New Theoretical Developments in Aeroacoustics and Aerodynamics

The Acoustic Analogy is studied regarding its application to Aerodynamics. The concept of generalized derivatives is reviewed and extended. As consequences, new versions of the generalized continuity, momentum, energy, and energy momentum conservation equations are presented. These conservation laws form a basis for theoretical ideas regarding three-dimensional, linear and non-linear, potential and non-potential, steady and unsteady flows of incompressible and compressible, inviscid and viscous fluids. Extensions made in the definition of generalized derivatives relate fluid properties to new surface terms linked to tangential flow. In integral form, some of these relations recall the classical circulation and downwash integrals of Aerodynamics. An iterative solution technique of the resulting singular integral equations is proposed.