Abstract
Once the first initial ripples have developed, they form according to the actual flow forces and sediment properties. In this paper, a semianalytical approach to determine the length of the developed ripples is presented. The theory assumes initial disturbances at the bed surface and corresponding flow separations resulting from an individual respective boundary layer. What causes the initial rhythmic perturbations is not the subject of this paper. Based on boundary layer theory, this approach explains a possible physical background for the existence and length of developed ripples in cohesion-free sediments. At the same time, the approach provides a distinction from dunes: ripples are sand waves affected by a viscous sublayer, and dunes are sand waves where this is not the case. Applications to Earth, Mars, and Titan are shown.
Highlights
The most striking difference is that ripples are small and in the subaqueous case, if the water depth is greater than about three ripple heights, they are independent of the water depth
We come to the conclusion that this range is dominated by the effect of flow acceleration on the turnover from viscous to turbulent boundary layer. This means that the bed forms in this range are ripples which are characterized by the acceleration effects of the viscous boundary layer
The turnover causes a significant increase in sediment transport rates, which results in local erosion and in a limitation of the ripple length
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in During the transport of granular sediment, a wavy bed forms under certain combinations of flow and sediment, independent of material and nature of the fluid. Beginning from the reattachment point, a new boundary layer develops (e.g., Plate 1966 [1]) These sedimentary waves appear in two main forms, the ripples and the dunes. The subject of this paper is the distinction between ripples and dunes in cohesion-free sediments and a theory of their evolved dimensions after they have emerged For this purpose, a semianalytical approach based on boundary layer theory is developed. Over decades, based on observations, various diagrams have been developed on the demarcation of the areas of ripples and dunes respectively Some of these diagrams are dimensional and apply to typical conditions on earth, i.e., sand and water. Yalin 1985 [16], based on an evaluation of data from different researchers investigated the length of developed ripples and derived a dimensionless representation which applies to various combinations of liquid and sediment.
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