SEPT. ")] TIDKS 773 



4. Tidal Charts 



Tidal charts give information about the geographical distribution of harmonic 

 constants. Normally the very important M2-constituent is represented; K2, Ki 

 and Oi are also sometimes given. In these charts the co-range lines (2-^^=: 

 constant) and the co-tidal lines (/c^/cr^ = constant) are drawn. Occasionally 

 there are also charts with lines of constant |i,^ and constant ^2,^. 



The range, that is the difference between high- and low-water, is 2^^, time 

 of high-water is t = K^jay. The elevation of sea-level at time ^ = is ^1, ^ and ^2, v 

 is the value at time t = {Kv + Trl2)lay. 



The tidal current expressed as a vector with components u, v runs in a tidal 

 period through an ellipse which is determined by wi, vi, uo, V2. Major and minor 

 axes, direction of these axes and time to of extreme velocity of this ellipse are : 



(1/\^2)(W1- + U2- + Vi^- + V2- ± [(Wi2 + W2- + Vr + V2")- - 4(^1^2 - ^l2Vl)-]'^}'K 



tan 28 = 2{'UiVi+uoV2)l{ui" + U2~ + vi" — V2"), 

 tan 2(7X0 = 2{uiU2 + viV2)l{ui~ + vi'^ — U2^ — V2"). 



The tidal charts are characterized by amphidromic points, in which the 

 range becomes zero and the co-tidal lines converge. In the same way there are 

 special points on those charts where the elements of tidal current are ellipses. 

 If the minor axis becomes zero, the current is an alternating one ; if minor and 

 major axes are the same, the tidal current is circular. Charts with these kinds 

 of elements of tidal ellipses seem only to exist for the Irish Sea (Bowden, 

 1955) and for the North Sea (Hansen, 1952). Fig. 5 gives the direction and 

 amount of the major axes of the semi-diurnal M2 tidal current ellipses in the 

 North Sea. Fig. 6 contains the direction and amplitude of tidal currents for 

 the Irish Sea. Atlases of tidal currents published by national authorities for 

 navigational purposes normally contain direction and velocity of tidal currents 

 for every hour before and after a certain initial time, for instance high water in 

 a harbour, or the moon's transit of the Greenwich meridian. 



In most simple cases co-tidal and co-amplitude lines are constructed solely 

 with the aid of observations on the coasts and on islands. This kind of inter- 

 polation normally does not allow the distribution of depth to bo taken into 

 account. Especially abrupt variations of depth are found along the continental 

 shelf and these may influence the development of tides and tidal currents in 

 large extended areas. In such cases it is difficult to decide to what degree 

 coastal observations are representative of the open ocean. 



A similar question arises in connection with oceanic islands. Here too the 

 tides may be influenced by the depth in the neighbourhood. As there are no 

 observations, it is necessary to consult theoretical work to get some idea of 

 what may happen in such cases. Thorade (1926) examined the behaviour of 

 waves passing the continental slope; Proudman (1925) investigated the de- 

 formation of tidal lines caused by islands, capes, bights, etc. In some of the 



