Understanding Aerodynamics: Arguing from the Real Physics

9

Theoretical Idealizations Revisited

In the preceding chapters, we looked at a wide range of aerodynamic phenomena, and we saw numerous examples of how theories based on conceptual models and simplifying assumptions allow us to construct explanations and make predictions without having to solve the full equations of motion. In this chapter, we'll take another look at the theoretical landscape, this time from the point of view of the models rather than the phenomena, taking a kind of inventory of the conceptual tools at our disposal. This will lead us to cover some of the ground we've already covered, but this time for the purpose of putting it all in a broad theoretical perspective, rather than the more phenomenological one we've taken sofar.

In Section 9.1, we'll look at the quantitative theories, categorizing them according to the type of model and what was done to simplify the equations. In Section 9.2, we'll explore the conceptual side, the tools available to us for doing Mental Fluid Dynamics (MFD).

9.1 Approximations Grouped According to how the Equations were Modified

The need for ad hoc models and simplifying assumptions was originally driven by the computational intractability of the full equations. This need is not as great now as it once was, but it is still there. Computers and solution algorithms have progressed to the point that solutions to the full NS (Navier-Stokes) equations for laminar flow can be calculated routinely, even for complicated 3D problems. Practical ...