Instabilities in Turbulence - I

This course covers the intricate concepts of turbulence in fluids, instability in fluid systems, and the application of eigenvalues and eigenvectors in linear equations. For instance, the course delves into the occurrence of turbulence in different systems such as pipes and convection, explaining how fluctuations in parameters can lead to turbulence. It also explores the role of non-linearity in fluid motion and how it contributes to the formation of patterns and chaos. The course further discusses the concept of rotating convection instability, focusing on the Navier-Stokes equation and the addition of the Coriolis force. It introduces the Taylor and Ekman numbers, which are related to rotation, and the importance of non-dimensional numbers like the Rayleigh number in determining instability conditions. Lastly, the course explains the significance of eigenvalues in determining the growth or decay of a system and provides an illustrative example of how eigenvalues and eigenvectors can be used to solve a linear algebra problem.