The V-momentum equation

INTERFACE:

   subroutine vequation(nlev,dt,cnpar,ty,num,gamv,Method)

DESCRIPTION:

This subroutine computes the transport of momentum in $y$-direction according to

$$\dot{V} = {\cal D}_V - g \dfrac{\partial {\zeta}}{\partial {y}} +... ...tial {y}} \,dz' - \frac{1}{\tau^V_R}(V-V_{obs})-C_f V \sqrt{U^2+V^2} \; , \quad$$ (14)

where $\dot{V}$ denotes the material derivative of $V$, $\zeta$ the free surface elevation and $B$ the mean buoyancy defined in (33). ${\cal D}_V$ is the sum of the turbulent and viscous transport terms modelled according to

$${\cal D}_V = \dfrac{\partial}{\partial {z}} \left( \left( \nu_t + \nu \right) \dfrac{\partial {V}}{\partial {z}} - \tilde{\Gamma}_V \right) \quad .$$ (15)

In this equation, $\nu_t$ and $\nu$ are the turbulent and molecular diffusivities of momentum, respectively, and $\tilde{\Gamma}_V$ denotes the non-local flux of momentum, see section 4.

Coriolis rotation is accounted for as described in section 3.4. All other terms are completely analogous to those described in section 3.5.

USES:

   use meanflow,     only: gravity,avmolu
   use meanflow,     only: h,v,vo,u,w,avh
   use meanflow,     only: drag,SS
   use observations, only: w_adv_method,w_adv_discr
   use observations, only: vProf,vel_relax_tau,vel_relax_ramp
   use observations, only: idpdy,dpdy
   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
 
   wind stress in y-direction
   divided by rho_0 (m^2/s^2)
   REALTYPE, intent(in)                :: ty
 
   diffusivity of momentum (m^2/s)
   REALTYPE, intent(in)                :: num(0:nlev)
 
   non-local flux of momentum (m^2/s^2)
   REALTYPE, intent(in)                :: gamv(0:nlev)
 
   method to compute external
   pressure gradient
   integer, intent(in)                 :: method

DEFINED PARAMETERS:

   REALTYPE, parameter                 :: long=1.0D15

REVISION HISTORY:

   Original author(s): Lars Umlauf
                       (re-write after first version of
                        Hans Burchard and Karsten Bolding)
   $Log: vequation.F90,v $
   Revision 1.10  2006-11-06 13:36:45  hb
   Option for conservative vertical advection added to adv_center
   Revision 1.9  2006-04-03 08:39:12  lars
   fixed bug in relaxation times - Thanks to Adolf Stips
   Revision 1.8  2005-11-17 09:58:20  hb
   explicit argument for positive definite variables in diff_center()
   Revision 1.7  2005/06/27 13:44:07  kbk
   modified + removed traling blanks
   Revision 1.7  2004/08/18 11:44:49  lars
   updated documentation
   Revision 1.6  2003/03/28 09:20:35  kbk
   added new copyright to files
   Revision 1.5  2003/03/28 08:56:56  kbk
   removed tabs
   Revision 1.4  2003/03/10 08:50:07  gotm
   Improved documentation and cleaned up code
   Revision 1.3  2001/05/31 12:00:52  gotm
   Correction in the calculation of the shear squared calculation
   --- now according to Burchard 1995 (Ph.D. thesis).
   Also some cosmetics and cleaning of Makefiles.