Time-Integrated Equations and Attractors for Long-Term Modeling of Estuaries

Abstract

Because of the special geographic features and high rate of biological productivity of the estuary, analyzing the evolution of an estuary over long periods is important for understanding and predicting environmental changes in the natural ecosystem. To predict the behavior of the varied flow conditions in natural phenomena, we require a simple mathematical model to analyze that behavior. Averaging methods are extensively used for fluid studies. Based on changing flow conditions, the time span could be divided into three periods, long, medium, and short. In this paper, a long-term averaging model for the estuary is introduced to predict flow variation, sediment transport, and bed morphology change. In addition, various variables that may influence the river system are discussed, and some reasonable values of these variables are estimated empirically. By introducing the time scales and instantaneous variables into the one-dimensional hydraulic equations of continuity, momentum, sediment transport, and bed morphology change, we obtain four simplified equations. A case study of the Snowy River is discussed. Based on these simplified dynamic equations, we identify four attractors by solving the equations numerically under certain boundary conditions.