Commit bf81afb0 authored by Olivier's avatar Olivier

Complete appendix section on field operators (div, grad, lap., curl)

parent 518eca1b
......@@ -134,7 +134,7 @@
\partialderivative{p}{x} \vec i + \partialderivative{p}{y} \vec j + \partialderivative{p}{z} \vec k & = & \rho \vec g \label{eq_threedgradientp}
\end{IEEEeqnarray}
We can simplify the writing of this last equation by using the mathematical operator \vocab{gradient}, defined as so:
We can simplify the writing of this last equation by using the mathematical operator \vocab{gradient} (see also Appendix~\ref{appendix_field_operators} p.\pageref{appendix_field_operators}), defined as so:
\begin{IEEEeqnarray}{rCl}
\gradient{} \equiv \vec i \partialderivative{}{x} + \vec j \partialderivative{}{y} + \vec k \partialderivative{}{z} \label{eq_def_gradient}
\end{IEEEeqnarray}
......
......@@ -107,7 +107,7 @@
&=& \diff \vol \left(\partialderivative{\vec \tau_{zx}}{z} + \partialderivative{\vec \tau_{yx}}{y} + \partialderivative{\vec \tau_{xx}}{x}\right)\label{eq_shear_force_x_tmp}
\end{IEEEeqnarray}
If we make use of the operator \vocab{divergent} written $\divergent{}$:
If we make use of the operator \vocab{divergent} (see also Appendix~\ref{appendix_field_operators} p.\pageref{appendix_field_operators}), written~$\divergent{}$~:
\begin{IEEEeqnarray}{rCcCl}
\divergent{} &\equiv& \partialderivative{}{x} \vec i \cdot \ + \ \partialderivative{}{y} \vec j \cdot \ + \ \partialderivative{}{z} \vec k \cdot \label{eq_def_divergent}\\
\divergent{\vec A} &\equiv& \partialderivative{A_x}{x} \ + \ \partialderivative{A_y}{y} \ + \ \partialderivative{A_z}{z}\\
......
......@@ -306,7 +306,7 @@
&=& \mu \left(\secondpartialderivative{u}{x} + \secondpartialderivative{u}{y} + \secondpartialderivative{u}{z}\right) \vec i\label{eq_tmp_shear_der}
\end{IEEEeqnarray}
Using the \vocab{Laplacian} operator to represent the spatial variation of the spatial variation of an object:
Using the \vocab{Laplacian} operator (see also Appendix~\ref{appendix_field_operators} p.\pageref{appendix_field_operators}) to represent the spatial variation of the spatial variation of an object:
\begin{IEEEeqnarray}{rClll}
\laplacian{} &\equiv& \divergent{\gradient{}}\label{eq_def_laplacian}\\
\laplacian{A} &\equiv& \divergent{\gradient{A}}\\
......
......@@ -80,7 +80,7 @@
With potential flow, these two conditions are addressed as follows:
\begin{enumerate}
\item We restrict ourselves to \vocab{irrotational} flows, those in which the curl of velocity (see Appendix~\ref{appendix_vector_operators} p.\ref{appendix_vector_operators}) is always null:
\item We restrict ourselves to \vocab{irrotational} flows, those in which the curl of velocity (see Appendix~\ref{appendix_field_operators} p.\pageref{appendix_field_operators}) is always null:
\begin{IEEEeqnarray}{rCl}
\curl{\vec V} &=& \vec 0
\end{IEEEeqnarray}
......
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