A model is a simplified representation of the dynamics of a physical system. The state of the system is described by a set of independent variables, and the dynamics of the system is described by a set of dynamical equations. Dependent variables are related to the independent variables by algebraic constraints. The Navier-Stokes equations describe the motion in a 3D compressible viscous fluid. They serve as a model for the fluid dynamics aspects of the atmosphere and oceans in which many processes take place with various length and time scales.
Dissipation is determined by viscosity, and convection by conductivity.
The zero-order transport equations are the 3D Euler equations that describe the motion in a 3D compressible nonviscous fluid. These equations are studied in a rotating system under the action of gravity for a stably stratified fluid. A parent model represents the part of the model dynamics that is under investigation. A hierarchy of parent models can be constructed ranging from the Navier-Stokes equations to the 2D Euler equation. Starting from the Navier-Stokes equations the viscosity can be neglected to obtain the 3D compressible Euler equations.