The competing effects of destabilizing thermal gradients and stabilizing compositional gradients (i.e. double-diffusive convection) play a major role in the structure and evolution of giant planets. They relate to the low observed heat flux of Uranus, the high metallicity of the envelopes of Uranus and Neptune, the erosion of the cores of Jupiter and Saturn, and the large radii of some observed transiting exoplanets. Extensive studies in the context of global oceanic mixing are not applicable because of the wide discrepancy between the governing parameters in the two cases. This collaborative project will perform state-of-the-art three-dimensional high-resolution numerical simulations of double-diffusive convection in the relevant parameter regime, analyze them to extract practical flux parameterizations, and modify an existing planetary evolution code (CEPAM) to account for the effects. This improved technique will then be used to address two particular questions: (i) How do the revised heat flux laws affect the thermal evolution and structure of the planets, and (ii) How are chemical elements mixed across their compositional interfaces. Progress here would be an invaluable step towards a better understanding of the global evolution of giant planets everywhere.
This work is interdisciplinary between geophysical and astrophysical fluid dynamics, and will naturally benefit both subjects, as well as training a graduate student. Dissemination to the scientific community will be enhanced by publication of a monograph on Double-Diffusive Processes by Dr.Radko.
Research report When a pot of water is placed on a hot plate, the water is set into motion, and caries heat from the bottom to the top. This phenomenon, known as "thermal convection", occurs because hot water is less dense than cold water, and therefore buoyant, which causes the hot water to rise and the cold water to sink. Convection can be caused by any process that influences buoyancy. For example, if a pot of salty water is left to evaporate, then salinity of the upper layers gradually increases; the dense, salty fluid starts to sink, and the less salty water starts to rise. We call this "compositional convection". In many situations, including most of the Earth's oceans, both thermal and compositional effects are present at the same time, and often compete against one another. In the equatorial oceans, for example, the Sun heats the upper layers, making them warmer, but also evaporates water at the surface, making it saltier. The density, and therefore the buoyancy, of the surface layers depends on both the temperature and the composition. In fact, in this situation convection can occur even if the surface layers are more buoyant than the layers beneath! To understand why, we must consider an additional physical process: diffusion. Suppose that a small warm and salty "blob" of water from the surface is displaced downward a little way. If it remains warm, then it will be more buoyant than its new surroundings, and will rise back up to the surface. However, if it loses its warmth to its surroundings quickly enough, through thermal diffusion, it soon matches the temperature of the ambient water. Since salt diffuses much more slowly, the blob remains slightly saltier than its surroundings, therefore denser than the ambient water, and sinks further. The sinking of these blobs of relatively salty water, mixes salt from the surface down into the deep ocean much more rapidly than compositional diffusion alone. Convection by salt fingers is usually called "thermohaline convection". It is thought to play an important role in controlling the salinity contrast between the surface of the ocean and much deeper regions in the tropics (where salty, warm water lies on top of cold and fresh one). In turn, this controls the properties of the global meridional overturn, which regulates the Earth's climate. The example above considered the situation where warm, salty water is lying on top of colder, less salty water, but double-diffusive convection can also occur in situations where the effects of temperature and salt are reversed, with warm, salty water underneath colder, less salty water. This situation is common in the Arctic ocean, where melting ice makes the surface water layers much colder and less salty than the water below. Double-diffusive convection also occurs in the interiors of stars and gas planets. In that case, the "water" is actually a mixture of hydrogen and helium gases, and the "salt" is actually heavier elements, such as carbon, oxygen, nitrogen, etc. Giant planets such as Jupiter and Saturn, for instance, are mostly composed of hydrogen and helium, plus small amounts of heavier elements. Typically, the heavy elements are most abundant deep in the interior of the planets, which is also where the temperature is highest, and so the effects of composition and temperature act in opposition. Here, as in the cases described earlier, double-diffusive convection plays an important role in carrying heat and heavy elements up through the interior of the planet. Until recently, very little was known about double-diffusive convection in giant planets. Ambient conditions cannot be reproduced in the laboratory, and must be modeled numerically. Our team developed a high-performance numerical algorithm specifically for this task, and thanks to that, we were able for the first time to simulate double-diffusive convection as it would occur in the interior of giant planets. We found that, depending on the relative strength of the thermal and compositional effects, the gas either develops into stacks of "layers" which are thermally and compositionally well-mixed and distinct from one-another, or begins to oscillate fairly strongly without going into layers. The efficiency of heat and compositional mixing depends quite sensitively on which of these two scenarios occurs, so we developed a theory to predict when one or the other are to be expected. We are currently developing the theory further, to quantify exactly how efficient the transport is in each case. Once these models are completed, we intend to combine them with global models for the evolution of giant planets, from their initial formation to the present day. This will enable us to place better constraints on the age of the Solar System gas giants, and on theories for their formation. It will also give us better tools to understand the increasingly detailed observations of extra-solar planets now available.
