4 ZETLON, ON TIDAL BOUNDARY-WAVES. 



old reaction-current theory of F. L. Ekman by a totally new one. Pettersson"» results 

 have to a large extent inspired the following researches, so I think it proper, for further 

 reference, to give here a brief account of his views upon the subject, referring to his own 

 paper for the details of it. 1 



Thus, according to Pettersson: 



I. The intermediate stratum between the surface- and the bottom-current in the 

 »Store Belt» is agitated by great submarine waves; 



II. These waves have the tidal period and are caused by the tides; 



III. The lack of any considerable tide in the surface of the Skagerak and the Katte- 

 gat must be due, to some extent, to the Atlantic tide diving under the Baltic surface-water 

 and progressing chiefly in form of a ii dal boundary-wave; 



IV. The isohalines of the intermediate stratum are inclined to the horizontal, falling 

 off towards the south; 



V. The intermediate layer is alternately compressed and dilated by the submarine 

 waves travelling in the upper boundarj^.of the bottom- water beneath it; 



VI. In that manner a pumping influence is exercised by the boundary -waves, which 

 causes the salter parts of the stratum to be transported into the Baltic, and again pushes 

 the fresher ones outwards into the Kattegat. For the effectivity of this operation the 

 inclined position of the isohalines is of essential importance. The pumping action is 

 the principal factor in the circulation of the Baltic, compared to which the hydrostatic 

 differences of pressure are of small importance. 



The first part of the present paper contains a theoretical discussion of the generation 

 of tidal boundary- waves. In the second part an account is given of some small-scale ex- 

 periments, undertaken with a view partly to illustrate the theory, and parti y to reproduce 

 some instances of tidal boundary-waves known from Hydrography. 



PART I. 

 A. On the Possibility of Tidal Boundary-waves being formed. 



Imagine an ocean of throughout uniform depth, filled, in the beginning, with homo- 

 geneous water, the free surface of which is exposed to a pressure, uniform in ti me and 

 space. For simplicity the ocean may have the form of an infinite straight channel, so 

 that the whole motion may be treated as two-dimensional. Now let tidal waves travel 

 along the channel. They will be af the kind called »long waves», i. e. their wave-length 

 will be very great, compared to the depth of the water. As is well known from Hydro- 

 dynamics, the motion is at a given instant the same for all particles of water lying in the 

 same cross-section of the channel, so that in the vertical dimension there is no variation 

 whatever in the velocity of the particles; moreover the pressure is everywhere equal to the 



1 Strömstudier vid Östersjöns portar, Svenska Hydrografisk-Biologiska Kommissionens skrifter III. 



