The solution of a partial differential equation arising in fluid flow theory

摘要

The partial differential equation E2Ψ = 0 that arises in ideal fluid theory associated with irrotational flow is investigated in toroidal coordinates. The operator E2 given by (2) is related to the Laplace operator ▿2. The solution Ψ, which represents the stream function, is shown to depend on Legendre, trigonometric, and hyperbolic functions.