whereas the axis intercept of $h$ increases with higher shear velocities. Hence, the dunes in a transverse dune field are located closer to each other for higher shear velocities.

![Relationship between spacing and height of the dunes for the shear velocities $u_* = 0.4$ ms$^{-1}$ and $u_* = 0.5$ ms$^{-1}$. The dependency seems to be linear.[]{data-label="fig:transv_spach"}](Figure11.eps){width="80.00000%"}

Dune velocity {#subsec:dunevel}
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The validity of Bagnold’s law, $$v_{dune} =  \frac{\Phi_{dune}}{h},
   \label{eq:transv_vdune}$$ where $\Phi_{dune}$ is the bulk flux of sand blown over the brink has been shown by observations of real dunes. According to a better fit is given by using instead of the height $h$ the characteristic length $l$, i.e. the length of the envelope comprising the height profile and the separation bubble. Bagnold’s law already fits quite well. Nevertheless, the Equation (\[eq:transv\_vdune\]) is generalized. The length of the envelope can be expressed as a function of the height. The function is developed into a Taylor series and orders higher than the linear order are neglected. This finally yields, $$v_{dune} =  \frac{\Phi_{dune}}{h+C},
   \label{eq:transv_vdune2}$$ where $C$ denotes a constant. In Figure \[fig:transv\_scalv2\] the dune velocities with respect to the height and their fits to Equation (\[eq:transv\_vdune2\]) are compared for the shear velocities $u_*=0.4$ 