4.2.3.3 Advection

The convergence of the advective fluxes $-\nabla_{h} \cdot (u \, {\bf u}_{h})$ and $-\nabla_{h} \cdot (v \, {\bf u}_{h})$ provide fundamental sources of nonlinearity to the equations of motion. They arise from the use of an Eulerian, rather than a Lagrangian, reference frame for describing the fluid motion. Their presence adds substantially to both the richness and complexity of fluid dynamics.