Interesting high def pictures of the biggest of the planets. It used to be big news getting pictures like this. Looking at the pictures reveals how Jupiter is utterly different from how gasses and fluids work on our planet. This is truly an ‘alien environment’ compared to our own pleasant planet. The material flows on Jupiter are ‘crooked’, it snakes and rolls differently probably due to the gravitational pull of the giant planet.
Pictures we see from this distant planet are colorful and detailed. The temperature of the planet as well as its great size has effects that are very different from our water/air/solids planetary materials!
Re-introducing viscosity: The Navier-Stokes equation
The equation of motion of an incompressible, (homogeneous), ideal fluid is Euler’s equation:
Ideal fluids are very nice mathematically. Especially potential flows in two dimensions can be studied using holomorphic functions! One could say that a whole “industry” evolved around the treatment of these kinds of fluid flows. It was even taught to some extend to engineers, before computers took over. A very nice, somewhat nostalgic reading is this:
• L. M. Milne-Thomson, Theoretical Aerodynamics, 4th edition, Dover Publications, New York, 2011. (Reprint of the 1958 edition.)
The assumption of “incompressibility” is not restrictive for most applications involving fluid flows of water and air, for example. Maybe you are a little bit surprised that I mention air, because the compressibility of air is a part of every day live, for example when you pump up a cycle tire. It is, however, not necessary to include this property when you model air fluid flows that velocities that are significantly lower than the speed of sound in air. The rule of thumbs for engineers seems to be that one needs to include compressibility for speeds around 0.3 Mach, see compressible aerodynamics (Wikipedia).
However, the concept of “ideal” takes viscosity out of the picture and therefore also turbulence and the drag that a body immersed in fluid feels. As I mentioned last time, this is called the D’Alembert’s paradox.
The simplest way to introduce viscosity is by considering a Newtownian fluid. This is a fluid where the viscosity is a constant, and the relation of velocity differences and resulting shear forces is strictly linear. This leads to the the Navier-Stokes equation for incompressible fluids:
If you think about plastics or honey, for example, you will notice that the viscosity actually depends on the temperature, and maybe also on the pressure and other parameters, of the fluid. The science that is concerned with the exploration of these effects is called rheology. This is an important research topic and the reason why producers of, say, plastic sheets, sometimes keep physicists around. But let’s stick to Newtownian fluids for now.
The ‘boundary layers’ of Jupiter are very active! We have still, little idea how big the ‘solid material’ of the planet is. The atmosphere may be 50 km thick but that is pure guesswork.
13,000 km of hydrogen and perhaps helium is increasingly compressed until it is liquid. But I doubt the planet’s core is fluids that are frozen. It is too big and I would suggest, too ‘hot’?
Jupiter is so big, if it were several times bigger, it might turn into a star. So what sort of core is there to this ‘gas giant’? We have no idea at all, just guesses.
Jupiter has an extremely powerful magnetic field, like a giant magnet. Deep under Jupiter’s clouds is a huge ocean of liquid metallic hydrogen. On Earth, hydrogen is usually gas. But on Jupiter, the pressure is so great inside its atmosphere that the gas becomes liquid. As Jupiter spins, the swirling, liquid metal ocean creates the strongest magnetic field in the solar system. At the tops of the clouds (tens of thousands of kilometers above where the field is created), Jupiter’s magnetic field is 20 times stronger than the magnetic field on Earth.
Even with the present pass-by of our probe, we know very little about this planet. It took years of sending probes to Mars to discover the truths about that planet.