models of two dimensional dunes can be used in the following sections. The advantage to omit the lateral dimension makes it possible to look at larger dune fields within a still tolerable cost of computional time.

A plain initial surface would lead to no change of the height profile. This is because the system needs at least one small fluctuation to begin dune growth. Therefore as initial surface a large number of low Gaussian hills is introduced.

![Surface after $1.49$ years. The shear velocity is $u_*=0.45 $ m s$^{-1}$, the boundary conditions are periodic in wind direction and open in lateral direction. Some slip faces can be seen. One unit corresponds to the length of $2$ m.[]{data-label="fig:transv_2d2"}](Figure4BW.eps){width="80.00000%"}

The simulation models dune dynamics for a dune field of a length and width of $400$ m and $200$ m, respectively. The boundary conditions are periodic in wind direction and open in lateral direction and the shear velocity is $u_*=0.45 $ m s$^{-1}$. First the Gaussian hills lead to a growth at their corresponding positions on the dune field. After some time they build a slip face which extends its size in lateral direction.

We assume that transverse dunes try to reach a 