i 3 2 DISCOVERY REPORTS 



Helland-Hansen and Nansen (1926) have facilitated the application of Bjerknes' 

 theorem to oceanographical problems by constructing charts of dynamical topography. 

 If an isobaric surface has the same dynamic depth at two points a and b, so that 

 D a = D„ in equation (6), then the velocity of the water movement at the upper isobaric 

 surface is equal to the velocity at the lower surface, and there is no movement relative 

 to the lower surface at right angles to the line ah. If the lower surface is known to be 

 horizontal owing to its being situated at a depth where the water is motionless, the line 

 ab, along which the surface has the same dynamic depth, can be regarded as the stream 

 line of the current at the upper surface. If the dynamic depth of a horizontal isobaric 

 surface below a shallower surface is known at a sufficient number of points a chart 

 showing the dynamical topography of the shallow surface can be constructed and the 

 contours or dynamic isobaths on the chart give, under the conditions assumed in the 

 specialized form of Bjerknes' theorem, a complete representation of the current stream- 

 lines. 



THE DYNAMICAL TOPOGRAPHY OF THE o AND 600 DECIBAR 

 SURFACES IN THE SOUTHERN OCEAN 



The topographical charts are based chiefly on the observations made at 106 stations 

 during the circumpolar cruise made by the R.R.S. 'Discovery II' in 1932-33, but in 

 order to make them more complete in the Drake Passage and the Scotia Sea seven series 

 of observations made by the R.R.S. 'William Scoresby' in 1929 have also been used. 

 The report does not aim at giving a complete account of the topography of the isobaric 

 surfaces but only shows the broad outlines; since the 'Discovery II' has made many 

 more observations since 1933 and is still at work, an attempt to produce a very detailed 

 chart would be premature. 



The temperature and salinity observations used were made at depths of approxi- 

 mately o, 10, 20, 30, 40, 50, 60, 80, 100, 150, 200, 300, 400, 600, 800, 1000, 1500, 2000, 

 2500, 3000 m., and then at further intervals of 500 m. down to the sea bottom. The 

 exact depths at which they were made were determined to the nearest 10 m. with the 

 help of depth measurements made with unprotected thermometers, and at most 

 stations, particularly at the greater depths, they were found to differ slightly from the 

 series of standard depths given above. 



In treating the data I have followed the procedure of Helland-Hansen 1 using 

 anomalies of specific volume and dynamic depth, but instead of referring them to a sea 

 of uniform temperature o° C, and salinity 35-00 °/ 0o I have adopted a standard of 

 temperature o° C. and density (o t ) 28-00. This standard is more convenient for use in the 

 Southern Ocean, giving smaller numbers to work with, and with it the labour of cal- 

 culating the anomalies was lightened tremendously by the help of a new set of tables 

 given to me in manuscript by Mr D. J. Matthews. The anomalies are generally found 



1 The procedure given in a report on the Scientific Results of the 'Michael Sars' North Atlantic Deep- 

 Sea Expedition : Physical Oceanography and Meteorology. The date of publication is not given in the report 

 but references in the text suggest that it was written after 1929. 



