Lagrangian particle random walk

INTERFACE:

   subroutine lagrange(nlev,dt,zlev,nuh,w,npar,active,zi,zp)

DESCRIPTION:

Here a Lagrangian particle random walk for spatially inhomogeneous turbulence according to Visser (1997) is implemented. With the random walk, the particle $i$ is moved from the vertical position $z_i^n$ to $z_i^{n+1}$ according to the following algorithm:

$$\begin{array}{rcl} z_i^{n+1} &=& z^n_i + \partial_z \nu_t (z^... ...al_z \nu_t (z^n_i)\Delta t) \Delta t\right\}^{1/2}, \end{array}$$ (241)

where $R$ is a random process with $\langle R \rangle =0$ (zero mean) and and the variance $\langle R^2 \rangle=r$. Set visc_corr=.true. for evaluating eddy viscosity in a semi-implicit way. A background viscosity (visc_back) may be set. The variance $r$ of the random walk scheme (rnd_var) has to be set manually as well here.

USES:

   IMPLICIT NONE

INPUT PARAMETERS:

   integer, intent(in)                 :: nlev
   REALTYPE, intent(in)                :: dt
   REALTYPE, intent(in)                :: zlev(0:nlev)
   REALTYPE, intent(in)                :: nuh(0:nlev)
   REALTYPE, intent(in)                :: w
   integer, intent(in)                 :: npar
   logical, intent(in)                 :: active(npar)

INPUT/OUTPUT PARAMETERS:

   integer, intent(inout)              :: zi(npar)
   REALTYPE, intent(inout)             :: zp(npar)

REVISION HISTORY:

   Original author(s): Hans Burchard & Karsten Bolding
   $Log: lagrange.F90,v $
   Revision 1.5  2005-12-02 21:06:09  hb
   Lagrangian routine included into source code documentation
   Revision 1.4  2004/08/19 09:24:57  hb
   Variance of random walk and background diffusivity explicitely prescribed --> Hidekatsu Yamazaki
   Revision 1.3  2004/08/18 16:09:39  hb
   Visser correction for viscosity evaluation included
   Revision 1.2  2004/03/22 10:14:24  kbk
   cleaned, store old index -> much faster, fixed conc. calc.
   Revision 1.1  2004/03/04 09:28:41  kbk
   general lagrangian 1D solver

LOCAL VARIABLES:

   integer         :: i,n,ni
   REALTYPE        :: rnd(npar),rnd_var=0.333333333,rnd_var_inv
   REALTYPE        :: visc_back=0.e-6
   REALTYPE        :: depth,dz(nlev),dzn(nlev),step,zp_old
   REALTYPE        :: visc,rat,dt_inv,zloc
   logical         :: visc_corr=.false.