This lesson covers the stability analysis of inviscid flow, focusing on the Rayleigh's equation and Orr Sommerfeld equation. It explains how to analyze these equations and apply them to different types of flows, such as boundary layer flow and parallel flow. The lesson also discusses the necessary conditions for inviscid instability, including the Rayleigh's inflection point theorem and Fjortoft's theorem. For instance, it explains that a necessary but not sufficient condition for inviscid instability is that the basic flow profile has a point of inflection. The lesson concludes with an application of these concepts to a parallel flow, demonstrating that it is neutrally stable.

- The Orr Sommerfeld equation and Rayleigh's equation are crucial for analyzing the stability of inviscid flow.
- The Rayleigh's inflection point theorem states that a necessary but not sufficient condition for inviscid instability is that the basic flow profile has a point of inflection.
- Fjortoft's theorem further states that it is necessary for U double prime into U minus UPI to be less than 0 somewhere in the profile.
- In the case of a parallel flow, the flow is neutrally stable as per the conditions derived from the Rayleigh's equation.

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