is incorporated in the roughness length $z_0$. For slices in wind direction the separation streamlines in the lee zone of the dunes are fitted by a polynomial of third order going through the point of the brink $x_0$. The length of the separation streamlines is determined by allowing a maximum slope of $14^0$ [@SauermannPhD2001]. Where the separation streamlines cross the surface at the reatachment point $x_1$, a new stream line is calculated as third polynomial attaching $x_0$ and $x_1$. The separation bubble guarantees a smooth surface and the shear stress in the area of the separation bubble is set equal to zero. Problems can arrive due to numerical fluctuations in the value of the slope of the brink where the separation bubble begins and its influence on the calculation of a separation streamline for each slice. To get rid of this numerical error the surface is Fourier-filtered by cutting the small frequencies. Figure \[fig:transv\_sinus\] depicts the separation bubble and an interesting similarity of the separation bubble profile to a sine function.

![The transverse dune profile $h(x)$, its separation bubble $s(x)$ and a sine function. The separation bubble ensures a smooth surface. The wind is coming from the left.[]{data-label="fig:transv_sinus"}](Figure3.eps){width="80.00000%"}

#### The 