derivative (also called the Lagrangian derivative, convective derivative, substantial derivative, or particle derivative). Suppose we have a flow field u, and we are also given a generic field with Eulerian specification F(x, t). Now one might ask about the total rate of change of F experienced by a specific flow parcel. This can be computed as where ∇ denotes the nabla operator with respect to x, and the operator u⋅∇ is to be applied to each component of F. This tells us that the total rate of change of the function F as the fluid parcels moves through a flow field described by its Eulerian specification u is equal to the sum of the local rate of change and the convective rate of change of F. This is a consequence of the chain rule since we are differentiating the function F(X(x0, t), t) with respect to t. Conservation laws for a unit mass have a Lagrangian form, which together with mass conservation produce Eulerian conservation; on the contrary, when fluid particles can exchange a quantity (like energy or momentum), only Eulerian conservation laws exist. See also Brewer-Dobson Circulation Conservation form Contour advection Equivalent latitude Generalized Lagrangian mean Lagrangian particle tracking Semi-Lagrangian scheme Streamlines, streaklines, and pathlines Trajectory (fluid mechanics) Stochastic Eulerian Lagrangian method Liouville's theorem (Hamiltonian) Notes References External links Objectivity in classical continuum mechanics: Motions, Eulerian and Lagrangian functions; Deformation gradient; Lie derivatives; Velocity-addition formula, Coriolis; Objectivity. Fluid dynamics Aerodynamics Computational fluid dynamics