The motion of a non-turbulent,
Newtonian fluid is governed by the Navier-Stokes equation:

The above equation can also be used to model turbulent flow, where the fluid parameters are interpreted
as time-averaged values.

The time-derivative of the fluid velocity in the Navier-Stokes equation is the material derivative,
defined as:

The material derivative is distinct from a normal derivative because it includes a convection term,
a very important term in fluid mechanics.
This unique derivative will be denoted by a "dot" placed above the variable it operates on.

Navier-Stokes Background

On the most basic level, laminar (or time-averaged turbulent) fluid behavior is described by a set of
fundamental equations. These equations are:

The Navier-Stokes equation is obtained by combining the fluid kinematics and constitutive relation into
the fluid equation of motion, and eliminating the parameters D and T. These terms are defined below: