|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.|
|fluid stress||T||2nd order tensor||N/m2|
|strain rate||D||2nd order tensor||1/s|
|unity tensor||I||2nd order tensor||1|