Solving the Model
The existence of the stochastic components in the model equations makes it difficult to solve them. If we integrate (1) , the velocity equation, we get:
(3) 
The last term in (3) must be replaced by which is given by:

NEEDS CHECKING (4) 
where
dt 
represents the integration step length 
N(0,1) 
represents a standard normal variate 
e 
is the eigenvalue of the matrix which models the space correlation which occurs due to the Wiener process W 
s 
represents the size of the random component 
The scheme for the solute flux equation (2) is similar. See (Kulasiri ,1997) for further information on the solution of the equations.