38 



BJ0RN HELLAND-HANSEN 



[REP. OF THE "MICHAEL SARS" NORTH 



difference of density, wfiile the amplitude is inversely pro- 

 portional to the same square root. The velocity with 

 which a boundary wave advances, is, according to 

 Helmholtz: 



1/ ~ • — ' — ^— g metres per second 



where s is the density (for sea water 5 =:^ 1 + 10^^ rr,), z 

 the thickness (\n metres) of the stratum of fluid, and g 

 the acceleration of gravity (9-8). The index 1 indicates 

 the upper stratum and 2 the lower. 



The amplitude (half the vertical distance between the 

 highest and lowest point of the wave) may, with sufficient 

 accuracy, be expressed by the formula: 



z. z^ l\v 

 a = — i — = A V 



Zi-\- Z2 c 



z, z. 



1 *'2 



^2 g 



metres, 



where .^ v is the difference of current velocity between 

 the upper and lower strata (in metres per second). 



From these formulae we see that the speed of propa- 

 gation is independent of l^ v, while the amplitude is 

 directly proportional to this quantity. In other words: 

 a boundary wave traverses a certain distance in a constant 

 time as long as the density and the thickness of each 

 stratum is unaltered, even if the current velocities are sub- 

 ject to variations in which case the amplitude varies. We 

 see, further, that by z, + Zo = const, the speed of propa- 

 gation as well as the amplitude have a maximum when 

 Zi = Z2, and decrease when the difference in thickness 

 between the two layers increases. 



Boundary waves are known from the dead-water 

 phenomenon, owing to the thorough investigations by 

 V. W. Ekman. Dead-water occurs only where a water 

 stratum with low densities rests on heavier sea-water, when 

 the difference in density is very marked. It has been sup- 

 posed that boundary waves may occur also in the open 

 sea, where the differences in density are much less marked. 

 A sudden gust of wind on the surface of the sea may, 

 for instance, create such a wave at a boundary surface 

 situated at some depth. Such boundary waves "generally 

 occur singly, but periodical oscillations may be produced 

 by a series of such waves, if the impulse creating them 

 be regularly repeated at certain intervals of time. We 

 consider it probable, for instance, that the tidal waves 

 passing into a basin across a sub-oceanic ridge, like that 

 between Scotland and Greenland, may give regular im- 

 pulses such as these. It is even possible that the tidal 

 waves may thus to some extent be transformed into boun- 



dary waves, which will advance with such reduced veloci- 

 ties" [Helland-Hansen and Nansen, 1909, p. 105]. 



The tidal wave coming directly from the North Atlantic 

 into the Faeroe-Shetland Channel passes the Wyville 

 Thomson Ridge. This ridge has a saddle depth of a little 

 more than 550 metres, and its mean depth is 450 — 500 

 metres. During the "Michael Sars" Expedition no hydro- 

 graphical stations were taken quite near the ridge. In 

 May 1924 numerous stations were worked by Danish, 

 Scottish and Norwegian research vessels in the Channel 

 and neighbouring areas, amongst others on both sides 

 of the Wyville Thomson Ridge. The observations exhibit 

 great local variations and it makes a great difference which 

 stations are selected for a comparison A Norwegian 

 station from May 12th, in 59'^ 36' N and 6° 34' W, bottom- 

 depth 707 metres, was situated on the southern side of 

 the ridge. To the north-west, on the other side of the 

 ridge, a Danish station was taken on May 6th, in 59"^ 59' N 

 and 6°7' W, bottom-depth 650 metres. The observations 

 (published in Bulletin Hydrographique for 1924, with 

 Appendix) gave: 



The effect of the ridge in shutting off the warm water 

 from the Atlantic at depths below 400 — 500 metres is very 

 conspicuous. On the northern side the density increases 

 rapidly downwards from 400 to 600 metres, while it is 

 practically constant at the southern side. 



The tidal wave passing the ridge gives rise to quite 

 strong tidal currents in the southern part of the Faeroe- 

 Shetland Channel down to the level of the ridge. There 

 is, in all probability, a marked decrease 'in the velocity 

 of the tidal currents at this level. It is impossible to calcu- 

 late in a satisfactory way the amplitude and speed of 

 propagation of boundary waves which may be formed in 

 these circumstances, for we have no observations of the 

 tidal currents at the depths in question and, moreover, 

 have not to deal with two homogeneous strata with a real 

 discontinuity at the boundary between them. The tran- 

 sitions in density are quite continuous, but the rate of the 

 vertical variations differs at different levels. For a rough 

 approximation we may, however, employ the formulae 

 given above and use the Danish observations quoted, 



*) The Norwegian observations were actually taken at 650 

 metres, which in this case makes no difference. 



