induced mixing resulting from the relative motion between the disposed material and 

 receiving water. The second phase, called dynamic collapse, occurs when the material 

 encounters a density gradient which, if strong enough, may prevent the material from settling 

 further. Bottom encounter is a special case of the strong gradient and is the situation 

 considered in the present capping model. The Koh and Chang (1973) report further 

 considers a long-term passive dispersion/diffusion process for those cases when settling may 

 be inhabited by a sufficiently strong density gradient in the water column. 



DESCRIPTION OF CAPPING MODEL 



In the present model, the goal was to draw on the work presented in the above reports 

 and provide a management tool that would not require the user to have overly extensive 

 background data, in the form of input parameters, to estimate the mound configuration of a 

 hypothetical disposal project. As an example, while the models described above require 

 input of the density gradient in the water column, this variable is not normally known at the 

 time of the disposal operation and, therefore, a uniform density was assumed. This led to 

 the conclusion that dumped material will eventually reach the bottom and the only gradient 

 encountered will be the bottom. The model was also designed to run on any PC-compatible 

 computer with a math coprocessor. 



The phases of disposal, therefore, which were considered in the DAMOS Capping 

 Model are the convective descent and bottom encounter. The two referenced reports derived 

 essentially the same equations describing the phases with the exception of the expression for 

 the velocity of the centroid of the collapsing cloud. The Brandsma and Divoky (1976) 

 equations were used because they were thought to avoid numerical difficulties inherent in the 

 Koh and Chang scheme. 



There were many coefficients that occurred in the equations which are not normally 

 measured and represented uncertainly in the model. In all cases, the recommended values 

 from the above reports were used and the user is not required to input them. If the user has 

 data that indicate different values for some of the coefficients, he may enter them into the 

 model by editing the file DREDGE. D. This file, which contains model coefficients as well 

 as fall velocities, in situ densities, and entrainment factors, is read each time the model is 

 run. DREDGE. D may be edited with any word processor which will produce a pure ASCII 

 text file. 



The relationships which comprise the model form a system of simultaneous 

 differential equations for each of the two phases considered. These are solved using a forth 

 order Rung-Kutta scheme. There are three differential equations in the connective descent 

 phase representing conservation of mass, momentum, and buoyancy. The above reports also 

 include conservation of vorticity and solid particles; however, in the absence of a vertical 

 density gradient, the change in vorticity reduces to zero. Koh and Chang (1973) argued that 

 settling of particles from a falling cloud may be ignored as long as the cloud and particles are 

 going in the same direction. During the dynamic collapse phase, the number of simultaneous 

 differential equations was increased to eight. In addition to the conservation of mass and 

 buoyancy, there were four equations for the conservation of solid particles (one for each 



