m s$^{-1}$ and sand influx is $q_{in}=0.017$ kg m$^{-1}$s$^{-1}$. On the left the first dune does not have a slip face. A final stationary surface is not reached.[]{data-label="fig:transv_evo3"}](Figure7.eps){width="80.00000%"}

![Surface of a two dimensional simulation with constant sand influx after $4.56$ years in the left figure and $45.58$ years on the right. The shear velocity is $u_*=0.5$ m s$^{-1}$ and sand influx is $q_{in}=0.017$ kg m$^{-1}$s$^{-1}$. On the left the first dune does not have a slip face. A final stationary surface is not reached.[]{data-label="fig:transv_evo3"}](Figure8.eps){width="80.00000%"}

The initiating dunes at the inlet of the dune field have increasing size in length and height. The increasing difference between the starting points and the first crest leads to the creation of bigger dunes. With increasing size the dunes have a lower velocity $v_{dune}$ (Section \[subsec:dunevel\]). Hence, dune spacing, the distance between adjacent crests, increases with time and no dune collides or converges with another. So real dune fields can maintain a structure of translational invariance without the effect of the breaking of symmetry which was found in Section \[sec:trans\_2dim\]. Dune fields where the sand influx stays rather constant in time can have a more regular structure than dune fields where the sand influx varies 