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Are there any types of wind or waves caused and produced only and exclusively by Earth's rotation? Not influenced by Earth rotation, but produced solely by it?

In the case of waves, are Rossby waves 1 and Kelvin waves 2 examples of that? Like, imagine the Earth as a single planet with no Sun (so no influence by the Sun's heat), no moon (so no tides) and no planetary internal hot core (so no influence by the heat from Earth's internal core). Then assume that somehow water is still liquid and air in its gas form, then, just by Earth's rotation, would there be any waves or wind (even if they would be very subtle)? Would there still be Rossby waves or Kelvin waves for instance? (I found a comment to a question in Quora that indicates that the answer is basically "yes" 3, but no sources are given, so I would like to see if someone could verify that)

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  • $\begingroup$ I haven't messed with wave formulas in too many years... but would think "caused only by" will be key to define... as I'd think you'd need a background difference to exist (caused by heating differential or such)? Though like I said, been too long for me to have much confidence in any answer of my own! $\endgroup$
    – JeopardyTempest
    Commented Aug 30, 2022 at 11:07
  • $\begingroup$ For instance, tides are in a sense "caused/produced only and exclusively" by lunar gravity. Yet the variation in that is due to the Earth's rotation (and the physics of the tides are due to the physics of water and the topography). So would that qualify as only and exclusively?? Would it qualify as caused "only" by rotation (if we didn't rotate, there'd be no tides) There's always connected factors. $\endgroup$
    – JeopardyTempest
    Commented Aug 30, 2022 at 12:43
  • $\begingroup$ @JeopardyTempest No, I wouldn't count tides ocurring due to the rotation of the Earth (although it is indeed a key factor). I meant like the direct cause or the primary source (which in the case of tides is the moon's gravity) $\endgroup$
    – vengaq
    Commented Aug 30, 2022 at 13:42

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Yes. Such a thing is called an inertial oscillation.

Kelvin waves are not examples of inertial oscillations. Kelvin waves balance the earth's rotation against the normal force of a topographic boundary. While some sources say that Rossby waves are inertial waves, they are not actually inertial oscillations in the strictest sense. One example of an inertial oscillation is the formation of the low level jet.

Mathematically speaking, an inertial oscillation can be described by the equation $\frac{d \vec{v}}{dt}=f \hat{k} \times \vec{v}$

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  • $\begingroup$ Thank you for your answer. So, just to confirm, as the question says, imagine the Earth as a single planet with no Sun (so no influence by the Sun's heat), no moon (so no tides) and no planetary internal hot core (so no influence by the heat from Earth's internal core). Then assume that somehow water is still liquid and air in its gas form, then, just by Earth's rotation, would there be any Rossby and Kelvin waves? And would there be any wind (I suppose the answer is affirmative as there would be low level jet currents as you mentioned, but just to confirm)? @BarocliniCplusplus $\endgroup$
    – vengaq
    Commented Aug 31, 2022 at 13:16
  • $\begingroup$ Yes. Rossby and Kelvin waves have indeed been identified on other planets. There would still be wind, because wind is a defining feature of fluid movement. It could even be from surface imperfections, friction, etc. $\endgroup$
    – BarocliniCplusplus
    Commented Sep 1, 2022 at 22:54
  • $\begingroup$ So just from Earth's rotation and nothing else (no other external factors that could for instance create differences of temperature too create winds) we'd still have winds (like low level jet currents) and waves (like Rossby and Kelvin waves), right? @BarocliniCplusplus $\endgroup$
    – vengaq
    Commented Sep 5, 2022 at 10:38
  • $\begingroup$ Principally, yes, although it would be difficult to identify without a perturbation. Even if at steady state, a wave with an amplitude of 0 is still a wave. Like Hooke’s law of springs still holds, even if the spring is at rest. $\endgroup$
    – BarocliniCplusplus
    Commented Sep 6, 2022 at 11:26
  • $\begingroup$ But would waves in the conditions I described have always zero amplitude, or they could also have more than zero amplitude? @BarocliniCplusplus $\endgroup$
    – vengaq
    Commented Oct 2, 2022 at 19:00

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