Theoretical study on stochastic model of sediment interchanges

Four motion states are supposed by Han: stationary, rolling, jumping and suspension. The step motion and unit motion are introduced as the fundamental concept of stochastic model. The nunit motion consists of several steps of the same motions. For a long time, Markov process with discrete states and time is used to describing sediment interchanges near the flow bottom. Therefore, the transport process is a Markov process with discrete states and continuous time. On the basis of the Han´s one-step movement transition probability of Markov with discrete states and time, the author obtains the transition law of the interchanges between various movement states of sediments with continuous time. The analysis of stationary distribution shows that the model can be applied to describe the general case for the sediment interchange process. Finally, the application of transition probability with continuous time to nonequilibrium transportation rate of bed load is discussed. This study demonstrates that the concept of transition probability with continuous time is a useful approach for sediment research.