Vertical jet diffusion in non linear density stratified fluid

Graduation date: 1967The simplified equations of motion proposed by Morton to determine\ud the extent of vertical travel of a forced plume in a linear\ud density stratified environment were re-written and solved in a way\ud which allowed them to be applied to any non linear profile of density.\ud For application to any specific situation it was shown that the solution\ud did not have to commence from a virtual point source, but rather\ud could start from the actual source of finite diameter, progressing in\ud steps through a number of segments of variable length. In each segment\ud a linear density gradient was specified which closely approximated\ud the actual gradient. A method was developed to find the virtual\ud point source, however, for those cases requiring the comparison\ud of flows in a linear gradient,\ud The equations of motion provided a method for achieving similarity\ud between model and prototype and this method was employed in\ud designing the physical model studies incorporated in this study.\ud Experimental values of maximum penetration and of the position\ud of the horizontally-spreading layer were obtained in a one meter\ud deep tank of 2.4 meters diameter. Stratification was obtained with\ud salt solutions of varying densities. The results from runs using five\ud different gradients and the results of analyzing the experiments of\ud others demonstrated that the method is suitable for obtaining a rough\ud approximation of the location of the bottom of the horizontal layer.\ud Its use for estimating maximum penetration is discounted on both\ud theoretical grounds and experimental evidence. Both levels were underestimated\ud by the mathematical model, in comparison to the experimental\ud values.\ud A computer program was employed to solve the equations, and\ud rounding errors as well as inefficient methods of quadrature were\ud found to account for as much as forty percent of the discrepancy between\ud observed and predicted values