The internal pressure-gradient


   subroutine intpressure(nlev)

With the hydrostatic assumption

$\displaystyle \dfrac{\partial {P}}{\partial {z}} + g {\langle \rho \rangle} = 0 \; , \quad$ (16)

where $ P$ denotes the mean pressure, $ g=9.81$ms$ ^{-2}$ the gravitational acceleration and $ {\langle \rho \rangle} $ the mean density, the components of the pressure-gradient may be expressed as

$\displaystyle - \frac{1}{\rho_0} \dfrac{\partial {P}}{\partial {x}}= -g \dfrac{...
...{\zeta}}{\partial {x}} +\int_z^{\zeta}\dfrac{\partial {B}}{\partial {x}}   dz'$ (17)


$\displaystyle - \frac{1}{\rho_0} \dfrac{\partial {P}}{\partial {y}}= -g \dfrac{...
...rtial {y}} +\int_z^{\zeta} \dfrac{\partial {B}}{\partial {y}}   dz' \; , \quad$ (18)

where $ \zeta$ is the surface elevation and $ B$ the mean buoyancy as defined in (33).

The first term on the right hand side in (17) and (18) is the external pressure-gradient due to surface slopes, and the second the internal pressure-gradient due to the density gradient. The internal pressure-gradient will only be established by gradients of mean potential temperature $ \Theta$ and mean salinity $ S$. Sediment concentration is assumed to be horizontally homogeneous.

In this subroutine, first, the horizontal buoyancy gradients, $ \partial_xB$ and $ \partial_yB$, are calculated from the prescribed gradients of salinity, $ \partial_xS$ and $ \partial_yS$, and temperature, $ \partial_x\Theta$ and $ \partial_y\Theta$, according to the finite-difference expression

$\displaystyle \dfrac{\partial {B}}{\partial {x}} \approx \frac{B(S+\Delta_xS,\Theta+\Delta_x\Theta,P)-B(S,\Theta,P)}{\Delta x} \; , \quad$ (19)

$\displaystyle \dfrac{\partial {B}}{\partial {y}} \approx \frac{B(S+\Delta_yS,\Theta+\Delta_y\Theta,P)-B(S,\theta,P)}{\Delta y} \; , \quad$ (20)

where the defintions

$\displaystyle \Delta_xS=\Delta x \partial_xS \; , \quad \Delta_yS=\Delta y \partial_yS \; , \quad$ (21)


$\displaystyle \Delta_x\Theta=\Delta x \partial_x\Theta \; , \quad \Delta_y\Theta=\Delta y \partial_y\Theta \; , \quad$ (22)

have been used. $ \Delta x$ and $ \Delta y$ are "small enough", but otherwise arbitrary length scales. The buoyancy gradients computed with this method are then vertically integrated according to (17) and (18).

The horizontal salinity and temperature gradients have to supplied by the user, either as constant values or as profiles given in a file (see obs.nml).


   use meanflow,      only: T,S
   use meanflow,      only: gravity,rho_0,h
   use observations,  only: dsdx,dsdy,dtdx,dtdy
   use observations,  only: idpdx,idpdy,int_press_method
   use eqstate,       only: eqstate1
   number of vertical layers
   integer, intent(in)                 :: nlev
   Original author(s): Hans Burchard & Karsten Bolding

Karsten Bolding 2012-12-28