ip_blumberg_mellor -

INTERFACE:

    subroutine ip_blumberg_mellor()

DESCRIPTION:

Here, the internal part of the pressure gradient is discretised according to Mellor et al. (1994). The crucial part of this term, which is $(\partial_x^* b)_k$ (in the case of the $u$-equation), is discretised between two vertically adjacent velocity points:

$$\begin{array}{l} \displaystyle \frac12(h_{i,j,k}+h_{i,j,k+1})... ...{i,j,k+1})- \frac12 (b_{i+1,j,k}+b_{i,j,k})\right), \end{array}$$ (116)

where $z^i_{i,j,k}$ is the $z$-coordinate of the interface in the T-point above the grid box with the index $(i,j,k)$.

The discretisation of $(\partial_y^* b)_k$ for the $v$-equation is done accordingly.

In this routine, as a first step, the interface heights are calculated in the T-points, in order to allow for the calculation of the coordinate slopes in the U- and V-points. In a second step, the expression (116) equivalent formulation for the $y$-direction are integrated up downwards, beginning from the surface. USES:

    use internal_pressure
  $ use omp_lib
    IMPLICIT NONE

REVISION HISTORY:

    Original author(s): Hans Burchard, Adolf Stips, Karsten Bolding

LOCAL VARIABLES:

    integer                   :: i,j,k
    REALTYPE                  :: dxm1,dym1
    REALTYPE                  :: grdl,grdu,buoyl,buoyu,prgr,dxz,dyz