Modelling instabilities in astrophysical fluid dynamics (ref: 4455)

天体物理学流体动力学研究的是在磁场存在的情况下导电流体的运动。这种与磁场相互作用的流动存在于整个宇宙中。一个被广泛研究的例子是太阳磁场的演化，已知它遵循22年的周期。太阳等离子体可以喷射到太空中，以太阳风的形式向地球传播，最终与地球磁场相互作用，产生地磁风暴和极光。理解这种行为以及其他各种磁驱动的天体物理现象的关键在于理解磁场和导电流是如何相互作用的。传统的应用数学方法是研究简化模型，这些模型将特定的物理过程分离出来，并允许对其进行深入研究。通过一步一步的方法，然后建立更复杂的模型。在这种情况下，博士生将建立不同复杂性的数学模型，以研究在重力和旋转存在下磁场和导电剪切流的相互作用和不稳定性。这将涉及到研究控制流体速度和磁场的非线性偏微分方程。这些问题将使用分析和计算技术相结合来解决。学生应该有很强的应用数学或相关领域的背景，并对流体动力学有浓厚的兴趣。该学生将在埃克塞特的地球物理和天体物理流体动力学中心工作，该中心是英国同类领先的研究小组之一，其研究包括天体物理流体动力学，天气和气候的流体动力学，行星和系外行星流体动力学，日地等离子体和空间天气，理论流体动力学以及数值分析和建模。

Astrophysical fluid dynamics concerns the motion of electrically conducting flows in the presence of magnetic fields. Such flows interacting with magnetic fields exist throughout the universe. A widely studied example is the evolution of the Sun's magnetic field, which is known to follow a 22-year cycle. Solar plasma can be ejected into space, travelling towards the Earth as the solar wind, and ultimately interacting with the Earth's magnetic field to produce geomagnetic storms and aurora. Key to understanding the behaviour, and a variety of other magnetically driven astrophysical phenomena, lies in understanding how magnetic fields and electrically conducting flows interact.The traditional applied mathematics approach is to study simplified models that isolate a particular physical process and allow its in-depth investigation. Through a step-by-step approach more sophisticated models are then built. In this vein, the PhD student will build mathematical models of varying complexities to study the interaction and instabilities of magnetic fields and electrically conducting shear flows in the presence of gravity and rotation. This will involve the study of nonlinear partial differential equations that govern the fluid velocity and the magnetic field. These will be solved using a combination of analytical and computational techniques. The student should have a strong background in applied mathematics or a related field and a keen interest in fluid dynamics. The student will work within the Centre for Geophysical and Astrophysical Fluid Dynamics at Exeter, one of the leading research groups of its kind in the UK, whose research encompasses Astrophysical Fluid Dynamics, the Fluid Dynamics of Weather and Climate, Planetary and Exoplanetary Fluid Dynamics, Solar-Terrestrial Plasmas and Space Weather, Theoretical Fluid Dynamics, and Numerical Analysis and Modelling.