Equation of Motion and Vorticity Transport

Fluid flow is established in response to an external action mediated by boundary motion, by the application of a surface force, or by the presence of a body force. The evolution of a transient flow and the structure of a steady flow established after an initial start-up period are governed by two fundamental principles of thermodynamics and classical mechanics: mass conservation, and Newton’s second law for the motion of a fluid parcel. The implementation of Newton’s law of motion in continuum mechanics leads to Cauchy’s equation of motion, providing us with an expression for the point particle acceleration in terms of stresses, and to the vorticity transport equation governing the point particle rotation. The derivation and interpretation of these equations in general and specific terms, and their solution for simple flow configurations will be discussed in this chapter.