1883.] 



On the Formation of Ripple-mark. 



35 



is being established, and when the amplitude of oscillation over 

 existing ripple-mark varies, are complex. As far as I have been able 

 to determine, the following is an account of the phenomena : — 



We begin with variation in amplitude of oscillation over existing 

 regular ripple-mark, where the height of the undulations is not a very 

 small fraction of the wave-length. 



When the amplitude of oscillation is small compared with the wave- 

 length, a pair of small vortices are established above the crest of 

 •each ripple-mark, rotating in opposite directions. In the mean 

 position the upward current is over the crest, and the current of 

 water tends to carry up sand from each furrow to the crest. The 

 dividing line of the vortices oscillates, but the bottom of the line has 

 much less amplitude of oscillation than the top, so that the dividing 

 line is alternately inclined to one and the other side of the vertical. 

 The vortices are thus carried backwards and forwards over the crest 

 of the ripple, but the current always tends to maintain the crest, 

 merely displacing very slightly the position of the highest point. 

 The vortex which is on the lee-side is more intense than the other. 

 We will call these the primary vortices. (See fig. 3.) 



Suppose now the amplitude of oscillation to be somewhat larger ; 

 then the primary vortices by their friction on the adjacent water 

 generate two other vortices. The upward current in these secondary 

 vortices has its mean position over the middle of a furrow, and the 

 current comes down immediately over the upward current of the 

 primary pair of vortices. It appears that sometimes only every 

 .alternate one of the secondary vortices is established. The upward 

 •current of the secondary vortices oscillates with a motion which is 

 very far from being harmonic. It remains at its elongation for a 

 long time and then darts across to the other elongation. (See 

 'fig. 11.) During this mode of oscillation the primary vortices are 

 carried much further backwards and forwards over the crests. 



With still larger amplitude of oscillation it is no longer possible to 

 distinguish the primary vortices, and the secondary vortices increase 

 in intensity. It seems probable that the primary vortices are no 

 longer both in existence during the whole oscillation, but that they 

 are alternately created and annulled, so that when one exists the 

 -other does not. If this be so the vortex which exists is that which 

 is on the lee side of the ripple in the state of motion at the instant. 



With strong oscillation the secondary vortices apparently do all 

 the work, and the primary vortex, if it exists, only exists for a short 

 time, whilst it may serve as a protecting vortex to the ripple-crest, 

 during the rapid transference of the dividing line of the secondary 

 vortices from one crest to the next. Each secondary vortex is alter- 

 nately a vortex under the lee of a ripple-mark as exhibited in fig. 10- 

 Mere description is hardly sufficient to explain the motion. 



I) 2 



