Mathematics

Turbulence plays a fundamental role in many different applications varying from aeronautical to environmental simulations. This course aims at giving an overview of the phenomenology and mathematical modelling of compressible turbulent flows. We will start from a first part focused on gasdynamics (thermodynamics, compressible navier-stokes equations, speed of sound, shock waves). The second part of the course will instead be focused on turbulence phenomenology and modelling. Starting from the adimensional form of the compressible Navier-Stokes equations ultimately leading to the study of energy transfers across scales in compressible turbulent flows. Finally, the two main topics will merge by studying the equations of compressible fluctuations, the Kovasznay decomposition and available analytical models for shock-turbulence interaction. Basic knowledge of continuum mechanics is required. Previous studies in more general fluid dynamics are encouraged but are not strictly necessary.The course notes are avaiable on official course page (https://niccolotonicello.weebly.com/teaching.html).