Author(s): Hidekazu Yoshioka; Koichi Unami; Masayuki Fujihara
Linked Author(s): Koichi Unami, Masayuki Fujihara
Keywords: Turbulent flow; Stochastic differential equation; Lagrangian particle transport model; Hyperbolic partial differential equation model; Turbulent diffusion coefficient matrix
Abstract: Transport phenomena in surface water bodies have extensively been studied due to their significant impacts on water environment. Flows in surface water bodies are turbulent in general exhibiting large fluctuations both in space and time. Transport phenomena in turbulent flows have conventionally been analyzed using deterministic mathematical models based on the parabolic partial differential equations with advection terms, which conflict with the law of causality because they have infinite speed of signal propagation. This study proposes a new hyperbolic partial differential equation model for solute transport phenomena in turbulent flows, which on the other hand, rigorously complies with the law of causality. For that purpose, a Lagrangian particle transport model, a system of stochastic differential equations governing both paths and velocities of conservative solute particles, is presented. The particle transport model assumes Gaussianity of turbulence, and its associated Kolmogorov‘s forward equation is of an elliptic-parabolic type partial differential equation. Exact solutions to the particle transport model are obtained under simplified conditions. A Galilean invariant hyperbolic partial differential equation model serving as the macroscopic solute transport equation, referred to as the GI hyperbolic model, is deduced on the basis of the linearity of the Kolmogorov‘s forward equation without assuming any empirical laws. Some basic properties of the GI hyperbolic model, such as characteristics and hyperbolicity, are studied and the turbulent diffusion coefficient matrix is analytically parameterized using the model parameters. Finally, simple identification methods for the model parameters that only use local velocity time series data as input are presented and applied to the data observed in an actual three-dimensional turbulent open channel flow. Values of the model parameters are successfully identified. The identified results show significant anisotropy of the flow field and the model parameters, indicating limited applicability of the conventional isotropic turbulence models.
Year: 2013