Anna suggested a gedanken experiment that would mimic a real experiment she thinks she can do. She would like to know the theoretical outcome under two circumstances: one where the working fluid is moist air, another where the working fluid is dry air. The purpose of this post is to figure out if this is the experiment Anna V is considering. If it is, I’d like to know
- What we would learn from doing the experiment (or the theory.)
- Whether or not anyone thinks this has anything to do with any of the claims being made by Makarieva about the origin of wind. (Because I’m trying to figure out the precise, essence of the issue that “matters” in that paper, and I’m trying to see if people can tell me what it is supposed to be.)
The, if this is the problem Anna V thinks will clarify something for her or if anyone thinks it will clarify something in Marieva, I’ll be happy to do it. Or, we can modify it to address something someone really want to learn. (Doing it and explaining it is slightly tedious, so I want to do the appropriate gedanken, and explain that not be doing any number of not very well explained problems, guessing at assumptions.)
Below are three pictures to illustrate a gedanken:
The figure to the left represents a vessel of known volume that we fill with some fluid. It might me dry air (in a second experiment it would be moist air.) We will know the pressure, temperature and volume. The temperature and pressure will be that of the surrounding room. We seal the thing.
In the center figure, we compress the container down to some particular volume doing so very quickly so there is no heat transfer. In my picture, I do this by pushing down on a piston or putting a weight on the top. (In anna’s she squeezes a balloon to pressurerize it.) We anticipate work can be done reversibly. We’ll squeeze until we reach a certain volume V1.
The temperature and pressure will rise… but we want to find out how much. So, I compute that. (First for air, then for moist air. We can compare results in a table.)
In the figure to the right. I then put this thing in the freezer. It cools. I don’t know what order I do things, but somehow, at the end, Anna’s balloon has shrunk enough that the elastic exerts no pressure– that’s why the arrow is gone. The pressure in the balloon equal that in the freezer. In my case, I somehow devise this thing to allow the force exerted on my container to go to zero when the container shrinks enough. (Maybe I rig up some sort of spring device? Beats me. )
In either case, I know the pressure in the container. I know the mass. I know the temperature equals that in the freezer. So, Anna wants me to find the volume.
Anna: Is this the problem you want me to do? What do we want to learn? Or do we want to do something else? Because this problem is totally do-able. I’m not sure what we learn about climate models, hurricane models or Makarieva, but it’s do-able! But if it’s not the problem you want done, let me know so I can do the problem you really want done.
Not sure I see the connection to Makarieva’s water-mass-loss wind paper, but OK.
Lucia,
I think the essential question re the AM paper is whether condensation in rising air tends to cause contraction, bringing air in from outside (which AM cites as the energy source for a hurricane, and I think winds in general), or to cause expansion. ACPD referees (of M08) think the latter.
I think the real question to try to get at is what happens at the moment of condensation. There has been much argument about whether this or that is adiabatic, but that’s really irrelevant. If the latent heat causes expansion at the time of condensation, and there is later contraction as the LH is transferred elsewhere, then that contraction is best attributed to the cooling process, rather than the condensation.
So in your post, “very quickly” is a key. It avoids mixing the concepts.
I’ve done the analysis here for an adiabatic cylinder with a piston seen as rarefying, not compressing. The math works both ways, provided there is a mist that can evaporate on compression.
Noel Barton has posted the table I think you want here. He has plotted the numbers here.
SteveF–
I’m not sure what any of the thought experiments in the discussion at TAV have to do with Makarieva’s water-mass-loss wind paper. But, there they are.
Do you think you understand section 4? What’s the geometry corresponding to all the stuff soon after
I mean.. I know there are “x” and “z” axes. I made a few sketches… guessed.. gave up at different points.
Lucia,
Is that just an attempt at describing a flow with (1) stagnation point at the origin, perhaps? Or maybe (2) convergence at the origin leading to vertical flow? Either (1) u = x, w = -z or (2) u = -x, w = z? I think the converging flow probably makes more sense, but I haven’t bothered to read any of the paper, so just a SWAG.
Lucia,
.
I understood that flow along ‘x’ and ‘y’ (both horizontal flow) were assumed to be essentially identical, and so the problem could be framed as a simpler 2-dimensional (horizontal and vertical) flow problem.
.
But the more I looked at what AM was saying, the more it seemed to me a purely mathematical exercise, somehow disconnected from the dominant physical process of adiabatic expansion and associated cooling condensing water out of moist air. While there is for sure a modest loss of gas volume due to condensation along the moist adiabat, the released latent heat of condensation and continuously falling pressure means that at all times and all places a rising parcel of moist air parcel is continuously expanding until it reaches the top of the convective system. As I understand AM’s theory, the latent heat of condensation makes exactly zero contribution of energy to a system like a hurricane. This strikes me as, well, a bit nuts.
.
I have not invested the many hours it would take to try to follow the math so that I could try to identify where the math disconnects form the physical reality, and I am not sure I could, even if I made that time investment. But I am pretty sure that transport of latent heat is almost certainly a major contributor of energy to systems like hurricanes (and thunderstorms), and any theory that claims otherwise is almost certainly wrong. At one point AM told me that heat was not transported form the ocean surface to the upper troposphere by hurricanes (and then lost to space).
.
That was when I was pretty sure she is wrong, since satellite images show huge volumes of air flowing out of the top of a hurricane, forming wispy cirrus streaks that radiate from the center of rotation with a characteristic slightly anticyclonic curvature. Vast convective air flows combined with coriolis force is all you need to form a cyclonic system.
.
It is true that mass loss from precipitation is not treated exactly by climate models (Gavin confirmed this), but the associated errors in mass flow can be not more than a few percent.
Andy– The problem arose when I was trying to sketch a first guess, and then tried to get things to be consistent as I traveled through section 4. Something must be unique about x=0 (The center point.) I thought: A stream tube in the center? But really, the paper ought to say a bit more in words or a sketch, and I couldn’t quite tease it out given some discussions as the argument progresses.
If someone else had figured out the geometry, then that might help me. Then I could figure out if the text is clear, but I’d missed something, or if it really isn’t clear and I could suggest Anastasia add a specific figure and words. I’m going to look a bit more tomorro.
Lucia said “•Whether or not anyone thinks this has anything to do with any of the claims being made by Makarieva about the origin of wind. (Because I’m trying to figure out the precise, essence of the issue that “matters†in that paper, and I’m trying to see if people can tell me what it is supposed to be.)”
Maybe I am underestimating what Makarieva is trying to express, but I don’t think she is saying that condensation is the origin of wind. Rather, I think she is trying to provide theoretical justification for why condensation has been a previously overlooked and potentially significant driver for the development of not only vertical mass movements but also horizontal mass movements in the atmosphere.
I am not sure how much help all of these Gedanken type thought experiments are since they seem to rely on a closed system when condensation in the atmosphere occurs in a essentially an open system constrained primarily by gravity.
Good morning 🙂 It was 20C outside all night due to a low and southern winds from the Sahara. Not very usual but not unknown for this time of the year in my corner of the world ( Greece)
So to the question:
The above proposed gedanken will answer whether there is drop in pressure from condensation with heat transfer allowed versus the dry air case. I believe from my two bags experiment that the answer is yes, and it does not answer the basic question on the Makarieva et al proposition, which I think is this:
The established models use differential heating induced circulation which depends on increase in pressure from condensation during adiabatic expansion of parcels of air. Makarieva proposes condensation induced circulation due to the pressure drop from condensation during adiabatic expansion of saturated air.
Both cannot be true at the same time, so one needs an experiment that will simulate a parcel of air expanding adiabatically.
Two parcels/, one with dry air for control and one with humidity should be allowed to expand adiabatically, in a real experiment. In a real experiment I would release from a plane two well insulated balloons with strong walls and measure the difference in expansion/compression visually :; . Maybe from a high flying helicopter? Condensation should happen spontaneously due to the pressure drop and consequent supersaturation in the second parcel.
In a gedanken one piston experiment should be enough, as long as latent heat is taken into account: After expansion, at condensation does the pressure rise or fall from the previous expanded value? The piston height immediately after condensation should measure this.
I think.
Suppose we find nothing happens in the adiabatic experiment, i.e. pressure neither goes up nor down due to condensation.
This would be an indication that the adiabatic assumption for rising parcels of air in the atmosphere cannot be valid and then other non adiabatic circulation mechanisms have to be examined since there are strong winds generated.
In non adiabatic conditions then the experiment you describe above should hold, heat evaporates, cold condenses, so it is a second stage gedanken, if the first gives stasis .
Then one has to go to the complicated circulation and transports in the A.M. model.
Lucia, have a look at this piston experiment
(He has built a cooling engine using passive thermodynamic principles.)
If the process is completely reversible when the adiabatic conditions hold, how can the parcel of air expanding adiabatically interact with the rest of the atmosphere and generate differential heating?
If someone else had figured out the geometry, then that might help me. Then I could figure out if the text is clear
Well I have read the paper and redid all the maths . N.Stokes did so too I believe .
Personnally I have found it crystal clear and could derive every equation in the paper rather easily, what of course contributes to the overall impression of clarity at least for me.
There is only one exception : the equation 34 .
Actually for the casual readers or those who only looked at the summary , the whole paper is concentrated in this one equation .
This one has to be derived independently from general considerations (e.g conservation laws ) .
While I can follow what Anastassia says about the justification of 34 , I cannot derive it . I still try .
Another important point that has also been noticed by some bloggers is that her system is not closed (the velocity components are free variables) .
It could of course be closed by taking 2D N-S but Anastatssia didn’t try .
So u and w are only “constrained” by physical considerations and averages . No mathematics here .
As for the geometry .
It is semi infinite horizontal planes what is the classical way to go from 3D to 2 D .
Lorenz does it with his chaotic equations too – one assumes that 1 of the 3 dimensions is infinite .
So I see her geometry as horizontal planes with X finite but Y infinite so that nothing depends on Y (or that every plane parallel to xOz shows the same solution what is a similar thing) .
Her boundary conditions are given by the plane of equation z = 0 .
The origin is irrelevant , it’s somewhere on the above plane .
Of course a N-S practician immediately notices that there can’t be any horizontal curls . A hurricane in this model would have 5 km height , 200 km width but an infinite size in the horizontal direction orthogonal to the width .
It’s a model of a flat planet extending infinitely in one direction .
Or a sphere where one says that only latitude matters and nothing is function of longitude .
Last but not least , this 2 D model and this geometry are chosen because the primary interest of Anastassia is to analyse flows that loop in a (random) plane containing the vertical (Oz axis) .
OT, but “Contact Lucia” is on the fritz.
On the volcano thread there was conversation about James Annan’s $10,000 bet with the Russian solar physicists. The ending dates of 1998-2003 and 2012-2017 seemed odd, being 6 years if inclusive, so I asked him. His interesting answers in the comments:
http://julesandjames.blogspot.com/2010/11/jules-pics-11082010-090400-pm.html#comments
Re: TomVonk (Comment#59720)
Thank you for this comment.
To have a better understanding of the whole picture (and the role of Eq. 34), one might choose to have a look here. This is a (formally) different view on the origin of a pressure gradient caused by mass removal of ideal gas. This derivation does not specify the nature of the sink term S altogether, it just presumes that some mass sink exists.
Tom–
Note: Equation 34 is in the section find troubling. 🙂
Let’s look stuff surrounding. 34:
The section begins by giving a very terse description of a geometry:
Based on what’s said:
* No time dependence. So ∂η/∂t = 0 for any η.
* 2-d (looks cartesian). I am assuming “z” and “x” have dimensions “length” and velocities have dimensions lenght/time.
* mixture or air and water.
There is no figure in the paper, but Anastasia has now provided this:
Continnuing from (Comment#59729),
We then get conservations equations for dry air (32), water vapor (33) with what appears to be a the mystery constitutive equation for the condensation source term (34) which tells us both that
S= w( ∂Nv/∂z – Nv/N ∂N/∂z ) and
S= wN( ∂γ/∂z)
It’s easy to show that N( ∂γ/∂z)=( ∂Nv/∂z – Nv/N ∂N/∂z ) follows from the definitions given way back in equation (2) that γ = pv/p where p is pressure for moist air.
At this point, what I, as a reader, think I know about 34 based on inspecting equ. 34 and discussion up to (34):
* The equation, as written, doesn’t merely say the partial pressure water vapor is a function of local temperature (possibly the vapor pressure). That would be Pv(x,z) = F(T). (That would involve some phenomenology)
* The equation doesn’t seem to be based on anything having to do with phenomenology of condensation.
*It’s something else.
The text then starts to explain (34)
I italized the part that makes me to “huh”. So, is there an unstated assumption that Temperature is a function of “Z” only in this thought experiment? I’m under the impression this is mostly a new geometry introduced in section 4, so I go back to the top of section 4 to see if this has been mentioned before: Nope. (So, is this a result from 3.2 where we were considering a hydrostatic pressure variation in a column? Are we supposed to carry it over? )
So, I now have two questions:
1) From now on, do we assume temperature is a function of “z” only?
2) If yes, is this a reasonable assumption given that the vertical velocity is different in different locations, so air at different “x”s has risen different amounts? (And what will it say about heat transfer etc.)
Continuuing (on the issue of T=function of (Z) only– and other things.
So, here she is suggesting 2 conditions that would permit T=function(Z) only (and likewise Nv = function of (z) only.)
With respect to the first possible condition: Is influx of water vapor via evaporation fro the surface sufficient to result in Temperature and absolute humidity being a function of elevation only? If stuff is rising and expanding at one (x) location, but not rising (and therefore not expanding) at some other value of (x), won’t this cause the temperature to vary as a function of (x)? (I get that we can assume T=constant at z=0. )
As for the 2nd possibility: Wouldn’t the pressure field moving violate the assumption stationarity? (i.e. we assumed ∂η(x,z)/∂t = 0 for all η ) If so, then equations (32) and (33) are now incorrect.
Re: lucia (Nov 10 12:39)
Lucia,
I tried to derive 34 round about here on Jeff’s first thread. I think it follows from 32, 33 with some ignoring of horizontal derivatives. It’s been reasoned in a first-principles way for a vertically rising flow, but from the same physics (mass conservation). It isn’t independent.
What then happens (using 32,33 and 34) is that after the algebraic manipulations, the unstated assumptions come back as results – the horizontal pressure gradients, etc.
There was some discussion of this on Judith’s thread too.
Anna v
I’m not seeing enough information in that comment to tell. Why do you a cooling engine would involve adiabatic conditions? Adiabatic means “no heat transfer”. So, a cooling engine cannot be adiabatic.
Anyway, I’m not sure what you are asking me.
Re: lucia (Nov 10 12:33),
Doesn’t that geometry imply a horizontal pressure gradient? I don’t see how you get a horizontal pressure gradient and not have a horizontal temperature gradient too.
Dewitt–
Do you mean in Anastasia’s figures? Maybe.
Her text seems to tell us the horizontal gradient in vapor pressure is zero. I assume she doesn’t set the horizontal pressure gradient zero. After all,one of her goals is to compute the horizontal pressure gradient and show it’s not negligible.
Re: lucia (Nov 10 19:51),
That can’t be right. We know the horizontal pressure gradient isn’t negligible. The pressure at the center of the hurricane is less than the pressure outside the hurricane. I’m pretty sure that it’s the cause of the pressure gradient that she questions. The conventional theory, if I understand it correctly, is that the pressure drop is caused by air movement driven by heat transfer from the surface to space. M10’s thesis is that the pressure drop is caused by water vapor mass loss and that heat transfer can be neglected, to first order anyway. One problem I see with that thesis is that I don’t see how it explain how a hurricane originates.
Re: lucia (Nov 10 15:12),
Sorry if I confused you. The reference to the engine in the parenthesis was in order to introduce the author. He built the piston experiment while studying his engine. The engine is not adiabatic.
The comment was referring to differential heating creation of winds, where the adiabatic hypothesis allows them to say that latent heat remains in the parcel of rising air.
Anyway the discussion has branched off to the new thread.
Sort of off topic but I know you are a cat lover!
http://www.bbc.co.uk/news/science-environment-11717510
“I would say cats know more about fluid dynamics than dogs.”
Dr Roman Stocker. MIT.