shear velocity and sand influx. $a$ is a measure for the growth rate. The growth rate seems to be smaller for a larger distance from the beginning of the dune field. There the dunes contain longer slip faces because of their higher age. We observe from Figure \[fig:transv\_scalhq\] that the growth rate should converge to a constant value for very large distances. The same relation is found for the spacing $d_{ij}$ of the dunes $i$ and $j$ (Figure \[fig:transv\_scalsc\]), $$d_{ij}(t) \propto \sqrt{b \cdot t},$$ where $b$ denotes a parameter which measures the spacing rate. This spacing rate approaches the same value for all dunes far away from the influx region. The values fitting well to these rates are approximately $b=8.53 \cdot 10^{-5}$ m$^2$s$^{-1}$ and $b=1.56 \cdot 10^{-4}$ m$^2$s$^{-1}$ for a shear velocity $u_*=0.4$ m s$^{-1}$ and $u_*=0.5$ m s$^{-1}$, respectively.

![Comparing the evolution of the spacing between dunes for different shear velocities. The spacing increases with the square root of time.[]{data-label="fig:transv_scalsc"}](Figure10.eps){width="80.00000%"}

Figure \[fig:transv\_spach\] shows the spacing height relationship which seems to be linear. This agrees with the data of measurements of transverse dunes in the Namib Sand Sea in Namibia by . For different shear stresses the slope stays constant 