96 



BJ0RN HELLAND-HANSEN 



[REP. OF THE "MICHAEL SARS" NORTH 



is the distance in dyn. metres between two points in the 

 sea and h the vertical distance in metres we have 



A Z) = 



10.' 



where g is an average value of g in the space between 

 the two points. 



If we have two points A and B (Fig. 37), with a 

 vertical difference of h metres (or i D dynamic metres) 

 and a distance / metres between them, and the angle 



Fig. 37. The gravitational force. 



between the line A B and the level surfaces D and D + 

 A D through A and B is y, the gravitational work done 

 in moving a unit mass from A io B is: 



W=Lg. sin y = l.g.~=:g.h^\0 i\ D. 



The acting force per unit mass in the direction 

 from /4 to B is 



U7_ 10 .1 D 

 ~ I ~ I 



(b) 



The hydrostatic pressure, p, is generally defined as 

 a force per unit area, /. e. per square metre in the m.t.s. 

 system. It has become custoinary in oceanography to 

 neglect the atmospheric pressure when dealing with the 

 pressure within the sea. The pressure at a depth of // 

 metres is then simply equal to the weight of the vertical 

 water column from the surface to h metres, covering a 

 horizontal area of 1 square metre. If the average den- 

 sity (compression included) is o, the average weight per 

 cubic metre is q. g, and the pressure 



p = Q. g. h ^^ Q. \0 D m. t. s. units, 



D being the depth in dynainic metres. When we intro- 

 duce specific volume (a) instead of density we get: 



D^ — ap. 

 10 



A pressure of 10° dyne/cm^ has been called a bar, 

 which almost corresponds to an atmosphere. The m.t.s. 



unit of pressure is 1/100 bar, or a centibar. V. Bjerk- 

 NES has introduced the decibar =^ 1/10 bar as a tec/i- 

 iiical unit of sea pressure. This corresponds to the pres- 

 sure exerted by a water column which is nearly 1 metre 

 high. The relation between dynamic depth and pressure 

 is expressed by one of the equations 



p' =^ Q. D decibars 

 D=^i(.p' dynamic metres 



When we know the vertical distribution of density 

 or specific volume in the sea, we can easily find the 

 pressure at a given dynamic depth or the dynamic depth 

 corresponding to a given pressure. The compression of 

 the water must be considered in the calculations. 



On account of variations in density the isobaric sur- 

 faces will not, as a rule, be parallel to the level surfaces, 

 but intersect them. In a level surface there will usually 

 be variations of pressure, and in an isobaric surface va- 

 riations of dynamic depth. We can draw isobars in a 

 chart for a certain dynamic depth, which is similar to 

 the isobaric charts used in meteorology. Or we can draw 

 isobaths for equal dynamic depth in a chart for a certain 

 isobaric surface, which is similar to topographical charts. 

 In a surface of equal depth (in ordinary metres) below 

 the surface of the sea there will, as a rule, be variations 

 both of pressure and of gravity potential (dynamic depth). 

 A dynamic chart for such a surface would therefore con- 

 tain two sets of lines, isobars and isobaths, while in the 

 isobaric charts or the topographical charts just mentioned, 

 we have only one set of lines. The latter charts are 

 therefore much simpler and more convenient for a dis- 

 cussion of the dynamics of the sea. 



Along a level surface the force due to differences in 

 gravity potential is 0. If occasionally the difference of 

 pressure is likewise 0, the water is subjected to no moving 

 force at all. But generally the pressure varies along the 

 level surface, with the result that a force will act in the 

 direction from a place with a higher pressure to a place 

 with a lower pressure. Let us suppose that we have a 

 station with the pressure p^ decibars at a dynamic depth 

 D and another station, / metres away, with the pressure 

 /7o at the saiTie level (pi > po), and imagine that we 

 have a straight tube with a cross section of one square 

 metre laid between the two points. The tube will have 

 a volume of / m^ and contain a mass of water m = q.l, 

 when q is the average density within the tube. This 

 mass will be moved by a force = /^j — p^ tech- 

 nical units or 10 (/>, — po) m.t.s. units in the direction 

 from the first station to the second and acquire an 

 acceleration a. Leaving friction out of account we have 



