TM No. 377 



The speed and direction data (on punch-cards) were programmed on a Bensen 

 Lehner electro-plotter, which provided a means of representing the Eulerian 

 data on a progressive vector diagram (sometimes called a Lagrangian hodagraph 

 diagram) depicting the head-to-tail addition of the current vectors for the 

 entire sampling period (see figure IV-7). The digital computer program for 

 this punch-card preparation is given in appendix D. The plot in figure IV-7 

 represents a graphical integration of the time variable velocity vector, 

 which is displayed as its scaler components § and 9 in figure IV-6. A 

 consecutive pair of points in the XY plane defines a vector representing 

 the average current speed and direction over a 20-minute interval* The 

 figure could virtually represent a time sequence of the Eulerian velocity 

 vectors, but not necessarily the pattern of flow at regions other than the 

 BBELS. The head-to-tail path is indicative of the geometric pattern (or 

 stream line) of the flow for a particle which is initially at the origin 

 of the first vector and then moves with the local mass of water. The par- 

 ticle would indeed follow the vector path if the local mass of water moved 

 as a solid, which, of course, is not the case. In the simple model of 

 rectilinear tidal motion with ho net displacement over the sampling period, 

 this vector diagram would present a simple line of oscillation. For a 

 rotating tidal current, in which the particles move in a circle with 

 constant angular velocity, the head-to-tail vector diagram would appear 

 as a circle with a period equivalent to the semi-diurnal tide* 



The most obvious motion depicted by the progressive vector diagram is 

 a mean flow moving to the WNW, The secondary motion displayed is a gross 

 meandering pattern which oscillates roughly about the mean vector direction. 

 During the period 29 April through 1 May, the mean flow tends toward the 

 west.- Then from 2 May through 6 May, the mean flow tends more to the north 

 at about 310°-320°T. On 7 May a disturbance in the pattern causes the mean 

 drift to shift more to the west. 



The dominant oscillatory motions of the progressive vector diagram are 

 displayed as cycloid-like meanders, the peaks of which show open loops or, 

 occasionally, a closed spike.. These are defined geometrically as prolate 

 and ordinary cycloids, respectively. Throughout the period of observation, 

 the rotational sense of the vector direction is clockwise or anti -cyclonic, 

 as was inferred from the time record of & . 



The times of high water (obtained from the trace of y in figure IV-6 

 and marked with an H on the vector path) occur near the time that the peak 

 of the cycloid is attained. In other words, the high water usually occurs 

 just prior to a change in gross current direction from north to east„ 



The pattern of the time of high water marked on the progressive vector 

 plot (figure IV-7) indicates a strong correlation of the tidal extremes 

 with the pattern of the velocity vectors, For example, the time of low 

 water occurs at the time of strongest flow to the west This point occurs 

 at the trough of the cycloid in the progressive vector diagram* 



81 



