342 Tides and Tidal Currents in the Proximity of Land 



the incoming and the outgoing Kelvin wave; the southern amphidromy is 

 somewhat disturbed compared to the northern. The co-oscillating tide takes 

 the aspect of a tide wave travelling anti-clockwise (contra solem) along the 

 shore ; the tidal ranges are always largest at the shore and drop to zero towards 

 the centres of the amphidromies. 



These investigations give valuable indications as to the extent to which 

 the earth's rotation influences the tidal phenomena. There where the influence 

 of the Coriolis force is small (narrow basins, small velocities and low geo- 

 graphical latitudes) both the independent and the co-oscillating tide have the 

 character of standing waves with very pronounced nodal lines; there where 

 the Coriolis force can develop more fully, both tides rather have the character 

 of waves travelling along the coast contra solem, with rotary currents in the 

 inner part of the bay. 

 (c) Influence of Friction 



The influence of friction on the tidal motions in adjacent seas can be 

 explained by referring to the influence of friction on seiches (see Chap- 

 ter VI, para. 2/b, p. 155). In the case of these periodical motions, the wave 

 energy is reduced primarily by the eddy viscosity, which is caused by the ir- 

 regularities of the ocean bottom and of the coasts. The simplest way of con- 

 sidering this viscosity is, as was already pointed out in the afore mentioned 

 chapter, to introduce into the differential equations for the horizontal water 

 displacements a term of the form Pidg/dt). It means that, if /? is constant, 

 the friction is proportional to the velocity of the motion. This assumption 

 does not quite correspond to our knowledge as to how the friction is related 

 to the velocities in case of a turbulent state of motion; however, it has the 

 advantage that the calculations can be completed until the end, thus per- 

 mitting one to survey better the frictional influence. The quantity (3 is not a con- 

 stant, as we know already from the damping curves of the seiches, but depends 

 upon the depth and the nature of the bottom. In the theory /S generally ap- 

 pears in the relation (3/o = fiT/ln, and it was shown that its order of magni- 

 tude, in relation to the mean depth, is given approximately by the following 

 quantities: 



h = 100 50 30 10 m and below 



b= 0-1-0-2 0-5 0-5-1-0 1-0-2-0 sec" 1 



With this assumption for the friction, the differential equations of the ho- 

 rizontal and vertical displacements of the water particles for independent and 

 co-oscillating tides can be integrated for a rectangular basin and uniform 

 depth, see Defant (1919). The changes in amplitudes and phases around 

 the bay shores, become larger when the friction increases. The horizontal 

 velocities are greatest in the vicinity of the nodal lines, and consequently 

 the friction is particularly noticeable there. The friction causes the abrupt 

 change of phase of half a period to be replaced by a gradual change. The 



