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Blackboard on Eq 34

Posted by Jeff Id on November 11, 2010

The M10 hurricane paper discussion is continuing now at the blackboard.  I haven’t mentioned it much but I do consider it one of the best examples of blog based science on the internet.  As usual, I’m way way too busy to have fun, but the discussion has lapsed into the derrivation of eq 34 which is what Nick initially brought up when the paper was first being discussed here.

1. kimsaid

I think it is just remarkable that we don’t know the answer to this fundamental question.

What else don’t we know? Don’t answer that.
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2. Geoff Sherringtonsaid

On a light note, Jeff, in reference to the derivation of eqn 34 you wondered elsewhere if condensation affected aircraft drag and you gave a nice image of a fighter leaving contrails. I’ll see you and raise you one. (No attribution possible for the following – it just appeared in my emails).

More seriously, it’s looking like Anastassia is on to a previously missing part of the overall storm mechanism. From reading early accounts of the difficulty of pushing piston aircraft through the sound barrier, I can envisage that there was an extra force to be overcome. Perhaps this is part of it.

This is neat example of real progress through blogging, no matter which consensus emerges. Nice to see good faith with good science.

3. DeWitt Paynesaid

Sorry, the <a href="“>parrot is really dead. Eqn. 34 in M10 is simply wrong. Anastasia’s assumption that dry air in a moist packet is hydrostatic while water vapor isn’t is not physical. Not to mention that Eqn 34 leads to a variety of impossible conclusions. See comments at The Blackboard here and here.

4. Anastassia Makarievasaid

#3 DeWitt Payne,

I really feel you are being unfair to me. First you asserted that dry air can be in hydrostatic equilibrium even if vapor is not, and the entire air will be nevertheless in equilibrium. I explained to you that this is not so. You insisted, but I explained again. You did not respond.

5. Anastassia Makarievasaid

#3 DeWitt Payne,

I really feel you are being unfair to me. First you asserted that dry air can be in hydrostatic equilibrium even if vapor is not, and the entire air will be nevertheless in equilibrium. I explained to you that this is not so. You insisted, but I explained again. You did not respond.

Then I encouraged you to build the graphs which show that when vapor is not hydrostatic, dry air is not hydrostatic either, provided air as a whole is hydrostatic. You did, and we have all seen that. I emphasized this point. Now you ascribe your original misunderstanding, “dry air in a moist packet is hydrostatic while water vapor isn’t”, to me. I think that you simply got confused in who thinks what about what.

See my other comments on “impossible conclusions” etc. in the Blackboard thread(s).

Dewitt

7. phinniethewoosaid

@Anastassia

I think the attention around your report is interesting, and your new insights and equations proposals are certainly valuable.

A possible issue with the equations might be they are not all standardised for the same S3 euclidean space (or whatever space is considered) And they have to if the are used in 1 set of Ordinary/Partial Differential Equations.
Variables (rates like S, w) should be compatible and defined in the ongoing Calculus, ie all can be brought/shrunk back to differentials in a same infinitesimal volume dV. Not sure if that is the case with eq 34 and all the references to “balloons” in discussions look suspicious. I Thought a small stiff same cartesian cube should be considered when proposing all equations.
It is possible to make a list of correct equations but that some equations in the list are not in same context.

8. phinniethewoosaid

note I am not insisting on integration/solving with rigid cubes..:)

I guess what i am at is that in the multiphysics problem of thermodynamics (state spaces, multidimensional) with say fluidmechanics in E3, one has to be careful with quantities in equations then (interior vs exterior, d’s versus deltas)

as an innocent passerby on the web, I stumbled upon and found this page intriguing:
http://www.av8n.com/physics/thermo-forms.htm

I guess it is ok to use a diversity of equations and laws in a text, but all have to be aligned for a purpose (eg throwing them in a finite element mincer) . not saying you’re not doing that, but certainly in the commentary and the many anecdotes brought up, things get comfusin.

De Witt, what do you think?

9. DeWitt Paynesaid

Mostly, that’s beyond my pay grade (which, since I’m retired, is zero). The problem is that AM hasn’t specified the path either, as far as I can tell. Maybe there is a path where equation 34 is valid, but I don’t know what it is, nor does anyone else who are far beyond my pay grade in this area like lucia, Nick Stokes, Jim D and Tom Vonk. For anything simple, equation 34 violates conservation of mass. Therefore anything based on it is probably false also.

Note that for a moist column of air, the pressure at every level with no vertical flow is higher than for a dry column. That means the pressure gradient force is outward, not inward. If you allow condensed water in the moist column to fall back to the surface, there is more than enough free energy in the moist column to push the dry air at the top of the column back to the surface at higher temperature where it can evaporate more water and continue the cycle, as long as there is horizontal movement to warm water. IR imagery clearly shows that hurricane tracks leave cooler surface water behind them (see here for example).

10. DeWitt Paynesaid

You say here:

Suppose we have p(z) and T(z) defined by the moist adiabat and Nv(z) defined by T(z). Let us now take a balloon with surface air and surface gamma. We raise this balloon in the predefined pressure and temperature field and condense vapor out of it as prescribed by s (8). What we found at a certain height z is that Nv/N within the balloon do not match the equilibrium moist adiabat Nv/N.

That’s wrong and I’ve demonstrated that here. Nv/N does match the moist adiabat and (8) correctly predicts the precipitation rate for a given vertical velocity. Your (34) doesn’t.

Then you state here:

In order that a hydrostatic equilibrium is maintained, one needs to add air in the column where condensation takes place. This is what is taken into account in Eq. 34 and not taken into account in Eqs. (1)-(8).

That’s wrong as well. There is no need to add air to the column. The pressure gradient for a static column is positive, not negative. For a moving column, the pressure gradient will only be negative at the surface.

And then there’s this:

Allowing dpv/dz to have a different value than dpd/dz does not violate hydrostatic equilibrium. dp/dz is still equal to -rho g as long as the vertical velocity is zero, or at least very small.

This is fundamentally incorrect. I would suggest that you give this a second thought. As you know, rho = rho_v + rho_d. If dp_d/dz = -rho_d g, but dp_v/dz not equal to -rho_v g, it is clear that total air dp/dz is not equal to -rho g. In this case vertical velocity cannot be zero (in fact, it will be huge, this is calculated by MG07 here, Section 3). Approximate hydrostatic equilibrium that corresponds to small velocities is incompatible with hydrostatic equilibrium of dry air.

Where did I say that dp_d/dz = -rho_d g? I can’t find it. I believe that’s called a straw man. Hydrostatic equilibrium is defined as dp/dz = -rho g. That means that dp_d/dz + rho_d g +dp_v/dz + rho_v g = 0. My calculations show that is indeed correct with no need for addition of any air anywhere in the column. My calculations also show that the pressure at every level in a static moist column is higher than in a static dry column. The pressure gradient is positive not negative so there is no driving force for addition of air to the moist column. Precipitation of liquid water in the moist column will not change that although it will reduce the pressure gradient slightly. But it will not make it negative anywhere.

11. anna vsaid

I think the hurricane trail will be cooler with either model.

Evaporation in Anastassia’s and all that rain dropped in the water should cool it.

12. DeWitt Paynesaid

I think the hurricane trail will be cooler with either model.

Possibly. But from what I understand from AM’d postings, the loss of heat from the track should be balanced bu\y a gain in heat elsewhere. I don’t see that. Of course I could be misunderstanding AM. If I went looking, though, I’m sure I could find posts where she says the heat engine model is not valid, or is not important. If heat isn’t lost to space, then it must show up elsewhere on the planet. If heat is lost to space, then the heat engine hypothesis is valid.

13. DeWitt Paynesaid

Jeff,

We really need an edit function for typos. You might talk to lucia about her’s. It’s working again.

That’s AM’s, not AM’d.

14. anna vsaid

The Climate Audit assistant works here too. It gives a preview option.

I use Firefox and it is an add on.

15. phinniethewoosaid

I refer to :
http://www.av8n.com/physics/thermo/intro.html
Feynman is mute in his expositions on Thermodynamics mixed with Newton, so let’s take this Caltech geezer then :)

-As you see from figure 0.1, the GCMs are in the pink zone :fluid MECHANICS (E3).
-This blog and certainly many of its comments are in the blueish IT zone (mostly jockeying around with Shannon NOISE)
-Thermodynamics (pulsating balloons sailing past(through?) dewing water droplets and maybe floes and hails of evaporating ice) are in the dark blue.

The 3 hv to be merged in a satisfactorily way, I am not sure it is possible at all ?

PS note the GCMs are maybe in yet some other zone of multiphysics I do not know,
but when we want to know where WIND (motion in E3 on a ball) comes from,
we certainly have to frame equations in xyz in the end?

Is there a post explaining how to use Latex here?

16. DeWitt Paynesaid

I have that as well as killfile. But you can still miss a typo when proofreading even in preview mode, which is what happened to me above.

I’ve tried to use Tex before with no success. It obviously works here.

test

$\frac{\partial(\rho_l V_t )}{\partial z}$

17. DeWitt Paynesaid

That actually worked. The Tex button in CA Assistant says leave a space at both ends. Don’t. There should be a space after the latex, but no space before the dollar sign at the end.

18. RuhRohsaid

Winnie; Who’s calling whom an old Tech “geezer” ?

Anyway, thanx for that terrific tutorial, avail as 187 page pdf at

http://www.av8n.com/physics/thermo-laws.pdf

that does not show as broken.

I clearly have some more remedial reading to do here…

Jeff, I don’t know how you maintain such a high S/N ratio on an og-noing basis.
The Airvent is still my first-checked page for ‘whassup’ in the climateconflict, ever since I found that link to the Russian server shortly after it was posted.