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SED12129-sup-0001-12129-VideoS1.wmvvideo/wmv37242KVideo S1. The video shows two animations: on the left side of the video, there is a sequence of pictures that show the evolution of the bedforms (Experiment 19; Table 1), and on the right side, there is a plot of the mean height (η – blue circles) and wavelength (λ – brown circles) as a function of time. There is a larger yellow circle in the diagram on the right side that indicates the mean height and wavelength represented in the image displayed on the left side. In addition, three vertical lines indicate the transitions of the four bedform development stages: (i) incipient bedforms; (ii) growing bedforms; (iii) stabilizing bedforms; and (iv) fully developed bedforms (see main text). Once the bedform reaches the fourth, or fully developed, bedform stage, the bedform is considered in morphodynamic equilibrium. There are two important observations that can be made from this video: (i) there is a temporal lag in the development history of two-dimensional (2D) oscillatory bedforms between the time required for these bedforms to reach equilibrium sizes (Eq. (3)) and the time to reach equilibrium planform geometry (i.e. the time for the bed to be fully 2D). This is shown in the video when the experiment reaches the fourth, or fully developed, bedform stage and the bed is still not at planform-equilibrium; and (ii) that for the case of 2D oscillatory ripples, once the bed reached the final equilibrium the bedforms stopped their migration and established a very defined wavelength and height that stayed fixed over time without any variations. These wavelengths and heights would persist until the flow condition was changed, and then the bed would break the two-dimensionality to rearrange itself to a new equilibrium stage that was stable with the new flow condition. This ‘stable equilibrium’ behaviour is a fundamental characteristic of two-dimensional oscillatory ripples, not seen in any other type of flow type or bedform.
SED12129-sup-0002-12129-VideoS2.wmvvideo/wmv27207KVideo S2. The video shows a sequence of pictures that show the evolution of the bedforms (Experiment 4; Table 1). Experimental conditions are shown at the start of the video. The diversity of sizes seen in the video, which is an inheritance condition of a dynamic-equilibrium, is considered to be the ‘normal’ stage of the bedform, where there is not a unique equilibrium wavelength and height but a spectrum of values.

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