The buoyancy equation

INTERFACE:

   subroutine buoyancy(nlev,dt,cnpar,nub,gamb)

DESCRIPTION:

This subroutine solves a transport equation for the mean potential buoyancy,

$$B=-g\frac{ {\langle \rho \rangle} -\rho_0}{\rho_0} \; , \quad$$ (33)

where $g$ is the accelaration of gravity, and ${\langle \rho \rangle}$ and $\rho_0$ are the mean potential density and the reference density, respectively. A simplified transport equation for $B$ can be written as

$$\dot{B} = {\cal D}_B \; , \quad$$ (34)

where $\dot{B}$ denotes the material derivative of $B$, and ${\cal D}_b$ is the sum of the turbulent and viscous transport terms modelled according to

$${\cal D}_B = \dfrac{\partial}{\partial {z}} \left( (\nu^B_t+\nu^B) \dfrac{\partial {B}}{\partial {z}} - \tilde{\Gamma}_B \right) \quad .$$ (35)

In this equation, $\nu^B_t$ and $\nu^B$ are the turbulent and molecular diffusivities of buoyancy, respectively, and $\tilde{\Gamma}_B$ denotes the non-local flux of buoyancy, see section 4. In the current version of GOTM, we set $\nu^B_t = \nu^\Theta_t$ for simplicity. Source and sink terms are completely disregarded, and thus (34) mainly serves as a convenient tool for some idealized test cases in GOTM.

Diffusion is treated implicitly in space (see equations (7)- (9)), and then solved by a simplified Gauss elimination. Vertical advection is included, and it must be non-conservative, which is ensured by setting the local variable adv_mode=0, see section 8.5 on page .

USES:

   use meanflow,      only: h,w,buoy,T,avh
   use meanflow,      only: w_grid,grid_method
   use observations,  only: b_obs_NN,b_obs_surf,b_obs_sbf
   use observations,  only: w_adv_discr,w_adv_method
   use util,          only: Dirichlet,Neumann
   use util,          only: oneSided,zeroDivergence
   IMPLICIT NONE

INPUT PARAMETERS:

   number of vertical layers
   integer, intent(in)                 :: nlev
 
    time step (s)
   REALTYPE, intent(in)                :: dt
 
   numerical "implicitness" parameter
   REALTYPE, intent(in)                :: cnpar
 
   diffusivity of buoyancy (m^2/s)
   REALTYPE, intent(in)                :: nub(0:nlev)
 
   non-local buoyancy flux (m^2/s^3)
   REALTYPE, intent(in)                :: gamb(0:nlev)

REVISION HISTORY:

   Original author(s): Hans Burchard & Karsten Bolding
   $Log: buoyancy.F90,v $
   Revision 1.8  2006-11-06 13:36:45  hb
   Option for conservative vertical advection added to adv_center
   Revision 1.7  2005-11-17 09:58:20  hb
   explicit argument for positive definite variables in diff_center()
   Revision 1.6  2005/06/27 13:44:07  kbk
   modified + removed traling blanks
   Revision 1.5  2003/03/28 09:20:35  kbk
   added new copyright to files
   Revision 1.4  2003/03/28 08:56:56  kbk
   removed tabs
   Revision 1.3  2003/03/10 08:50:06  gotm
   Improved documentation and cleaned up code
   Revision 1.1.1.1  2001/02/12 15:55:57  gotm
   initial import into CVS