The spectral evolution of sedimentary bed forms

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Abstract
A potential-flow based analytical model is developed for the temporal development of the spectra of ripples and dunes generated on an initially flattened bed by an open-channel flow. The analysis predicts the occurrence of two distinct spectral peaks at small times; the physical origin of each is explained. One of the peaks has spatial frequency equal to that given by the Airy relation for a small amplitude stationary free-surface wave. These results are confirmed by Jain's (1971) experimental data. Jain's data also are used to determine quantitativevalues of the lag distance andHayashi's (1970) inclination factor, α, which appear in the sediment-transport relation used in the analysis. A variance-cascade model is used to derive the ‘minus-three-power law’ that describes the spatial spectra of rippIes and dunes at higher wavenumbers. Finally, the relation between the Froude number and dominant wavelength implied by Jain & Kennedy's (1971) non-dimensionalized spectra is discussed and compared with data presented by Jain (1971) and Nordin (1971).

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