Mathematical modelling in fluid mechanics

The art of constructing idealized models is discussed. The models are considered as asymptotic limits of a more general model, as some suitably chosen small parameter approaches zero. Attention is given to a Navier-Stokes model (for gases), boundary-layer theory, lifting-line theory, and slender-body theory. An investigation of cases of nonuniform limiting behavior is conducted. Ad hoc models can be employed in connection with engineering situations calling for the prediction of flows which are too complex for other model types or which are physically not well understood. The considered ad hoc models are related to potential flow, numerical fluid dynamics, turbulence models, and vortex methods.