Including ocean currents

The Eikonal equations can be extended in order to handle ocean currents; the system can be written compactly in vector form as[16]

$\displaystyle \frac{d\mbox{$\mathbf{r}$}}{d\tau}$	$\textstyle =$	$\displaystyle \frac{c^2}{\Omega }\mbox{\boldmath$\sigma$}+ \mbox{$\mathbf{v}$} ,$	(A.15)
$\displaystyle \frac{d\mbox{\boldmath$\sigma$}}{d\tau}$	$\textstyle =$	$\displaystyle -\frac{\Omega }{c}\mbox{\boldmath$\nabla$}c - \mbox{\boldmath$\si... ...{\boldmath$\sigma$}\cdot\mbox{\boldmath$\nabla$} \right) \mbox{$\mathbf{v}$} ,$	(A.16)

where $\mbox{$\mathbf{v}$}$ represents the vector of currents and

$\begin{displaymath} \Omega = \frac{c}{c\left( 1+\mbox{$\mathbf{v}$}\cdot\mbox{\boldmath$\sigma$} \right) } . \end{displaymath}$

(A.17)

Orlando Camargo Rodríguez 2012-06-21