Internal Waves 



533 



A closer investigation of this differential equation shows an infinite number 

 of solutions, corresponding to an infinite number of internal waves of the 

 same period, but with different velocities and different vertical distribution 

 of rj. These waves are designated as waves of first, second etc., order, where 

 the wave of zero order is the regular tide wave at the surface. In the wave 

 of first order the vertical displacement in the entire water mass from the 

 surface to the bottom has the same direction with a maximum amplitude 



40 80 120 160 



/>/r, X io 4 



Fig. 222. Relationship between the period T of cellular waves and the stability of the 

 stratification {E = rig) for different ratios between the horizontal (A x ) and vertical (A,) 

 dimensions of the cells; +, observations in the Fehmarnbelt 1937; •, observations in the 



Baltic 1944 (Neumann). 



in one depth. The wave of second order is characterized by vertical dis- 

 placement in opposite direction within the upper and the lower layer; there 

 are two maxima of amplitudes. The waves of third order have three maxima 

 in the vertical, and the wave of fourth order four maxima, etc. The horizontal 

 velocity is always zero in the depth where the amplitude of the vertical dis- 

 placement reaches a maximum. Accordingly, the horizontal velocity is zero 

 at one depth for the wave of first order; and within the wave of second order 

 the horizontal velocity is zero ^t two levels and so on. 



In this theory the rotation of the earth and friction have so far been 

 neglected. If one wants to consider the rotation of the earth we have to add 

 to the first equation of (XVI. 25) a similar one for the direction of the co- 

 ordinate >', perpendicular to the direction of progress of the wave. In both 

 equations Coriolis acceleration of — 2co£ and -\-2co£ respectively has to be 

 added. In this case a> = Qsincp and £ is the horizontal displacement cross 



