78 



Symposium on Microseisms 



sure fluctuation it must be uniform in space, 

 i.e. it must be applied equally at all points of 

 the fluid. This indicates that below a certain 

 depth, in a strictly space-periodic motion, the 

 pressure fluctuations are uniform and equal to 

 the fluctuation p(t) in the mean pressure on 

 the bottom, which has been evaluated. The 

 effect of the waves, at great depths, is then 

 the same as would be produced by an oscillating 

 pressure applied uniformly at the upper sur- 

 face of the fluid — for example an oscillation of 

 the atmospheric pressure. Alternately one may 

 imagine a rigid plane or raft to be floating on 

 the surface of the water and completely cover- 

 ing it, and the pressure to be applied to this 

 plane by means of a weight attached to a 

 spring and oscillating in a vertical direction. 



6. An experimental verification — The above 

 results were verified experimentally (Cooper 

 and Longuet-Higgins 1951) in the fol- 

 lowing way. Waves were generated at one 

 end of a wave tank and allowed to travel to- 

 wards the far end, where they were dissipated 

 on a sloping beach. The pressure beneath the 

 waves was detected by means of a hydrophone 

 and was recorded continuously. On starting 

 the motion from rest, no appreciable pressure 

 fluctuations were recorded until the wave-front, 

 travelling with approximately the group-veloc- 

 ity of the waves, passed over the hydrophone. 

 The pressure fluctuations then built up quickly 

 to a constant amplitude, and had a period equal 

 to that of the waves. The amplitude agreed 

 well with the first-order theory; it diminished 

 exponentially with depth, and was negligible 

 below about half a wavelength. 



A vertical barrier was then placed in the 

 wave tank, between the hydrophone and the 

 beach, which reflected the waves back over the 

 hydrophone. As soon as the reflected wave 



Figure 7. Graph of C,, C„ , C, and C. as 

 function of oh/ft, > showing the relative am- 

 plitude of the vertical displacement of the 

 "sea bed" in the first four modes. 



Figure 8. The form of the wave spectrum in 

 a circular storm. 



y 



Figure 6. The regions of interference of two 

 groups of waves in the spectrum. 



Figure 9. Wave interference caused by mov- 

 ing cyclonic depression. 



