Characteristics of Meandering Compound Channel Flow Evaluated With Two-Layered, 2-D Method

Abstract

Based on a numerically-generated boundary-fitted orthogonal curvilinear coordinate system, a 2-layered, 2-d mathematical model for unsteady flows with complicated boundaries is presented. It is employed to evaluate the change of flow patterns such as water surface level, velocity vector, Lagrangian pathline and friction factor in sinegenerated meandering compound channel in terms of water depth ratio between in main channel and in flood plain. It is concluded that the over-bank flow is impacted severely by the meandering main channel flow when the flow depth on flood plain is shallow, and is almost independent of that when hu/hi is greater than 0.9, except the super-elevation of water surface due to the meandering in-bank flow. The bulk friction factor (f or f78C, ) changes with hu/hi very interestingly.

Development of Two-layered model for compound open-channel flow

“…The governing equations for two-dimensional, two-layered shallow water approximation for incompressible flow under hydrostatic pressure condition can be derived using Navier-Stokes equation (Chau and Jin 1995;Jin et al 1998). The layer-averaged continuity and momentum equations in rectangular coordinate system for upper and lower layers can be written as…”

“…τ 0x = τ bx , etc. The bed and interface shear stresses and flow velocities at interface of the two layers, appearing in Equation (8), are expressed empirically similar to that of adopted by Jin et al (1998).…”

“…The shear stress at the interface between the upper and lower layers is expressed as (Jin et al 1998…”

“…Chau and Jin (1995) developed a two-layered, two-dimensional model based on finite difference approach using CFD-based numerically generated boundary fitted orthogonal coordinate system and used to simulate density stratified unsteady flows in a natural water-body with complex topography. Later on, Jin et al (1998) applied this model to simulate turbulent flows in a sinusoidal meandering compound open channel. In both the above-mentioned numerical studies (Chau and Jin 1995;Jin et al 1998), grid 'block' technique was used and, also, boundary fitted orthogonal curvilinear grids were generated in the physical plane which was transformed into rectangular grids in the computational plane resulting in complicated mathematical formulations with additional transformation relations.…”

“…Later on, Jin et al (1998) applied this model to simulate turbulent flows in a sinusoidal meandering compound open channel. In both the above-mentioned numerical studies (Chau and Jin 1995;Jin et al 1998), grid 'block' technique was used and, also, boundary fitted orthogonal curvilinear grids were generated in the physical plane which was transformed into rectangular grids in the computational plane resulting in complicated mathematical formulations with additional transformation relations. Prandtl's mixing length approach was used as closure for modeling the turbulent shear stress terms.…”