The memory can vary by about four orders of magnitude in time.

The results of the numerical calculations with different sand influxes $q_{in}$ at the same shear velocities lead to the conclusion that there is a direct dependency between influx and height growth of the first dune (Figure \[fig:transv\_scalhq\]). The nearer the sand influx gets to the saturation flux of saltation transport the slower increases the height of the first dune. Hence, dune fields where the sand influx varies strongly in time around the saturation flux of saltation initiate first dunes with different heights. So there can be smaller dunes moving faster into bigger ones and the symmetry breaking explained in the Section \[sec:trans\_2dim\] will occur.

![Evolution of the height of the dunes beginning at the position where the wind comes in. The shear velocity is $u_* = 0.4$ ms$^{-1}$. The height increases with the square root of time.[]{data-label="fig:transv_scalhq"}](Figure9.eps){width="80.00000%"}

In the following some relations found for the time evolution of transverse dunes are presented. Figure \[fig:transv\_scalhq\] indicates also that height versus time increases with a power law as was also found in the model of , $$h(t) \propto \sqrt{a \cdot t},$$ where $a$ is a parameter which is dependent on 