Chapter IX 



The Geophysical Structure of the Sea 



1. Introduction 



Since the ocean currents are displacements of water masses the distribution of mass 

 in the sea becomes of particular importance in all hydrodynamic investigations. It 

 is specified by the distribution of the density or of the specific volume, which are both 

 determined by the thermo-haline structure of the ocean. In addition to the distribution 

 of mass there is an internal field of force due to the distribution of pressure of the 

 water masses in both vertical and horizontal direction. The atmospheric pressure which 

 exerts a varying force on the surface of the sea must be also considered a source for 

 disturbances. In addition to these forces the only external conservative force, the 

 gravity, must also be taken into account, since it intervenes in an essential way in all 

 phenomena involving the movement and equilibrium of the water masses of the oceans. 

 Thus the fields of gravity, of pressure and ofrjiass in the ocean play an important part 

 in all hydrodynamic investigations. For a quantitative description of a phenomenon 

 the magnitude of the units used is essential. At the present time the absolute units of 

 the CGS system [cm, g, sec] are preferably used, but in many cases according to the 

 magnitude of the numerical values there are practical advantages in the use of larger 

 units, usually obtained by multiplication by a suitable power of 10. The metre (10^ cm) 

 is a suitable unit of length in dynamic oceanography, but the nautical mile, which is 

 the length of an arc of one minute at the equator (1852 m), is also used. The metric 

 ton, the mass of a cubic metre of water with a density of 1 (10® g) is frequently used as 

 mass unit together with the second, the minute and the hour as units of time. The 

 velocity may be defined in absolute units (cm sec~^) but is also frequently given in 

 nautical miles per hour (= 1 knot = 51-4 cm sec~^) (Maurer, 1938). 



2. The Distribution of Gravity and Gravity Potential 



Gravity is the result of the force of attraction of earthly masses and of the centri- 

 fugal force of Earth rotation. Its distribution at the surface of the Earth can be found 

 by pendulum measurements, for which it is suflftcient to use its normal values. At the 

 present time the most frequently used formula for a calculation of gravity is that of 

 Heiskanen and Cassini; Lambert, 1931 : 



g^ = 978-049 (1 -f 0-0052884 sin^ cf, - 0-0000059 sin^ 2<^ [cm sec-^]. (IX. 1) 



Calculations of the gravitational acceleration within the sea must take into account the 

 density of the water mass and also the result of the potential theory that the outer 

 shell of a sphere exerts no attraction on a point in the interior of the sphere. If k is 

 the gravitational constant, M the mass of the Earth and R the radius of the Earth 



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