Currents in a Strait 537 



rhythm which will also give rise to variations in the oceanographic factors. It can be 

 shown that the small periodic variations in the slope of the sea surface, produced by 

 the passage of the tidal wave, will be accompanied by waves at the internal boundary 

 layer of corresponding form, but of increased amphtude which will affect the normal 

 water interchange between the two seas. 



A disturbance of the internal boundary surface in a sea strait due to a periodic displacement of the 

 sea surface (tide) can be treated theoretically in a simple way. The equations of motion for both layers 

 can be obtained from equation (XVI. 11), taking the local accelerations du^'dt and du^ldt, respectively, 

 into account. A periodic displacement of the sea surface can be given the form 



Ci = ^acosA^exp(/par), (XV1.18) 



where the variation in the surface gradient has a wavelength A, a period a and amplitude a. These 

 periodic vertical displacements of the sea surface give rise to corresponding variations in the upper 

 and lower currents of the form 



Ml = v{z)a sin Ajc exp {/ {■r}ihy)at) and u^, = ^{z)y sin Xx exp {/ (r)lh^)at)} (XVI. 19) 



and these will be associated with a period vertical displacement of the boundary surface 



$2 = 1^7 cos Aa- exp ( / ^ at) (XVI.20) 



v_ 



hlg 



v{z) and <P(z) fix the vertical velocity distributions in the upper and lower currents, respectively, and 

 follow from the differential equations of motion mentioned above and the corresponding boundary 

 conditions, y in equation (XVI.20) is the magnitude of the variations of the internal boundary surface ; 

 its value is given by 



Pj—a\\-^-^M\. (XVI.21) 



— Pi L Pi J 



Pi— P\ L Pi 



Since M (see p. 520) is always negative, it is clear that the variations of the boundary surface will 

 always be the reverse of those at the sea surface, and since y is inversely proportional to the difference 

 in density between the two water types they will be many times (of the order of about 1000) greater 

 than the latter. 



Variations of this type appear in all extensive series of observations. Schott (1928) 

 has investigated the observations made by the "Dana" expedition in the eastern part 

 of the Strait of Gibraltar and obtained the results shown in Fig. 249. Values for the 

 layer from 100 to 200 m were combined to eliminate the irregularities in individual 

 values and to accentuate the connection with the tidal period. The isotherms and 

 isohahnes rise and fall in time with the sea surface tide at Gibraltar; here the oscilla- 

 tions of the internal boundary reach the large value of 70-80 m. Similar results were 

 obtained at the "Dana" station for 14-15 July 1928 by Jacobsen and Thomsen 

 (1934) where the 37%o isohaline had an average amplitude of 66 m, at neap tides 

 42 m, and at spring tides 90 m. 



Similar vertical oscillations in the density transition layer were found at the 15- day 

 anchor station in the Strait of Bab el Mandeb ; they follow the rhythm of the tidal 

 currents and have amplitudes of up to 100 m. In this case there is a phase shift of 3 h 

 between the current curve and the thermo-haline curve. This is shown in a particularly 

 clear manner by taking the mean of 5 semi-diurnal periods. (Table 144.) The extreme 

 values of temperature and salinity occur at the times of current reversal. Here, as in 

 the Strait of Gibraltar, the main cause of the variations in the density transition layer 

 is the passage of tidal waves. These quite large displacements of the boundary layer 

 can also be explained quantitatively by the theory. Assuming the amplitude of the 



