This lesson covers the concept of stability theory in fluid dynamics, focusing on the transition from laminar to turbulent flows. It explains the significance of the critical Reynolds number, which indicates the point at which flow becomes turbulent. The lesson introduces the concept of perturbations in parallel flows and how these disturbances, if small, can be analyzed using linear stability analysis. It also discusses the use of Fourier analysis and the Squire's theorem to simplify the momentum equation into a linear, fourth-order ordinary differential equation known as the Orr-Sommerfeld equation. By solving this equation and finding the eigenvalues, one can determine the critical Reynolds number.

- The critical Reynolds number indicates the point at which flow becomes turbulent.
- Small perturbations in parallel flows can be analyzed using linear stability analysis.
- Fourier analysis and the Squire's theorem can be used to simplify the momentum equation into the Orr-Sommerfeld equation.
- Solving the Orr-Sommerfeld equation and finding the eigenvalues helps determine the critical Reynolds number.

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