--- manual/s_overview/appendix_ocean.tex 2001/08/08 16:16:19 1.1.1.1 +++ manual/s_overview/appendix_ocean.tex 2001/09/11 14:39:38 1.2 @@ -1,4 +1,4 @@ -% $Header: /home/ubuntu/mnt/e9_copy/manual/s_overview/Attic/appendix_ocean.tex,v 1.1.1.1 2001/08/08 16:16:19 adcroft Exp $ +% $Header: /home/ubuntu/mnt/e9_copy/manual/s_overview/Attic/appendix_ocean.tex,v 1.2 2001/09/11 14:39:38 cnh Exp $ % $Name: $ \section{Appendix OCEAN} @@ -11,14 +11,15 @@ \begin{eqnarray} \frac{D\vec{\mathbf{v}}_{h}}{Dt}+f\hat{\mathbf{k}}\times \vec{\mathbf{v}}% _{h}+\frac{1}{\rho }\mathbf{\nabla }_{z}p &=&\vec{\mathbf{\mathcal{F}}} -\label{eq-zns-hmom} \\ +\\ \epsilon _{nh}\frac{Dw}{Dt}+g+\frac{1}{\rho }\frac{\partial p}{\partial z} -&=&\epsilon _{nh}\mathcal{F}_{w} \label{eq-zns-hydro} \\ +&=&\epsilon _{nh}\mathcal{F}_{w} \\ \frac{1}{\rho }\frac{D\rho }{Dt}+\mathbf{\nabla }_{z}\cdot \vec{\mathbf{v}}% -_{h}+\frac{\partial w}{\partial z} &=&0 \label{eq-zns-cont} \\ -\rho &=&\rho (\theta ,S,p) \label{eq-zns-eos} \\ -\frac{D\theta }{Dt} &=&\mathcal{Q}_{\theta } \label{eq-zns-heat} \\ -\frac{DS}{Dt} &=&\mathcal{Q}_{s} \label{eq-zns-salt} +_{h}+\frac{\partial w}{\partial z} &=&0 \\ +\rho &=&\rho (\theta ,S,p) \\ +\frac{D\theta }{Dt} &=&\mathcal{Q}_{\theta } \\ +\frac{DS}{Dt} &=&\mathcal{Q}_{s} +\label{eq:non-boussinesq} \end{eqnarray} These equations permit acoustics modes, inertia-gravity waves, non-hydrostatic motions, a geostrophic (Rossby) mode and a thermo-haline @@ -194,15 +195,15 @@ \begin{eqnarray} \frac{D\vec{\mathbf{v}}_{h}}{Dt}+f\hat{\mathbf{k}}\times \vec{\mathbf{v}}% _{h}+\frac{1}{\rho _{c}}\mathbf{\nabla }_{z}p^{\prime } &=&\vec{\mathbf{% -\mathcal{F}}} \label{eq-zpe-hmom} \\ +\mathcal{F}}} \label{eq:ocean-mom} \\ \epsilon _{nh}\frac{Dw}{Dt}+\frac{g\rho ^{\prime }}{\rho _{c}}+\frac{1}{\rho _{c}}\frac{\partial p^{\prime }}{\partial z} &=&\epsilon _{nh}\mathcal{F}_{w} -\label{eq-zpe-hydro} \\ +\label{eq:ocean-wmom} \\ \mathbf{\nabla }_{z}\cdot \vec{\mathbf{v}}_{h}+\frac{\partial w}{\partial z} -&=&0 \label{eq-zpe-cont} \\ -\rho ^{\prime } &=&\rho (\theta ,S,p_{o}(z))-\rho _{c} \label{eq-zpe-eos} \\ -\frac{D\theta }{Dt} &=&\mathcal{Q}_{\theta } \label{eq-zpe-heat} \\ -\frac{DS}{Dt} &=&\mathcal{Q}_{s} \label{eq-zpe-salt} +&=&0 \label{eq:ocean-cont} \\ +\rho ^{\prime } &=&\rho (\theta ,S,p_{o}(z))-\rho _{c} \label{eq:ocean-eos} \\ +\frac{D\theta }{Dt} &=&\mathcal{Q}_{\theta } \label{eq:ocean-theta} \\ +\frac{DS}{Dt} &=&\mathcal{Q}_{s} \label{eq:ocean-salt} \end{eqnarray} Note that the hydrostatic pressure of the resting fluid, including that associated with $\rho _{c}$, is subtracted out since it has no effect on the