Divergence damping initialisation

The velocity increments may be initialized by the iterative application of a divergence damping operator. In iteration step $n$ new estimates of velocity increments $u^{n}_I$ and $v^{n}_I$ are updated by:

$$\left\{ \begin{aligned}u^{n}_I = u^{n-1}_I + \frac{1}{e_{1u} } ... ...2} \left( {A_D \;\chi^{n-1}_I } \right) \end{aligned} \right.,$$

where

$$\chi^{n-1}_I = \frac{1}{e_{1t} e_{2t} e_{3t} } \left( {\delta _... ...n-1}_I} \right] +\delta _j \left[ {e_{1v} e_{3v} v^{n-1}_I} \right]} \right).$$ (13.5)

By the application of (13.4) and (13.4) the divergence is filtered in each iteration, and the vorticity is left unchanged. In the presence of coastal boundaries with zero velocity increments perpendicular to the coast the divergence is strongly damped. This type of the initialisation reduces the vertical velocity magnitude and alleviates the problem of the excessive unphysical vertical mixing in the first steps of the model integration [Dobricic et al., 2007, Talagrand, 1972]. Diffusion coefficients are defined as $A_D = \alpha e_{1t} e_{2t}$, where $\alpha = 0.2$. The divergence damping is activated by assigning to nn_divdmp in the nam_asminc namelist a value greater than zero. By choosing this value to be of the order of 100 the increments in the vertical velocity will be significantly reduced.