MATHEMATICAL SCIENCES

For the first time, scientists have found the thermally unstable criterion for “spinning ellipsoidal objects” It may be able to analyze fluid systems in wood, Saturn and black holes


Researchers at the Shanghai Astronomical Observatory of the Chinese Academy of Sciences have deeply analyzed the thermal instability problem in the ellipsoid Boussinesq fluid in rotational self-gravitational equilibrium through theoretical derivation, and obtained for the first time the criterion of fluid thermal instability inside a rapidly rotating ellipsoidal object, which can not only be directly used to understand the convective dynamics of significant non-spherical planets such as Jupiter and Saturn, but may even be used to study extremely flat rotating fluid systems such as black hole accretion disks. On October 28, the relevant research was published in the “Fluid Physics Review” and selected by the American Physical Society as a recommended result by the media.

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3D numerical simulation of linear thermal instability in ellipsoidal fluids Photo courtesy of respondent

“Including accretion disks, stars, planets, the vast majority of celestial bodies in the universe are mainly composed of fluids. Accretion disks and stars are made up of hot plasma, giant planets like Jupiter and Saturn are mostly made up of hydrogen helium gas, and even for rocky planets like Earth, most of the mantle and core beneath the crust flow. Kong Dali, a researcher at the Shanghai Astronomical Observatory of the Chinese Academy of Sciences, told China Science News, “Whether and how these fluids move is crucial to celestial bodies, and even determines the fate and appearance of celestial bodies.” ”

For example, our earth has active geological tectonic movements, such as volcanoes, earthquakes, and plates, because the earth’s core and mantle are very active; The moon and Mars are lifeless planets, which can be mainly attributed to the fact that they have lost their strong fluid movement inside.

There are many factors that cause fluid movement inside celestial bodies, the most important of which is called the “thermal convection” mechanism.

Kong Dali introduced that heat convection is a very common phenomenon in our daily life, such as boiling hot water, as the temperature of the bottom of the kettle rises, the hot water surges upward, and the heat gradually transfers from the bottom to the entire kettle in the process. Similarly, the internal heat of a celestial body and the external cold, if the temperature difference between the inside and the outside is too large, will drive the occurrence of thermal convection, which is called “thermal instability” in fluid mechanics.

Therefore, “How can thermal instability occur in celestial bodies?” What are the different characteristics of heat convection in different situations? “It has become a classic scientific problem that has lasted for decades, attracting a group of scientists to invest in it. However, so far, all studies have ignored the non-spherical shape of celestial bodies due to the centrifugal force generated by rotation, so the plausibility and validity of this series of research conclusions based on spherical approximations have never been tested by any theory or numerical analysis.

On the basis of the rapidly rotating non-spherical stable layered model, Kong vigorously supervised Li Wenbo, a doctoral student at the State Key Laboratory of Lunar and Planetary Sciences, Macau University of Science and Technology, to deeply analyze the thermal instability problem in the ellipsoidal Boussinesq fluid in rotational self-gravitational equilibrium, obtain the analytical solution of the linear critical mode and critical parameters of global heat convection for the first time, and systematically explore the relationship between non-spherical shape and convective dynamic bifurcation properties.

“For the first time, we rigorously consider the shape of a celestial body that deviates from the spherical shape produced by rapid rotation, answer the above two classical scientific questions through theoretical analysis and numerical simulation, and systematically study the control effect of ellipsoidal flattenness (that is, the difference in the rotation rate of celestial bodies) on the conditions for the occurrence of thermal instability.” Li Wenbo said, “Before this work, no method or model had the ability to study oblate ellipsoidal objects, and no scholar could judge how the non-spherical shape of celestial bodies would affect thermal convective motion.” ”

“The results prove that for a rapidly rotating planet with a large flattening rate like Jupiter, the critical parameters of non-spherical rotational convection will vary significantly compared to the results under spherical approximation.” Kong Dali said, “If the non-spherical model that is self-consistent with the rotation of celestial bodies is strictly adopted, the convective transport efficiency inside many fast-rotating planets and stars will be very different from the expectations of predecessors.” ”

In view of this, the American Physical Society pointed out in the media recommendation that fast-rotating planets like Jupiter and Saturn will deviate significantly from the spherical shape. Therefore, studying thermal instability in flat ellipsoidal fluids will help to understand convection processes in these planets. “At the same time, the new method may even help explore extremely flattened disk-like systems such as black hole accretion disks.” (Source: China Science News, Zhang Shuanghu, Huang Xin)

Related Paper Information:https://doi.org/10.1103/PhysRevFluids.7.103502



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