The basic equations of oceanic motions describe all fluid motions on all space and time scales. All these motions and scales cannot be resolved simultaneously, neither observationally nor computationally. In the remainder of this book we therefore consider approximations to these equations. These approximations reduce the physics. They suppress certain processes, modes of motions, and scales. All these approximations can be obtained in a systematic manner by asymptotic expansions. These expansions clearly identify the circumstances under which a certain approximation holds and the errors involved in making this approximation. These approximations should thus be distinguished from idealizations. These merely assign specific values to parameters that describe the fluid and its environment. Typical idealizations are ideal fluids (λ = D = D′ = ν = ν′ = 0), non-rotating systems (Ω = 0), incompressible fluids (c = ∞), and two-dimensional flows (ω = ∂/∂z = 0). Such idealized systems might be much more amenable to analysis. However, it is unclear how they relate to the real ocean. Real fluids are not ideal. They diffuse salt, momentum, and heat. Ideal fluids do not. Real fluid flows are irreversible. Ideal fluid flows are time-reversible. Similar remarks apply to the other idealizations. There are, of course, oceanic motions that behave approximately as if the fluid were ideal or non-rotating or incompressible or two-dimensional. One would like to understand the circumstances under which this is the case and the errors involved in any such approximation. Asymptotic expansions address this question in a systematic manner.