state of translational invariance. For an illustration of this dynamics see Figure \[fig:transv\_2d2\]. The slip faces become wider until they reach the lateral boundary and extend over the entire width of the simulated fields. Thus the slip face traps all the sand going over the brink. The trapped sand relaxes there through avalanching and maintains the angle of repose constant. Shear stresses of the wind field transport more sand over the brink than that which is transported down at the slip face by avalanches. Hence, transverse dunes are growing wherever there is a part of their lee zone in which saltation transport can be neglected (Section \[sec:trans\_const\]). When dunes grow the length of their separation bubble increases. But for a dune field with a limited length due to the periodic boundary condition and to a certain number of dunes which increase their mutual distance there is a state where the number of dunes must decrease by one. This leads to a displacement of the dune with the lowest height which looses its sand to the next dune situated upwind. In this state the system breaks the symmetry of translational invariance and a part of the slip face disappears. There sand 