Thermal Instabilities in Turbulence — Lesson 1

This lesson covers the concept of turbulence in fluids, focusing on how it occurs and the factors that influence it. The lesson begins with an explanation of turbulence and its occurrence in different systems, including pipes and convection. The instructor then delves into the concept of instability in fluids, explaining how fluctuations in parameters can lead to turbulence. The lesson also explores the role of non-linearity in fluid motion and how it contributes to the formation of patterns and chaos. The instructor uses the example of a hot plate and cold plate to illustrate convection and the formation of turbulence. The lesson concludes with a detailed discussion on the equations for velocity field and temperature, and how they are used to understand turbulence.

Video Highlights

00:52 - Discussion on instability in fluids and how fluctuations grow leading to turbulence
02:57 - Discussion on the concept of convection and how it affects turbulence.
04:28 - Explanation of the assumptions made in the study of turbulence and the setup of equations for the same
14:01 - Explanation of the process of linearizing the system and using Fourier modes for instability calculation
22:18 - Explanation of the process of applying the Craya-Herring basis to the equations and resolving the buoyancy term.
34:37 - Explanation of the process of solving the equations and the prediction of a two-dimensional field.

Key Takeaways

- Turbulence in fluids is a complex phenomenon that is influenced by various factors such as instability and non-linearity.
- Instability in fluids occurs when fluctuations in parameters lead to exponential growth, resulting in turbulence.
- Non-linearity in fluid motion can lead to the formation of patterns and chaos, contributing to turbulence.
- The equations for velocity field and temperature are crucial in understanding and predicting turbulence in fluids.
- The concept of Fourier modes is essential in converting partial differential equations to ordinary differential equations for easier analysis of turbulence.