Saturday, October 29, 2005

The butterfly flap.....

has spread from Roger Pielke Senior's blog to Stoat and James' Empty Blog and sci.environment and who knows where else. Along the way, we discover that RPS (just lazy, not disrespectful, I save that for RPJ), believes that momentum is not conserved in the atmosphere. Mr. Rabett stuck his oar in briefly, saying that #22

"Dissipative forces exist on a macroscopic level, but then again, so do infinite heat baths. On the other hand, they result not only in the loss of conservation of momentum, but also of conservation of energy. However, as soon as you start looking at the bath in microscopic detail, dissipative forces disappear and you regain the conservation laws.

To the extent that a model treats part of the system as an infinite bath for energy or momentum, you can beat the conservation laws but you have to be careful in the analysis lest you push the assumption too far. It appears to me that the surface of the earth is such an energy bath for atmospheric dynamics models, as the surface of a pipe is for fluid flow. However, as long as the perturbation stays away from the wall it will not dissipate. Since the surface is in all climate models, and since the models show that small perturbations in the atmosphere propagate, for the purposes of this discussion, the butterfly flaps."
 a position that I maintain, and sensible people agree with. Within the atmosphere, momentum IS diffused to larger and larger volumes so that any particular molecule has an infinitely small share, but it IS conserved. Along the way, Eric Swanson in sci.environment raised the point that radiative emission might dissipate momentum. Certainly greenhouse gases in the atmosphere emit photons.

Eli Rabett has intensively consulted with the techno-bunny elite on this point. Along the way, we came up with some wrong answers, drafted a few papers for the journal of last resort, and finally found an answer which was so pleasing that we went out for a few beers to celebrate. My colleagues have designated me to provide the answer to a world waiting with baited breath (have you ever kissed someone who spent the day swallowing worms??).

Momentum is clearly conserved on emission of a photon, it is merely partitioned between the molecule and the photon. De Broglie came up with the idea that photons have momentum, and this is certainly shown by the Compton effect. So what happens in the atmosphere? As usual, there are three cases.

IF the photon is absorbed by another molecule in the atmosphere, momentum is conserved, merely transferred from one molecule to the other. This is boring

IF the photon is absorbed by the surface or in the ocean then momentum is conserved, but since roughly the same number of photons strike the earth going north or south, or east or west, there is no net change in the momentum of the earth and it may be treated as an infinite dissipative sink for momentum. This is uninteresting**

IF the photon is emitted to space, then momentum is transferred from the atmosphere to an infinite sink which is REALLY dissipative. This is both surprising and pleasing (to me, but then again I blog Saturday night, so my standards may not reach yours).

**This is not the case for energy transferred from the atmosphere to the earth by radiation. This is not uninteresting.


James Annan said...

Hi Eli,

A minor detail in the whole argument, but why will a photon emitted to space dissipate momentum in the atmosphere? Isn't it as likely to create it, and more generally, the net effect wil cancel to zero?

EliRabett said...

What I meant to say, is that the momentum is lost FROM the atmosphere. You raise an interesting point. Since the component of the momentum in the vertical is positive (toward space) for all photons lost to space and the earth is spherical the net is zero (the earth abides), but locally it is not.