Timeline for In a non-rotating sphere of fluid heated from the centre, what does the flow look like?
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| Feb 23, 2023 at 16:32 | comment | added | hyportnex | I do not know so I do not suggest anything except I tried to (re)interpret your question following the comment of @AtmosphericPrisonEscape. There maybe some topological restriction between spherical surfaces that prevents the development of cells as compared to between planes, but I have no idea; I am not even an amateur in this field... I have checked some of my old fluid dynamics notes and literature but found nothing about this. | |
| Feb 23, 2023 at 15:49 | comment | added | rake | @hyportnex The situation you suggest (an unstable equilibrium analogous to the Rayleigh-Bénard instability), if it would result from the setup I described, would indeed answer my question. Do you suggest that there would be an unstable, no-flow situation? | |
| Feb 22, 2023 at 15:19 | comment | added | rake | @AtmosphericPrisonEscape thank you for the suggestion (2); I had not thought of expansion. Presumably at some degree of expansion, we will lose as much heat to radiation as we gain from the heating, and so there is no energy source for further expansion, which would store gravitational potential energy. At this point, then, we are faced with the original question. Perhaps this results in a spherically symmetric temperature gradient with no convection, and this system is in an unstable equilibrium? Where, as hypnortex suggests, a perturbation would lead to the formation of cells. | |
| Feb 22, 2023 at 14:48 | comment | added | AtmosphericPrisonEscape | @hyportnex Read again "But when we have no way of breaking the spherical symmetry, what happens?" OP wants to keep symmetry by magic and asks what happens then. | |
| Feb 22, 2023 at 14:37 | comment | added | hyportnex | @atmosphericprisonescape The Rayleigh-Benard instability happens between the plates despite the complete symmetry of the setup, and then the slightest perturbation will cause the build-up of the convection cells. My reading of rake's question is if the same kind of instability can evolve in a spherically symmetric geometry with a sufficiently high thermal and gravitational gradient, and I do not think you are answering that question. | |
| Feb 22, 2023 at 13:16 | comment | added | AtmosphericPrisonEscape | 1.) As in reality no system is perfectly symmetric, convection will always occur. 2.) if you still want to suppress convection just for the sake of the argument, then outwards expansion will occur until a new hydrostatic equilibrium is found. If no new equilibrium can be found, then at some point the system will loose mass into its boundary condition/ infinity, akin to a stellar wind. | |
| Feb 22, 2023 at 11:32 | history | edited | Qmechanic♦ |
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| S Feb 22, 2023 at 9:56 | review | First questions | |||
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| S Feb 22, 2023 at 9:56 | history | asked | rake | CC BY-SA 4.0 |