OCS Study MMS 95 - Data Center

where x is downwind distance, cm ; and d is a dispersion coefficient, cm2 sec-1 .Similar models are described by Csandy (1972) to describe a plume resulting from acontinuous oil spill .The x,y points that lie on the boundary of the detectable plume satisfy theequation9ex -rx _ y 2 -cd = 02n u a 4 u 2a2 ~ (3)where cd is the minimum detectable thickness of oil, cm ;r is the e-folding time ordegradation constant (r = 0 .693/(86,400T), sec-1 ; T is a degradation half life, days ;and s is given by (2) .The model requires that the size and shape of the detectableplume is dependent on the parameters q, cd, u, r, and d, which we will refer to asthe parameters .Some insight can be gained into these equations by scaling them interms of some simple dimensionless variables .A natural scale length for theproblem is given byL=du (4)Substituting the dimensionless variables Y=y/L, X=x/I., R=rd/u2, and Q=q/(dcd) into(1) giveszC=1 Q exp(-RX - )(5)2-18