Morphodynamic processes on Earth are a result of sediment displacements by the flow of water or the action of wind. An essential part of sediment transport takes place with permanent or intermittent contact with the bed. In the past, numerous approaches for bed-load transport rates have been developed, based on various fundamental ideas. For the user, the question arises which transport function to choose and why just that one. Different transport approaches can be compared based on measured transport rates. However, this method has the disadvantage that any measured data contains inaccuracies that correlate in different ways with the transport functions under comparison. Unequal conditions also exist if the factors of transport functions under test are fitted to parts of the test data set during the development of the function, but others are not. Therefore, a structural formula comparison is made by transferring altogether 13 transport functions into a standardized notation. Although these formulas were developed from different perspectives and with different approaches, it is shown that these approaches lead to essentially the same basic formula for the main variables. These are shear stress and critical shear stress. However, despite the basic structure of these 13 formulas being the same, their coefficients vary significantly. The reason for that variation and the possible effect on the bandwidth of results is identified and discussed. A further result is the finding that not only shear stress affects bed-load transport rates as is expressed by many transport formulas. Transport rates are also significantly affected by the internal friction of the moving sediment as well as by the friction fluid-bed. In the case of not fully rough flow conditions, also viscous effects and thus the Reynolds number becomes of importance.

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.

Numerous questions and problems on Earth and questions with respect to other planets arise from morphodynamic processes caused by sediment movements driven by flows of fluids, such as water, air and other gases. A sediment surface opposes the current with a resistance that is determined by its skin or grain roughness. As soon as sand waves, such as ripples and/or dunes, are formed, these bedforms cause a further resistance to the flow, the so-called form roughness. Dependent on the dimensions of the ripples and dunes, the form roughness can be much more pronounced than the skin roughness. The relevant literature provides a large number of solution approaches based on different basic ideas and different result quality. The aim of this paper is a comparative analysis of solution approaches from the literature. For this purpose, 14 approaches to bedform-related friction in the subaqueous case are evaluated using 637 measurements from laboratory and natural settings. We found that all approaches were significantly more accurate for ripples than for dunes. Since this was equally the case for all approaches tested, it is reasonable to assume that this is caused by measurement inaccuracies for dunes in the natural case rather than due to the approaches themselves. The approach of Engelund 1977 proved to be most accurate among all approaches investigated here. It is based on the Borda–Carnot formulation and an additional empirical term. An analytical derivation and justification is provided for this additional term.

In sediment mechanics, the conditions for the onset of sediment movement are of particular importance. However, despite decades of research, questions remain unanswered. Thus, physical logic suggests that sediments move more easily on beds inclined in the direction of flow than on horizontal beds and that transport rates are correspondingly increased. However, numerous studies have shown that sediments require increased rather than decreased shear stress to move on sloping beds and that transport rates are lower instead of increased. Since an early publication on this issue by Ashida and Michiue in 1973, many possible effects have been suggested for this apparent contradiction. The literature almost consistently concludes that high relative roughness (d/h), i.e., low water cover (h/d), is mainly responsible for this contradictory effect. This is true for current-induced sediment transport and for the initiation of debris flow. In this paper, an analytical solution for the effect of small water coverage on the transport process is developed. Effects of low coverage also occur on beaches during wave runup and runoff and thus control the formation of steep or less steep beaches. The present paper shows that the effect of turbulence damping occurring under low water coverage plays a decisive role here.

As soon as a granular sediment has been set in motion by the currents of droppable fluids or by wind, sand waves form as smaller ripples or larger dunes. The relevance of this phenomenon lies in the roughness effect against the currents and the influence on sediment loads. Likewise, their physical understanding helps us to estimate past flow conditions by means of fossilized sand waves, as well as those on distant planets with proven ripples and dunes, such as Mars and Titan. In the literature, diagrams exist based on observations for the conditions under which the various forms of sand waves develop. However, the cause of their formation is unclear. Various theories have been discussed regarding the further development of ripples once they have formed, but none of them explains the fundamental mechanism that generates the very first ripples. These occur simultaneously over a large area and almost instantly, with a fairly even distance from crest to crest. This contribution presents a solution for how this is possible based on hydrodynamic instability.