CHARACTERISTIC ANALYSIS OF TURBID UNDERFLOWS

Some analytical solutions are derived for the one-dimensional, vertica lly integrated, time-dependent equations describing turbid underflows. The system of equations is hyperbolic, therefore, the method of chara cteristics may be used to transform the partial differential equations to a system of ordinary differential equations, which may then be int egrated for the solution. The resulting analytical solutions provide a valuable tool which may be used not only to verify a numerical method , but also to gain insight into the behavior of the equations. It is a lso shown that the two-dimensional equations cannot be transformed int o a system of ordinary differential equations and therefore cannot be integrated exactly. However, the characteristic decomposition of the e quations yields important information about the physics of the turbidi ty equations and also provides insight into the appropriate constructi on of numerical techniques for solving the multidimensional equations.