Meanders 135 



table of h and v for a meander with radius of curvature ^ = (2/3) x 10'' cm. 

 and a = 10~''/cm. The values of v are then plotted against h for both cyclonic 

 and anticyclonic curvature. The results, scaled from the plot, are shown 

 in table 8. The diflference is most pronounced for small values of ^/Ag. The 

 proper place for a test is probably at about A/^o = 0-2. 



Since the total transport of the Stream in a crest is greater than that 

 through a trough, the meander pattern moves, as a whole, downstream. The 

 rate of this progression may be found by the following simple reasoning. 

 First evaluate the total transport T : 



J a;=2/(3a'£ 



T= I vMx 



(23) 



^"^^{2^ Qccm 



When the values of parameters introduced above are used, the transport 

 at the crest is greater than that through the trough by about 10 per cent 

 of the average transport. Suppose that the shape of the meander is 



x = Xq cos {ky — vt) . (24) 



At time t = 0, the rate of increase of volume W of warm water between 

 ky = and ky — n due to the motion of the meander is 2xQliQ{vlk). This, of 

 course, must be equal to the excess of transport through a crest {ky = 0) 

 over that through a trough {ky = n), chJSa^^?. But at ^ = and y = 0, the 

 radius of curvature ^ is also given in terms of the equation 



3^x 



hence 



V c^k^ 

 k^'Of 



(26) 



The rate of progress of a meander with a wavelength of about 300 km. 

 is therefore about 5 cm. /sec. The actual movement of meanders ought to 

 be studied extensively by means of the air-borne radiation thermometer. 



