- the local rate of change , described in Sec. 2.5 ;
- advection of by , described in Sec. 2.8 ;
- diﬀusion of by ;
- a “source” due to , described in Sec. 2.12 .
Note that, since constant, , where denotes the Laplace operator.
The term models diﬀusion across the surface of the ﬂuid element. Diﬀusion generally represents the transport of a ﬂuid property — here, momentum — due to ﬂuctuating motions that are not captured by the bulk motion that is represented by the continuum velocity .
Fluctuations include any random motion of particle constituents of matter, e.g. molecules, and turbulent structures. Through these motions, particles can pass across a surface boundary, transporting property through a gradient of (above, left).
“Laplacian”11 describes a term of the form where is a diﬀusivity coeﬃcient.12 A Laplacian term is conservative since all variables are to the right of a divergence, as described in Sec. 2.9 . It is also bounded since it tends to decrease high values and increase low values as shown above.
The Laplacian represents a ﬂux due to across the surface, per unit volume, as