Properties of the dead-zone model of longitudinal dispersion in rivers

The dead zone equations were solved with the use of the Laplace transform technics. The solution was a base to derive the three moments of the pollution concentration distribution in a river. They differ from the moments published so far, because they were calculated from the solution of the pure boundary problem. This approach is easier to apply in calculations of the pollution concentration distributions and it covers a wider range of cases when we deal with natural field data. Main features of the model equations were analysed from the point of view of the theory of dynamic systems. The transfer function was derived and analysed as well as the frequency-response function. The dispersion relation for the dead zone equations was also obtained and analysed for different parameters of the model.