and these harbor waters exchange, to a greater or lesser degree, with 

 the adjacent coastal waters. 



Consider such a harbor having a volume V and an exchange co- 

 efficient of Y (per day). The exchange coefficient is the fraction of the 

 voluine of the water in the harbor which is renewed each day by ex- 

 change with the adjacent coastal waters, and by inflow of lajid drainage. 

 Y is thus comparable to the radioactive decay coefficient, and a "half- 

 life" for the harbor water can be defined in the same way as radioactive 

 half- life. 



The tj/2in equation 1 is then the half-life of the area, axid is re- 

 lated to Y by 



0.693 



1/2 



Y 



Further, consider a particular discharge of effluent into the har- 

 bor. Following the initial mechanical dilution, turbulent diffusion will 

 lead to further dilution at approximately an exponential rate, at least 

 during the early stages of diffusion when contaminated volume is small 

 compared to the volume of the harbor. 



A major part of the analysis of the problem of disposal of nuclear 

 wastes into the sea and coastal waters requires sufficient knowledge of 

 the rates of mixing so that the dilution of any introduced liquid can be 

 estimated correctly. 



The diffusion model employed in this analysis : It has always 

 been difficult to make such an estimate because of the lack of a satis- 

 factory general theory of diffusion in the sea; rates of diffusion (the 

 so-called eddy diffusivity coefficients) required by existing theory were 

 known adequately only for certain special cases where direct measure- 

 ments had been made. Recently, however, Joseph and Sender (1958) 

 have proposed a horizontal diffusion equation which seems to permit a 

 useful statistical description of the time change of concentration of a 

 diffusing substance. The following paragraphs discuss the application 

 of this diffusion equation to the problem of waste disposal from nuclear- 

 powered ships. 



Joseph and Sender consider the introduction at time t = of an 

 amount M of a substance into a small area either of the sea surface or 

 at some deeper level. This small area is regarded as the "point" 

 source for isotropic horizontal diffusion along a thin homogeneous ajid 

 isentropic layer. After time t the distribution is described by concen- 

 tric isopleths around the point of maximum concentration. This point 

 is not fixed but moves downstream with the prevailing current. It is 

 further postulated that the velocity of a diffusing particle is independent 

 of distance from the origin, but that the mean dispersion increases in 

 linear fashion with increasing distance. 



31 



