# Question about the physics of hurricanes

I've a basic misunderstanding about the formation of tropic cyclones. From the absolute point of view, cyclones form in order to conserve total angular momentum - air masses at different latitudes have different specific angular momentum due to earth rotation (their distance from the earth's axis of rotation is different), so when a low pressure system forms, radial air flow towards the center has to rotate (in the rotating-earth frame of reference) cyclonicaly in order to conserve angular momentum. Putting it in a different point of view, the Coriolis force deflects the radial winds to create the "tropic cyclone" system.

What i don't understand is this: one can say that the circulation system has angular momentum in the direction of the local vertical at the eye of the storm (it's local zenith direction). But such angular momentum vector has component in a direction perpendicular to the earth rotation axis! so it cannot conserve angular momentum. So what am i missing here? is it something in my basic understanding of the Coriolic force? or maybe my knowledge of the physical structure of the storm is lacking something.

I'd also like to know if there are models that predict maximal tropic storm size as function of latitude. I read the thermodynamic model in wikipedia excellent article on tropic storm, but this model gives upper bound about wind speed and specific rate of energy production (rate of energy production per unit area of sea surface), and doesn't give information about the size of the storm. I think that for estimating sizes one needs to use mechanical conceptions.

• It is not a geostrophic balance that leads to formation of hurricanes. It is a cyclostropic balance.
– user1066
Sep 9, 2019 at 7:50
• As far as I understand it in this mindset (it's been a while), you're right to say that a vortex (outside of a point vortex at the Pole) doesn't truly conserve angular momentum across the vortex... this results in secondary phenomena due to variation in the angular momentum (Coriolis parameter) by latitude within the circulation. However it's worth noting that the change in angular momentum across the vortex should be comparatively small vs the angular momentum of the vortex if it is a well developed one... Sep 9, 2019 at 19:22
• ...but such asymmetry in the change in angular momentum would still have impacts... I believe the primary resulting term is a cross-vortex motion called the Beta Effect, which results in northwest motion in NH (southwest in the SH) at low latitudes at least. I'd think it also has higher-order terms that distort or even imbalance the vortex, but that they are too small in comparison to the scale of angular momentum continually imparted into the vortex to be of large consequence. Sep 9, 2019 at 19:32
• When it comes to size, I don't remember seeing any work on "maximum potential", though this paper Observed Tropical Cyclone Size Revisited seems to touch on some factors. Thing is the radial structure of the wind in vortices seems to vary quite a bit based upon factors like the structure/source of the initial trough, surrounding pressure fields, and the cyclone energetics, such that I believe even similar MPI-reaching storms have widely varying sizes... Sep 9, 2019 at 19:45
• ...and then when tropical cyclones transition to a cold core balance structure (extratropical transition) it seems to greatly outweigh the other factors and alter the vortex size much more, so such "potential" may end up being of relatively little consequence in many regions. Now MPI was a bit beyond me even way back when... so I may be overcomplicating it all and there may be a simpler answer (that's why I didn't find my input useful enough to write it into an answer!) Searching Kerry Emanuel's pages or journals.ametsoc.org may be good spots to start to see if more work has been done Sep 9, 2019 at 19:49