Spectral analysis of compound dunes

Successive multibeam echo sounder surveys in a tidal channel on the North Sea coast reveal the dynamics of subaquatic compound dunes. Mainly driven by tidal currents, dune structures show complex migration patterns. Common methods for the analysis of bedform migration are based on the description of average characteristics as dune length, height and celerity. Their application to superimposed structures is dissatisfying as the recognition of dunes is subjective and work intense. Thus the bathymetric signal of a cross-section of compound subaquatic dunes has been approximated by the sum of a set of harmonic functions, derived by Fourier transformation. Dune migration has been analysed and quantified by taking into account the phase differences of individual harmonic constituents. The separate re-composition of harmonic constituents with zero or low phase shifts sums up to what can be regarded as the stable part of the original signal. On the other hand the summation of constituents with high phase differences forms the purely kinematic signal. The further analysis of the kinematic signal revealed spectral properties of the concerning components, which lead to the formulation of a simple phenomenological model. Although the model is by no matter meant to represent the natural system of bed-formdynamics and super-position, it was shown to be capable of reproducing some morphological characteristics of compound dunes as e.g. their asymmetric shape. Model shortcomings have been identified as the lack of a wiping-out function and the necessity of including extreme events in the model forcing.