The Origin and Growth of Ripple-Mark. 565 



The Origin and Growth of Ripple-Mark." By Mrs. HERTHA 

 AYBTQN. Communicated by Professor W. E. AYRTON, F.E.S. 

 Eeceived April 21 ; received in revised form May 26 Read 

 June 16, 1904. 



(Abstract.) 



The object of the investigation was to determine how ripple-mark 

 started in perfectly smooth sand, apart from accidental variations of 

 surface friction ; how the ripples grew; how the amplitude and depth 

 of the water affected them; and whether there was any connection 

 between ripple-mark and kindred phenomena, such as the dust figures 

 in a Kundt's tube. 



In the course of the investigation the causes, form, and mode of 

 action of " ripple vortices " in the water were determined, and the 

 fact that no vortices of this kind can form in a current flowing 

 steadily in one direction over an obstacle was demonstrated, both 

 theoretically and practically. Also many minor details came to 

 light, such as the fact that each ripple is continually travelling, as a 

 whole, and why it does so. 



As regards the starting of ripple-mark, it was found that a single 

 ridge forms, on perfectly smooth sand, wherever the water happens to 

 have the same place of maximum longitudinal velocity during several 

 oscillations. That as soon as this ridge is high enough (less than a 

 millimetre is sufficient), the water, in flowing over it, forms a spiral 

 vortex with horizontal axis, which starts a new furrow and ridge in 

 the lee of the first on one side during one swing and on the other 

 side during the next. That the vortex that forms in the lee of each 

 of these two ripples in turn originates a new ripple there, and that 

 in this way, fresh ripples are begun with each succeeding swing of the 

 water till the whole sand is ripple-marked. 



It was shown that the " ripple vortices " only came into existence 

 during the time when the water was rising above the mean level, and 

 the causes and manner of formation of the vortices were given. 



It was found that when the place of maximum horizontal velocity 

 was constant, not merely for several oscillations, but for a considerable 

 time, as at the loop, for horizontal motion, of a stationary wave, the 

 ridge mentioned above grew into a ripple-marked heap which was 

 highest at the loop and lowest at the nodes. By oscillating water in 

 the simplest possible way, i.e., so that it alternately rose and fell at 

 one end of the trough while it alternately fell and rose at the other, 

 a stationary wave having its length twice the length of the trough 

 was obtained, and in this case a ripple-marked mound arose of which 

 the apex was at the middle of the trough one loop of the wave and 



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