370 The Representation of Oceanic Movements and Kinematics 



and the stability are omitted from these charts. This type of representation is usually 

 chosen for current charts which are based less on direct current measurements and more 

 on a qualitative assessment of the horizontal distribution of the temperature, salinity 

 and other factors which the system of currents at the sea surface must reflect. 



A more comprehensive representation of the currents in an ocean has been used 

 by Meyer (1923) for an evaluation of Dutch observations on the currents in the At- 

 lantic during February. Figure 158 shows a part of this chart. Here also the stream lines 

 were broken up into a series of arrows of equal length but their thickness was used as a 

 measure of the current constancy (stabiHty), the feathering as a measure of the velocity 

 and the amount of data available was indicated inside the breaks in the shaft of the 

 arrow. The singularities in the current field are not shown so clearly by this type of 

 representation and are therefore indicated by special signs, particularly in the case of 

 the more important lines of convergence and divergence. These charts already permit 

 a deeper insight into the nature of the water movements at the sea surface of the ocean 

 under consideration and also allow an estimate of the reliability of the chart at any 

 particular area of the oceanic region. Similar but somewhat modified representations 

 have been chosen by Schott (1926, 1935) and Schumacher (1940, 1943). 



In assessing the value of a chart and in its use, it is necessary to keep in mind the 

 relatively large uncertainties which still remain attached to them. The number of 

 observations on which the charts are based in the individual degree squares varies 

 considerably and is often so small in some of the squares that chance can be rather 

 important. These difficulties, however, may decrease with time since the number of 

 observations collected by hydrographic institutes increases from year to year and 

 mechanical evaluation of these data by computing machines is much faster than was 

 previously possible. 



3. Special Cases of Current Fields Near Land and at the Boundaries of Water Masses 

 (Compensation Currents) 



The boundaries of the sea, fixed either by coast lines or by the topography of the 

 sea bottom, exert a considerable influence on the pattern of the ocean currents and 

 especially on the form of the current field. For each steady current (potential flow) 

 the water in the immediate vicinity of a solid boundary surface (coast or sea bottom) 

 tends to approach the boundary as closely as possible. The effect of such disturbances 

 is thus shown rather far from the source of disturbance in the current field and also in 

 the distribution of the oceanographic factors (temperature, salinity, etc.). The most 

 simple cases, which occur also in nature again and again can be expressed mathe- 

 matically by the method given on p. 327 ; a few of these can be briefly treated here. 



(1) Plane flow around a cylindrical obstacle (island) is given by a function 

 F = U{z + {a^lz)). Introducing in r = x + '>' polar co-ordinates, then 



z — /-(cos (f) -}- i sin ^) = re^'l' 



and the velocity potential O and the stream function ^ will thus be given by the 

 expressions 



= t/ jr + -J cos and "F = U Ir - ^-| sin cf,. 

 One stream line is the .v-axis for which sin <^ = 0, another one is the circumference 



