ABSTRACT
The analytical methods to be described later in this chapter and in Chapter 6 are all based on PDE models. There is one method, however, that is applicable even when the dynamic equations that describe the system are not known. The method, commonly referred to as dimensional analysis, is useful for deriving scaling laws that relate physical quantities of interest to other quantities that characterize the system under consideration. Although the dynamic equations that describe the system need not be known, some preliminary understanding of the problem is needed, in order to make a judicious choice of the quantities that are most relevant to the problem in question, and in some cases certain assumptions have to be made. A successful implementation of the method may require a posteriori justification of these assumptions by empirical studies. We begin with an overview of the method (Section 5.1.1) followed by a more detailed exposition (Sections 5.1.2, 5.1.3, 5.1.4), and conclude with another application of dimensional analysis-the simplification of
model equations by expressing them in terms of dimensionless quantities consisting of rescaled state variables, time and space coordinates and a reduced set of parameters (Section 5.1.5).
