Basic principles

Constructing numerical models of marine systems usually involves setting up a series of partial differential equations, specifying boundary conditions and then “running the model”. Your purpose may be to establish the value of parameters (e.g. rates of reaction or the magnitude of some property), estimate fluxes, or make some prediction about the future state of the system. Although you can sometimes choose a physical problem that is simple enough to be modeled with analytic solutions (an example would be Munk's 1966 “Abyssal recipes” model; Chapter 13), more often than not you will encounter situations where the processes or the geometry of the system are too complex to allow analytic solutions.

Don't get us wrong; analytic solutions are nice. They can often provide you with a nice conceptual, intuitive feel for how the system responds, especially in an asymptotic sense. However, for realistic geometries, you will find that the few analytical solutions provided in many books are infinite series solutions. Be very, very careful when dealing with those series solutions. Pay particular attention to the assumptions made in deriving the solutions, to the conditions under which they ought to be applied, and especially to convergence issues.