Depends on exactly what you want to know more about.

Fluid dynamics in general An Introduction to Fluid Dynamics by Batchelor is good. Hydrodynamic and hydromagnetic stability is a classic book on fluid instabilities by Chandrasekhar which includes convective instabilities. Introduction to Modeling Convection in Planets and Stars: Magnetic Field, Density Stratification, Rotation by Glatzmaier is good for the more numerical modelling side but also includes theory. Internally Heated Convection and Rayleigh-Bénard Convection by Goluskin is a good book on convection. An Introduction to Magnetohydrodynamics by Davidson is great for some dynamo theory. Self-Exciting Fluid Dynamos by Moffatt and Dormy is a tough read but focused on all kinds of dynamo theory. Chris Jones lecture notes on Dynamo theory are also great.

For double diffusive convection Pascals notes in the previous post are an excellent place to start.

In the words of one of my colleagues "99% of the universe is fluids, the remaining 1% is just details". Fluid dynamics is everywhere, it is actually harder to think of things that do not involve fluid dynamics than otherwise. I extend this not just to geophysical and astrophysical fluid dynamics but all of physics, engineering, biology, medicine, chemistry, and probably more.

That quoted line summarises it quite nicely really. Convection is great for dynamo action as not only does it provide the kinds of turbulent motion that is great for inducing magnetic field, but it acts as an energy source. Prior to any freezing of species one would imagine the fluid to be well mixed and essentially only a single phase homogeneous fluid. For a single phase single composition fluid convective instability sets in under the Schwarzschild criterion which essentially says that the instability sets in when the temperature gradient is larger than the adiabatic gradient (the temperature gradient at fixed entropy, we fix the entropy as temperature is a function of density and pressure and so mathematically the gradient is a partial derivative). In physical terms the way I think of this is there is an amount of heat a static fluid can transport through conduction, but if the amount of heat the system is trying to push through the fluid is above this amount then instability sets in, the convection then transports the heat by physically moving it.

If the fluid also has compositional gradient then we fall under the Ledoux criterion for convective instability and it is easier for convection to set in. This is known as compositional convection or double-diffusive convection. Mathematically the compositional gradient is subtracted from the adiabatic thus lowering the actual temperature gradient required to onset the convective instability. The best way to physically understand this is through parcel arguments which really require figures so instead I will refer to Pascal Garauds excellent lecture notes which are more related to astro than geo. The result will be more efficient heat transport and more energy available for dynamo action.

Another process is two phase fluids which is the freezing out of material. This I know a lot less about as I am more concerned with starts than terrestrial planets but I am in the same boat as the rest of the fluids community in this regard as even the hydrodynamic (no magnetic field) problem has only recently begun to be properly worked on. In simplistic terms it can be thought of in a similar way to compositional convection in the sense that it provides an extra source of energy that can power the dynamo.

The bottom line is, convection is a natural way of producing a dynamo and stronger convection will lead to a stronger dynamo. Thus any mechanism which can aid convection or act as a source of energy/entropy will be beneficial for dynamo.

> However, with evidence from the rock record of a dynamo for the past 3.5-4.2+ billion years, this leaves a long gap where it is more difficult to explain what drove the geodynamo.

Dynamo theory also suggests that the Earth has had a dynamo since its formation (in the impact process that formed the Moon). The reason being is that one can argue that in the present day the Earths dynamo is subcritical which essentially means it can maintain a strong field but not magnetize the core from a weak magnetization state. If this is correct and Earths dynamo is subcritical now then it is almost certainly subcritical throughout its life (since it was more rotationally constrained in the past, faster rotation) and so the dynamo must have existed since the formation of the Moon.

We expect helium rain in the interior of Jupiter.

This is incorrect and neglects the entire fields of colloids, non-Newtonian fluids, rheology, and possibly others.

Jelly is a perfect example of a substance that is both fluid AND solid and is regarded as a colloid possessing the thixotropy property.

This is not really the definition of fluid as there actually is no strict boundary between what is and is not a solid. Indeed as others have noted but incorrectly commented on, things like the mantle, pitch, and jelly are examples of substances that have a dual nature in both being solid AND liquid.

 

To quote George Batchelor (taken from An Introduction to fluid dynamics), "The distinction between solids and fluids is not a sharp one, since there are many materials which in some respects behave like a solid and in other respects like a fluid." ... "But, even supposing that these two definitions could be made quite precise, it is known that some materials do genuinely have a dual character.".

 

What this really means, and what fluid dynamicists recognise, is trying to constrain a substance/object into being a solid or a fluid has more to do with humans desire to define things in discrete buckets and less about the actual physical world.

I have added an edit to this answer linking to your answer in that second one. I do not really follow science news so was unaware of this fiasco! I have since seen tweets of distant colleagues trying to set the record straight as well as one world leading (astro) researcher suggesting that Superman might have been involved...

Given the arrival of another very similar question in this subreddit I suspect you are correct that this paper (or more likely the press release I assume it got) has caused some confusion. I can imagine that this particular sentence "This globally consistent pattern suggests that inner-core rotation has recently paused." which is in the abstract has been misunderstood by a nonzero number of people!

edit to add... when I initially answered the question there was no context text showing just a title. Not sure if the context was added later or this is a weird bug of reddit.

There is a difference between the inner and outer core. The inner core is approximately solid while the outer core is liquid and is the region that produces the geodynamo. The geomagnetic reversals are more related to the fluid motion in the outer core than the rotation (and/or differential rotation) of the inner core.

Yes to be fair I have missed the gravitational coupling between inner core and mantle (actually I was not overly aware of it as I am more on the astro than geo side of fluid dynamics, so my interactions with deep earth people tend to be where there is over lap, i.e. dynamo theory).

Lorentz forces, that is, forces due to the induced magnetic field of the outer cores geodynamo. I believe this is one of if not the leading mechanism proposed to explain this. Another mechanism would be angular momentum transport by thermal convection in the inner core. However, it is thought that the thermal conductivity within the inner core is too large and so the inner core is stably stratified (no convection and hence no radial transport of angular momentum).

Edit - I have been made aware of a rather amusing debacle in the reporting of a recent paper that is causing a lot of confusion. When I answered the question only the title was showing so my answer was very general to what we know of the inner core and its super rotation (although I did neglect the gravitational coupling between the departure of sphericity of the inner core and the mantle). See this threads top answer which is in context of the recent media hysteria!

> magnetic dip north is the location where the magnetic field is oriented vertically

Presumably in general magnetic dip poles do not strictly need to some as a single pair and could come in any number of pairs? I am essentially thinking along the lines that there is no strict mechanism to enforce that only two such locations would exist in a general astrophysical dynamo (for example there are many locations with locally vertical field at the surface of the Sun).

It should be noted that despite it being the well accepted theory there are still many unknowns around the exact details of the process (Cattaneo and Hughes 2022).

To be pedantic, it scales as the inverse cube to leading order as there are infinitely many higher order terms in the Taylor expansion.

(A more expanded explanation of this in words...) From potential theory the force that results from a potential is simply the gradient of the potential. We can Taylor expand the potential to make our lives easier. The resulting leading order force scales as the inverse square and this term just describes uniform acceleration that results in orbital motion. All higher order terms are the tidal force. The leading order term is usually the dominant and hence we approximate the tidal force as an inverse cube law.

It varies continuously. We typically define these regimes in the asymptotic limit of infinite or infinitely small. The frozen flux theorem is strictly applicable for the case of infinite conductivity (infinite Rm) which is non-physical but a very good approximation for most stellar applications.

You have two things to consider here which is materials science and magnetohydrodynamics (MHD). I am not a materials scientist so can not comment on the possibility of an inherently magnetic gas. However, I am an active researcher of MHD so can comment on that aspect of the problem.

> Could one theoretically manipulate such a gas in a meaningful way with magnets? I.e. if gas was placed in a hermetically sealed cylinder with some spinning magnets at the top and bottom, or on the sides or whatever, could you create a predictable vortex / any predictable fluid flow within the tube? Assuming you find some smart person to piece out all the complicated math of spinning magnetic fields and fluids etc.

Yes if such an electrically conducting gas exists (all gasses are electrically conducting actually but only weakly so. They can be ionized to be more so but then they are plasmas). The flow of any electrically conducting fluid can change in response to a magnetic field. This is a major aspect of astrophysical fluid dynamics. We can consider two regimes which are categorized by the magnetic Reynolds number (Rm). This non-dimensional number can be thought of as a measure of electrical conductivity. In the simple case with low Rm then the field strongly influences the flow but the flow does not strongly influence the field. The high Rm case is more difficult as the field and flow are strongly coupled and Alfvens frozen flux theorem is applicable (which essentially says that the fluid flow is frozen to the magnetic field and vice versa). So both cases result in the ability for the field to manipulate the fluid flow. The latter being significantly more challenging.

Star mass only really effects the probability of a planet of a certain mass being formed.

 

We expect that lower mass objects are more common and so there is no theoretical reason to believe and star has a lower mass limit. At the opposite end of the spectrum, we have observed giant planets around M class stars. So we know that even the lower mass stars can form the more massive planets. With the exception of massive stars, we have observed giant planets around all stellar classifications of type A (from memory) or lower mass. However, we do not expect the most massive stars to have any real difference in the mass of planets that can form around them. The reason we do not observe them is simply because it is harder (the stars are very bright and the planets would need to have wider long period orbits). So we expect that all stars can host planets covering the full spectrum of planetary masses (up to 14 Jupiter masses where the classification of brown dwarf begins). What will be affected is the occurrence rate of certain planetary masses as a function of the stellar mass (for example we expect to see less giant planets around low mass stars, although metalicity also seems to play a role).

 

There is a slight caveat to this which is when one considers the grey area of brown dwarfs. Currently, despite what the IAU says, we are not sure if brown dwarfs should be classified as stars, planets, or something separate. At the heart of this issue is the fact that brown dwarfs can form through planetary formation pathways as well as stellar formation pathways (Jeans instability of an interstellar cloud). In particular, gravitational instability of the protoplanetary disc is a planetary formation pathway which can lead to the formation of the most massive brown dwarfs. The requirement for gravitational instability is that the disc is massive which would only be expected around the most massive stars. So if we define brown dwarfs as planets if they follow a planetary formation pathway, then the most massive planets could only form around massive stars.

> It's mostly random how it starts but anything 2m from the corona for example will immediately get torn apart both by coronal mass emissions and by gravity.

It is mostly the stellar wind that results in a pushing of the protoplanetary disc from the host star not magnetic realignment events. More massive stars are hotter and have a stronger wind and hence will mean the minimum distance for planet formation will be further from the star than for a lower mass star. This is not really a random effect as the strength of the wind is a function of the stellar luminosity which in turn is a function of the stellar mass. This inner region where there is no disc is well outside the Roche limit for gravity to cause tidal disruption of a planet during the formation stage.

> You can't have gas giants at those distances because their atmospheres will get blasted off.

This is actually still debated. In-situ formation of Hot Jupiters is not actually conclusively excluded. Indeed, we have observations that are difficult for migration pathways to explain. See Dawson and Johnson 2018 for a good review of Hot Jupiter formation pathways.

> Once you get far enough from that the size of the planets becomes truly random.

I would disagree with this too. The formation of planet mass is not truly random and is determined to first order by the disc density distribution. You simply will not get massive planets forming in regions of low density.

> We think with current science that if you don't get gas giants on the outer perimeter you may not get a ton of smaller planets on the inner perimeter because of comets etc... not being blocked but that's still highly theoretical.

If this is suggesting that gas giants block comets or debris from the outer regions of the system then this too is incorrect. Giant planets cause as much stuff to come into the inner system as they do attract them into their own mass.

Not a rock person but would the theoretical carbon planets not have significantly different rocks?