392 



General Theory of Ocean Currents in a Homogeneous Sea 



done by the turbulent motion in unit volume is, however, rj(8uldzy. The condition 

 for the decrease of the turbulence in the disordered flov^ and its transformation into 

 an ordered flow is thus that the dimensionless stratification quantity 



(glp)(Spl8z) 



(duldzf 



>l 



(XIII.21) 



In earlier investigations it has mostly been assumed that rj and A are numerically 

 equal, i.e. that the mechanism of mixing of a material property is identical with that 

 of the impulse or momentum transport. Then 17 would be equal to A, and since the 

 stabiUty of the stratification would be given by (l/p)(8p/ez) = E (pt. I, p. 196), the 

 condition for the suppression of the turbulence would be 



gE 



;^> 1. 



(XIII.22) 



(duldz)' 



The expression on the left-hand side has been denoted the Richardson number Ri. The 

 upper limit at which all turbulent motion is extinguished is thus given by Ri = 1 ; how- 

 ever, in reality smaller values are sufficient. Referring to the latter statement, theoretical 

 and experimental investigations of Taylor (1931) and Goldstein on small oscillations 

 in a stratified flow with a linear decrease in velocity have shown that the limit can be 

 expected at Ri = 0-25 or |. 



In oceanography it has usually been found (see pt. I, p. 104) that the ratio rj-.A is 

 of the order of 5 to 20. In the equatorial regions of the Atlantic Ocean in the density 

 transition layer (thermocline) dpjdz is of the order of 3 to 9 X 10-* for a 20 m height 

 interval. The decrease in velocity du/dz should be between 5 and 10 cm/sec for every 

 20 m, so that Ri must be between 6 and 69 (Defant, 1936c, p. 296 and 363). It is 

 clear that these figures are sufficiently high to prevent the occurrence of turbulence in 

 the tropospheric deeper currents, as has been found by observation. 



Observations at two stations in the Baltic for which there was almost no turbulence 

 to be observed in the transition layer gave according to Gustafson and Kullenberg 

 (1936) Ri-numbers of 0-59 and 0-95 which are in accord with the hmiting values given 

 by Taylor. Detailed measurements have been made by Jacobsen (1913, 1918) at 

 Schultz's Grund (Kattegat) and in the Randersfjord, which are very suitable for 

 answering the question under consideration. Table 1 17 give as summary ofall the values 

 derived from these measurements. 



Table 117. Turbulence and Ri-numbers at Schultz's Grund {according to 



Jacobsen) 



