Thomson’s theorem

Thomson's theorem, also known as Kelvin's circulation theorem, is a fundamental concept in fluid mechanics, specifically within potential flow theory. It states that in a fluid that is initially free of vorticity (swirling motion), the vorticity will remain zero as the fluid moves, provided certain conditions are met, such as the absence of viscosity at interfaces.1

This theorem simplifies the analysis of fluid flow, particularly when dealing with potential flow, where the velocity can be described by a scalar potential. This approach allows for the application of well-established mathematical methods, like Laplace's equation, to solve for fluid velocity and pressure distributions. However, the theorem's applicability is limited by the presence of vorticity, which can be introduced at interfaces between the fluid and solid objects or free surfaces. When vorticity is present, the fluid's behavior becomes more complex, and potential flow theory may no longer be sufficient.12