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

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

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

Karsten Bolding 2012-12-28