumping more rain on its contributory watershed – is increased. That is how and why rivers flood – due to heavy rain in the contributory watershed upstream of the point where flooding occurs.

Flowing ice acts just the same as flowing water, just at a much slower one dimensional velocity.

TimTheToolMan
Reply to  Duane
April 4, 2022 12:52 am

None of that addresses the conversion of the water’s potential energy to another form of energy as it falls and especially when it stops at the bottom.

The kinetic energy is converted to heat. Maybe some is used creating sound and some is used to wear away at the base but the majority will turn up as heat which will be transferred to the ice to further melt it.

If you dont believe the potential energy is converted to heat, then what do you believe that energy is converted into when the water essentially stops at the bottom?

Gordon A. Dressler
Reply to  Duane
April 5, 2022 12:13 am

Duane, you posted: “. . . a simple non-varying elevation head difference is all that is needed to keep ice or liquid water flowing at a constant velocity due to the acceleration of gravity.”

That statement is specifically incorrect in the context of glacial ice in the real world. Glacial ice at a constant elevation head difference will still have varying velocity, hence varying kinetic energy, as the bulk viscosity of the ice varies (e.g., due to development of cracks or crevasses), as the density varies (e.g., ice at -30 °C is 0.3% more dense than ice at -5 °C), and as the average coefficient of friction at the ice/rock interface varies (e.g., due to varying meltwater lubrication and varying amounts of till at the interface).

mkelly
Reply to  Duane
April 3, 2022 6:27 am

Friction heating is what is blamed for the ice dam collapse that created the Scab Lands. Or should I say collapses as it probably happened several time.

Duane
Reply to  mkelly
April 3, 2022 5:27 pm

Nope – frictional heating is completely insignificant. If an ice dam collapses it is entirely due to other factors, such as a large increase in upstream driving head (such as a massive increase in precipitation in the upstream watershed), or an earthquake …or the gradual buildup in stress within the ice that eventually exceeds the shear strength of the ice.

Dan Hughes
Reply to  Nick Stokes
April 3, 2022 5:51 am

So far in these discussion I have been the only person to cite and write equations, many taken directly from textbooks. I think that when mathematical models of physical phenomena and processes are the subject, equations provide a good focus point and allow for identification of potential problems

Also so far, no one has pointed out any errors in any term in any of those equations. With good reason because the source has been textbooks. If you think that any equations that I have cited are incorrect explicitly note the equation and the textbook source.

The local-instantaneous PDE for conservation of total energy, represented by the sum of internal plus kinetic plus potential energy, has the usual LHS of the time-rate of change of this sum plus convection of this sum.

The RHS side includes the rate of energy change by conduction within the fluid, plus rate of work done by body forces, usually limited to gravitational forces, plus rate of work done by pressure forces within the fluid, plus rate of work done by viscous forces. The rate of work done is of course power.

Potential energy due to gravity, a conservative force, gets to be included in the time derivative because as a vector gradient of a scalar potential it is time constant. Other body forces that meet this requirement can be also included.

Nowhere in the conservation of total energy equation does viscous dissipation of kinetic, or potential, energy appear. The latter with good reason.

The various local-instantaneous PDE formulations for conservation of thermal energy, in terms of internal, or enthalpy, or temperature, contain accounting of effects of the irreversible rate of thermal energy increase due to viscous dissipation. And it is always an increase, viscous dissipation being always positive.

The local-instantaneous PDE formulation for kinetic energy RHS also includes the viscous dissipation term that we’re looking for, and it is negative definite; always a loss.

The reason the term does not appear in the equation for conservation of total energy is because the process is an interconversion within the fluid and cancels when the sum of the equations is formed.

I’m certain that The Google, plain or scholar, can lead you to exhaustive developments and discussions of all these equations in reports, papers, videos, and lecture slides, filled with all the partials, del, div, grad, and tensor calculus your heart could ever want.

Additionally, again because of association with viscosity and kinetic energy, the RANS literature, both 2-parameter and Reynolds-closure, is filled with exhaustive development of viscous dissipation, that being one of the 2 parameters.

Bird [1957] developed a macro-scale version of the kinetic energy equation. That equation is used because if the subject is viscous dissipation and conversion of kinetic energy into thermal energy, the kinetic energy equation sound like a good starting point. Bird, Stewart, and Lightfoot [1960], and thousands of others, have summarized Bird’s results. 

R. Byron Bird, “The Equations of Change and the Macroscopic Mass, Momentum, and Energy Balances,” Chemical Engineering Science, Vol. 6, pp. 123-131, (1957). 

R. Byron Bird, Warren E. Stewart, and Edwin N. Lightfoot, Transport Phenomena, 1st Edition, John Wiley & Sons, Inc., New York, (1960).

TimTheToolMan
Reply to  Dan Hughes
April 3, 2022 6:06 am

You say “so far, no one has pointed out any errors in any term in any of those equations. With good reason because the source has been textbooks.”

In the Curry thread mdander said the following

“The problem with equations from a textbook written in 1960 is that you have to be very careful to use them in a way that applies to the physical situation being examined.

In chapter 7 of Bird, Stewart and Lightfoot, the flow described is through a closed system where volume in = volume out — as you say in your pdf “a simple closed channel like a straight pipe”. The situation under a glacier is nothing like a simple closed channel. Much more water exits the bottom of the glacier than is melted on top (the paper suggests about 0.5 cubic km on the surface dropping down, whereas the melt rate of greenland is estimated to be over 200 cubic km).

How exactly does the viscous dissipation along a simple closed channel relate to viscous dissipation when the water that has fallen combines with two orders of magnitude more water?”

And that seems like a pretty good response.

Dan Hughes
Reply to  TimTheToolMan
April 3, 2022 6:12 am

I did not address flows under the glacier. I addressed the flow down the tunnel relating to the representation shown in a figure in the News Release.

News release, “Accelerating Melt Rate Makes Greenland Ice Sheet World’s Largest “Dam” – Generating Huge Amounts of Heat From Hydropower,”  https://scitechdaily.com/accelerating-melt-rate-makes-greenland-ice-sheet-worlds-largest-dam-generating-huge-amounts-of-heat-from-hydropower/

TimTheToolMan
Reply to  Dan Hughes
April 3, 2022 10:01 am

So where are you suggesting the potential energy goes if not as heat?

LdB
Reply to  TimTheToolMan
April 3, 2022 9:05 pm

You have surface area moving thru air … think about it where do you think it goes and good luck measuring it?

TimTheToolMan
Reply to  LdB
April 4, 2022 12:55 am

The answer is obvious and I’ve stated it many times as has Nick. Why dont you tell me where you think the potential energy goes?

Dave Miller
Reply to  Dan Hughes
April 4, 2022 11:17 am

BSL!

I’ve often thought that posters here who are talking energy flows should have been forced to struggle first with those 400 or so pages of partial differential equations.

It’s clear most haven’t 😉 .

Forty years later visualizing that bright red tome still raises my anxiety level!

Gordon A. Dressler
Reply to  Nick Stokes
April 3, 2022 10:01 am

Nick Stokes posted: “Energy is conserved, you know.”

That is simply not true, in context, when one considers the reality of a glacier (or other mass of ice) resting on land or being supported by water. One simply cannot assert that “energy is conserved” in the ice mass due to the unavoidable fact that heat energy exchange is taking place across the ice-land interface or ice-liquid water interface.

TimTheToolMan
Reply to  Gordon A. Dressler
April 3, 2022 1:24 pm

Of course you can. If the potential energy isn’t going into heating, then it has to be accounted for elsewhere. But where?

Gordon A. Dressler
Reply to  TimTheToolMan
April 3, 2022 3:31 pm

As I stated, the energy arising from the decrease in altitude (i.e., the decrease in potential energy) of a moving glacier is going from the ice mass into the supporting underlay, whether it be soil, rock or water.

Some of that energy could also be going out via thermal convection to the atmosphere (yes, ice can transfer energy without necessarily melting), but this is less likely because any snow on top of the glacier acts as a pretty good thermal insulator.

Duane
Reply to  Gordon A. Dressler
April 3, 2022 5:29 pm

Nope – then potential energy of the ice mass due to gravity, or elevation head, is converted to kinetic energy of the ice mass itself.

LdB
Reply to  Duane
April 3, 2022 9:07 pm

Actually both and into inter atom bond stress and quite a few other things. Even moving it’s not all kinetic you have sound (the cracking noise) it is a fairly complex problem.

Last edited 8 months ago by LdB
Gordon A. Dressler
Reply to  Duane
April 3, 2022 9:54 pm

Really?

No energy required to overcome friction at the bottom of the glacier?

Who knew?

LdB
Reply to  Gordon A. Dressler
April 3, 2022 10:06 pm

Nick defined the frictionless world and Duane is playing in that world 🙂

TimTheToolMan
Reply to  Gordon A. Dressler
April 4, 2022 3:12 am

As I stated, the energy arising from the decrease in altitude (i.e., the decrease in potential energy) of a moving glacier is going from the ice mass into the supporting underlay, whether it be soil, rock or water.

You’ve misunderstood the problem. The question isn’t about the energy of a moving glacier, its of meltwater falling into a crevice at the top of the glacier and falling hundreds of meters.

Gordon A. Dressler
Reply to  TimTheToolMan
April 4, 2022 7:35 am

No, I did not.

It was Duane on April 3, 2022 5:38 am (currently the second posted comment to the above article) who broadened the above article’s subject matter to include the conversion of the potential energy of the glacier. In fact, he repeatedly comes back to that point, sometimes substituting “ice mass” for “glacier”, as above on April 3, 2022 5:29 pm.

I was replying to Duane and others specially in regards to the subject of glacial ice movement and related effects, including how the change in the glaciers potential energy gets transferred away from its interface with supporting rock.

Yes, the issue discussed in the above article is specific to meltwater being heated due to it being “compressed” by falling over a given vertical distance. However, the article states the (revised) calculations were done using isentropic compression of subcooled water (yielding the concllusion: “temperature increase is estimated to be about 0.01 K per 100 m”).

I previously commented on the absurdity of assuming water falling through crevasses in a glacier can be modeled using an isentropic compression methodology.

I’ll go even further: assuming a glacier has crevasses about 1000 m (more than half a mile) deep, the issue of falling meltwater having its temperature raised by a total of 0.1 K under such an proposed condition is just insignificant! Just consider that the mass of meltwater falling through a glacial would be at most, what, .01% of the mass of the glacier?

TimTheToolMan
Reply to  Gordon A. Dressler
April 4, 2022 1:29 pm

Re responding to Duane, no you didn’t. The thread was in response to Nick’s energy conservation statement.

“Their calculation is correct. What you never explained, in last post or this, is where else the energy could have gone. Energy is conserved, you know.”

You even quoted it in your first response.

Gordon A. Dressler
Reply to  TimTheToolMan
April 4, 2022 5:03 pm

You posted: “Re responding to Duane, no you didn’t.”

Not correct. As documented above, at April 3, 2022 9:54 pm I replied to the comment Duane had posted at April 3, 2022 5:29 pm.

Truth matters.

TimTheToolMan
Reply to  Gordon A. Dressler
April 5, 2022 1:46 am

I’m guessing you’re on a phone because the thread is clear on a PC screen that indents correctly. Yes truth matters and you’re mistaken.

Gordon A. Dressler
Reply to  TimTheToolMan
April 5, 2022 8:28 am

You appear unaware that there can be threads within threads.

If you want to walk back your use of the non-specific term “the thread”, please go ahead . . . no skin off my back.

TimTheToolMan
Reply to  Gordon A. Dressler
April 5, 2022 1:39 pm

It’s easy to follow the replies using the who replied to who and Duane wasn’t part of it. But I’ve fallen in the trap Willis avoids by wrestling with a pig.

Gordon A. Dressler
Reply to  TimTheToolMan
April 5, 2022 6:08 pm

Hmmm . . . all along I thought the relevant phrase was “trying to teach a pig to sing”.

That’s were I’m coming from.

Reply to  Gordon A. Dressler
April 3, 2022 1:45 pm

Energy may be transferred, but it is always conserved. The point of these various calculations is that it won’t stay in that water, but it is added to the local environment.

Gordon A. Dressler
Reply to  Nick Stokes
April 3, 2022 3:46 pm

In the above article, which I take to be included in your phrase “these various calculations”, there is this direct statement:
“The described process corresponds to isentropic compression of liquid water by increasing the pressure by about 1 MPa, through a change in elevation of 100.0 m.”

As I have posted elsewhere, the condition of isentropic compression of liquid water, or even the ice of a glacier, has no relevance to the real world conditions that result when a glacier is in contact with air and also in contact with underlying soil, rock or water. Glaciers are NOT adiabatic.

Indeed, energy is conserved but one then has to evaluate the exchange of energy in glaciers with the Earth’s atmosphere, lithosphere and (in many cases) hydrosphere. Good luck with that.

LdB
Reply to  Gordon A. Dressler
April 3, 2022 9:09 pm

+100 correct

DMacKenzie
Reply to  Nick Stokes
April 3, 2022 1:35 pm

I think most WUWT readers can calculate the potential energy change of a kg of water over a 100 metre elevation change. We just don’t think it’s relevant to glacial anything….

Gordon A. Dressler
Reply to  DMacKenzie
April 3, 2022 4:41 pm

Well said!

Loren C. Wilson
Reply to  Nick Stokes
April 3, 2022 7:08 pm

0.2K per 100 meters is correct for water flowing downhill. The potential energy goes into heat, as stated in the article. We agree that energy is conserved. If the process is just compressing liquid water, then the increase in temperature for a one MPa increase in pressure at constant entropy is 0.015 K for water at 293.15 K and 1 MPa going to 2 MPa.

Gordon A. Dressler
Reply to  Loren C. Wilson
April 3, 2022 10:03 pm

Some of that converted potential energy, maybe even most of it, could be going in the heat of vaporization of water, assuming the relative humidity of the adjacent atmosphere is below 100% (that is, energy absorbed by water evaporation).

It need not all appear as sensible heat, as reflected by increased water temperature.

Loren C. Wilson
Reply to  Gordon A. Dressler
April 4, 2022 4:39 am

Correct. For a river flowing downstream, evaporation is going to cool the river much faster than viscous heating. This all depends on the many factors that control evaporation (relative humidity of the air, wind and water speed, temperature, surface area, spray, etc.) Rivers usually warm as they flow, but this is mostly due to flowing from a cooler location to a warmer one.

TonyL
April 3, 2022 12:39 am

“compression of subcooled liquid water isolated from interactions with its surroundings, the temperature increase is estimated”

Anybody see what is wrong with this?
Subcooled liquid water, that is to say liquid water below it’s freezing point.

Way Back In The Day:
Thermodynamics class. We were shown how the properties of states of water could be calculated beyond what was physically possible. This was taken as an exercise in a theoretical abstraction just to show the power of thermodynamic calculations.
Here we see it put to use, in a “practical” sense.
One wonders what would be the result if the calculation was applied to ice, as the real-world situation is.
The number 0.0000 comes to mind.

Gordon A. Dressler
Reply to  TonyL
April 3, 2022 4:48 pm

One needs very specialized conditions to subcool liquid water—things like particulate contamination (nucleation points), movement of the water, noise and shocks (say from the grinding of ice over irregular rock surfaces) . . . you know, the conditions that normally exist at the bottoms of glaciers—make it laughable to assert that subcooled liquid water exists, to any significant degree, anywhere near glaciers.

Duane
April 3, 2022 4:57 am

Horrible level of understanding. The flow of ice is just like the flow of liquid water, the only difference being the much higher viscosity of semi-solid ice, with kinetic energy being non-zero but inconsequential.

Ice flows downhill, and loses potential energy due to losing elevation. Heating of the ice is non-zero but also inconsequential. The only heating is at the interface between ice and rock due to friction.

This is of a piece with the warmunists’ completely bass ackwards misunderstanding of the meaning and source of more rapid flow of glacial ice to the sea, and accelerated calving of icebergs. They stupidly insist that that is a result of melting ice. But simple physics and hydraulic engineering equations prove that accelerated ice movement can only come from thicker ice upstream of the glacial boundary, i.e., MORE ICE. The bottom surface profile (the rocks underlying the ice) does not change at a rate sufficiently to affect volumetric flow velocity. The acceleration due to gravity is a constant, and the friction between ice and rock is also a constant. Therefore the only energy source that can drive a higher ice flow rate is the higher elevation head, or potential energy, of the ice surface upstream.

Duane
Reply to  Duane
April 3, 2022 5:34 am

Clarification to my statement in my first para above. That is there is a PERCEPTION that the kinetic energy of a flowing glacier is inconsequential, but the perception is wrong. Ice moves slowly, and even on steep mountain glaciers is measured in just feet per day. However, the typical large glacier in Arctic or Antarctic regions is thousands of feet thick and miles wide, up to even tens or hundreds of miles wide. Thus even the very slow linear velocity of such an ice mass still contains a humongous kinetic energy relative to the change in potential energy of a flowing glacier.

Reply to  Duane
April 3, 2022 1:50 pm

 the friction between ice and rock is also a constant”
Very much not so, as anyone who has tried to walk on melting ice could attest. The stiffness of the ice is very temperature dependent.

Duane
Reply to  Nick Stokes
April 3, 2022 5:40 pm

You don’t understand friction at all. Friction is a function of two properties: the viscosity of the fluid, and the roughness of the surface over which it passes. Viscosity does vary with temperature, but on a very small scale. So if friction with the underlying rock results in heat energy added to the bottom of the ice mass, it increases the temperature of the ice such that the ice at the interface melts, then thereafter the temperature gets stuck at 0 degrees C due to the phase change and so cannot further change the viscosity until the entire overlying ice mass melts. And as I point out elsewhere, as soon as any ice melts at the interface it functions as a lubricant (far lower viscosity) that serves as a negative feedback, greatly reducing friction. In any event the frictional heating at the ice-rock interface is an extremely localized phenomenon, affecting a thickness of only a few millimeters of ice.

LdB
Reply to  Nick Stokes
April 3, 2022 9:11 pm

Try walking on the ice with an ice skate or better still look up how an ice skate works and think about the stupidity of your comment … constant indeed the man claims 🙂

Last edited 8 months ago by LdB
TimTheToolMan
Reply to  LdB
April 4, 2022 3:14 am

Nick said “Very much not so”

Then irony.

TimTheToolMan
Reply to  Duane
April 4, 2022 1:19 am

friction between ice and rock is also a constant.

I’ll bet you regret saying that.

Kevin kilty
April 3, 2022 9:44 am

I will admit to being baffled by the intent of this topic. First, in thermodynamics one has to specify the thermodynamic path of the process — otherwise the process is ill-defined. If the process is adiabatic, that is if the gravitational potential lost all goes into internal energy of the ice (K.E. is negligible), then a simple energy balance like the one Nick Stokes outlined is appropriate except for the heat capacity issue (ice has less than half the specific heat of water). On the other hand if heat transfer with some reservoir occurs along with flow to a lower elevation, then the process could even be isothermal, that is no temperature change at all. Process path is all important here.

On the third hand, some of the discussion seems to be about the latent heat of pressure (heat of transfer) of ice which is another topic entirely.

Gordon A. Dressler
April 3, 2022 9:52 am

From the above article: “The described process corresponds to isentropic compression of liquid water by increasing the pressure . . .”

C’mon, really???

The fundamental requirement for an isentropic process for any arbitrary control volume is that the evolution of state within that control volume must be adiabatic and reversible. “Adiabatic” means that no energy can be exchanged across the surfaces of the control volume.

If one draws any control volume around a vertical extent of water ice within a glacier, it is seen to absurd to believe that there is no energy exchange (i.e., heat flow) at the bottom . . . from the ice to the underlaying rock/soil base, or vice versa from the supporting rock/soil base to the ice overlay.

So, it’s nice that Isenko et al. [2005] describe a theoretical process, but it is one without any connection to reality.

Dr. Jimmy Vigo
April 3, 2022 10:50 am

I published this comment in my FB blog site De Facto CHEM:

See the picture of this article? Well, that’s a very common plot covered in basic classes of chemistry, specifically in the first 2 chapters of General Chemistry 2 when discussing the stages that substances go through when crossing the melting and boiling points. It has a few “hiding issues” that the eyes of the lay people thinking that climate change  is a matter of “common sense”: however science reality proceeds from hidden uncommon sense.

This is called a phase change diagram and is used in this article to make a point about the “dangerous melting of ice glaciares”. I haven’t competed the reading but wanted to explain a few details of the science about it:

€ looking at the plot from low left to upper right, below the temperature of freezing zero degrees Celsius, water is solid (ice). Upon warming, the molecules of water start vibrating/moving faster (increased kinetic energy), this is marked by absorption of thermal energy (heat) that can be measured with a thermometer; call this stage 1.

€ on stage 2, the lower flat line is the melting point temperature, where molecules of water re-arrange to a separation between molecules that turns ice into cold liquid water. This is also accomplished by energy absorption but it is a form of thermal energy called latent heat that is NOT measurable with a thermometer.

€ on stage 3, the second or middle inclined steep line of the graph is water molecules moving faster with increased kinetic energy until they reach the boiling point at 100 degrees Celsius at the seal level, and slightly below that for areas that are higher in altitude due to decreased atmospheric pressure. This thermal energy is also measurable by thermometer.

€ on stage 4, the second flat line is the area where the molecules separate even more to convert liquid water into steam/vapor. This is another latent heat not measurable by thermometer.

€ on stage 5, water molecules gain kinetic energy to reach high speeds to keep the vapor stage above boiling, not shown in this plot.

Each of this stages have a separate mathematical formula to calculate the amount of heat needed to bring any volume of water from below freezing to above booming: 5 formulas in total, I’m not going technical here discussing them; if you are one of my ex-students reading, you may recall working on these plots.

The issue is that that the “melting of glaciers increasing oceanic volumes” seems to include technical data on this satages, especially in the section of the complicated cases of crossing the phases from solid to liquid to gas where thermal energy is used to separate molecules to allow the physical change WITHOUT a measurable change in temperature, the flat line areas; see that the line is elongated horizontally but not vertically, meaning that there’s a change in energy but not in temperature like the 3 inclined lines.

I will read the details of this article and share more information about what are they claiming with this more complex and realistic issue of water thermodynamics.

JBVigo, PhD

https://wattsupwiththat.com/2019/04/25/basic-science-4-keys-to-melt-fears-about-ice-sheets-melting/

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