Vertical boundary conditions

Next: Mode splitting Up: The -coordinate system Previous: The -coordinate system Contents

The new boundary conditions for the vertical velocity, $\omega$ , in equation (36) become

$\begin{displaymath} \omega (0) = \omega (-1) = 0. \end{displaymath}$

(45)

The new conditions at the surface ( $\sigma = 0)$ becomes

$\displaystyle \frac{K_M}{D} \left( \frac{\partial U}{\partial \sigma}, \frac{\partial V}{\partial \sigma} \right)$

$\textstyle =$

$\displaystyle \frac{1}{\rho_0} (\tau_{0x},\tau_{0y}),$

(46)

$\displaystyle \frac{K_H}{D} \left( \frac{\partial T}{\partial \sigma}, \frac{\partial S}{\partial \sigma} \right)$

$\textstyle =$

$\displaystyle (\dot{T_0},\dot{S_0}) ,$

(47)

and at the bottom ( $\sigma = -1$ ) the boundary conditions become

$\displaystyle \frac{K_M}{D} \left( \frac{\partial U}{\partial \sigma}, \frac{\partial V}{\partial \sigma} \right)$

$\textstyle =$

$\displaystyle \frac{1}{\rho_0} (\tau_{bx},\tau_{by}),$

(48)

$\displaystyle \frac{K_H}{D} \left( \frac{\partial T}{\partial \sigma}, \frac{\partial S}{\partial \sigma} \right)$

$\textstyle =$

$\displaystyle 0.$

(49)

Helge Avlesen 2004-05-10