# Determining Planet rotation period that would allow for global Wind Cell

I'm trying to figure out how quickly a planet could rotate while also having a single air flow cell, such as Hadley cells, that would circle from hot pole to cold pole, etc. as in the case of Tidally Locked Planets and Venus. I.e. what is an estimate minimum time one area of a planet must bake under a star to form the required temperature differential for a single air cell, assuming an Earth-like atmosphere and oceans to regulate it to some degree. Or, how much could you increase Venus's rotational rate without disturbing the single wind cell.

I don't understand a lot of the math around atmospherics, so I'm going off of what I can glean from papers and what we know about Venus and planets tidally locked to red dwarfs. I'm trying to ride the fine line of a planet being somewhat hostile, but still livable. So long "days" and "nights" and near constant winds that are strong, but not Venus's ridiculous wind speed strong nor temperatures that will fry or freeze a person. In the setting I'm working on the subject planet was terraformed for the sake of emulating Earth conditions, so it wouldn't make sense for said planet to have been chosen if the end product was near inhospitable. Desperation/limited options can justify this to some degree, but to the extent of walk outside an instantly die.

As I understand it, a global wind cell would feature a constant, slowly migrating cloud layer following under the hot pole slowly migrating parallel with the equator, creating seasons of "day-summer" and "night-winter". Axil tilt negligible no for simplicity's sake. Any given point on the planet would essentially have constant wind flow that, throughout the planets day-night period, would slowly shift its angle throughout all 360 degrees, ignoring geographical feature of course.

I'm just not sure if I can handwave a "day" of say 90~ 24 hour periods without making the planet inhospitable due to wind strength/temperature. Also, the presence of extremely frequent hurricanes/cyclones formed along the vertical equator? I've read mixed things on that regard. My current work around is focusing on habitable east-west bands between the central hot-pole storm and possible vertical equator storms, but again wind speed and temp remain a concern.

The paper "ATMOSPHERIC DYNAMICS OF TERRESTRIAL EXOPLANETS OVER A WIDE RANGE OF ORBITAL ANDATMOSPHERIC PARAMETERS", seems like it might have some answers, and did shed some light on some things, but a lot of it is beyond me. Seems like at 1/16th rotation rate you already get some pretty significant leveling out of longitudinal temperature differences, at least.

• My answer here feels relevant, but that’s also the shameless self promotion talking Mar 7, 2019 at 7:52
• Also, to clarify - your planet has one hot pole and one cold pole, as in it’s rotating on an axis that constantly points at the star? And the equator is medium temperature? Mar 7, 2019 at 7:54
• Ah, I'll have to go back and edit for clarity. The planet rotates on an axis in the same way Earth does, just much slower. Its not tidally locked, but it is rotating slow enough so that hot and cold "poles" slowly migrate along the equator. Essentially the day cycle is so long that the temperature differential creates one large Hadley cell of winds migrating from hot pole to cold pole, etc., as you would theoretically see in a tidally locked planet, and as we can observe on Venus. Mar 8, 2019 at 0:42
• I guess just imagine increasing Venus's rotational rate, but at what point would the wind currents divide into multiple Hadley cells. Except with earth like conditions and similar temperature conditions. I saw your previous answer, and in a lot of ways that would make my job easier lol, but I still threw this out here in case someone had an answer. Mar 8, 2019 at 0:44

## I don't think your planet will have Hadley Cells at all

Hadley cells form due to the conservation of angular momentum as fluid particles move about an axis or rotation, getting either closer to the axis or further away from it. They're the result of large-scale air movements toward or away from the axis of rotation, as the spherical shape of the Earth and the equatorward movement of the air decrease the radius of their rotation, thus increasing the speed at which they rotate about the axis.

However, in your setup, the "hot" pole and "cold" pole aren't aligned with the axis of rotation. In a tidally-locked setup, the planet's still rotating about its vertical axis, it's just doing so with the same period as the period of revolution about the star. Air movement will be (near the surface) toward the "hot" pole and away from the "cold" pole, but the main air movement isn't in such a fashion as to significantly increase or decrease the fluid particle's radius.

Because the overall movement of fluid particles isn't significantly changed by their movement toward or away from the poles, there doesn't seem to be any reason for them to break up the single circulation cell that would form - there's no large-scale changes in radius or speed to account for. Someone else may actually be able to run the formulas on this, but I'm pretty sure that tidally locked planets won't have Hadley Cells at all. Cool question!

• Any idea how slow the planet would need to rotate in order for Hadley cells not to form? Mar 9, 2019 at 4:30
• @QuiGonJon Rotate about the axis perpendicular to the plane of revolution, or rotate about the axis that passes through your “hot” and “cold” poles? Mar 9, 2019 at 16:02
• About the axis perpendicular to the plane of revolution Mar 10, 2019 at 7:24
• Um. That’s what I was trying to point out in my answer - you can spin it as quickly or as slowly as you’d like, because the air isn’t flowing in such a way as to be broken up by conservation of angular momentum. Mar 10, 2019 at 15:51
• I think there is some miscommunication going on, or I'm just horrible misunderstanding something. How about this. Slow down earths rotation. Do we know when air cells would convert to something we would see on a completely tidally locked planet? From papers I've read when you get to 1/16th rotational rate the air cells are much less prominent (might only be 2 at this point?) but still there. I could probably handwave 1/32 rotational rate, but I'm invested at this point lol Mar 11, 2019 at 13:28