The bending Factor
The approach proposed by VAN DE WIEL (2003) considers plants as flexible elements and, therefore, incorporates mechanical aspects in the analysis. In his work, VAN DE WIEL (2003) refers to the study carried out by RAHMEYER et al. (1999), in which mechanical and resistance properties of different plant species were tested. RAHMEYER et al. (1999) stablished a relationship between the force required to bend the plant to an angle of 45 degrees in terms of the plant’s modulus of elasticity (E) and its moment of Inertia. VAN DE WIEL (2003) suggests that this relationship can be generalized to: F_α= 6EI/H^2 (sinα )^2 (10)
By definition, the force Fα applied to the vegetation equals the drag force FD applied by the flow. The …show more content…
(2011) discusses the improvements made to Van de Wiel’s vegetation roughness model. Two adjustments have been conducted in order to account for the contribution of leaves and branches to drag force. First, the streamlining factor (bv) is incorporated in the determination of a new calculated stem diameter (dveg). Second, a method for the determination of plant density (δ) is also presented. Plant density is another factor considered for the determination of dveg.
Calculated stem diameter …show more content…
A methodology for its determination is presented in BLAMAUER et al. (2011).
4.2 Two-Dimensional (2D) Hydrodynamic Modeling
This section provides an overview of the theoretical fundamentals of the 2D hydrodynamic modeling. It is divided into four subsections dealing, first, with the governing equations of 2D-Modeling. Secondly, the methods used for spatial discretization are briefly discussed. Afterwards, the different types of grid structures used in numerical modeling are described. Then, to conclude on the fundamentals of 2D hydrodynamic modeling, the approaches available for the temporal discretization are briefly explained. 4.2.1 Governing Equations
Two-dimensional Hydrodynamic models are governed by the 2D shallow water equations (NÉELZ and PENDER, 2009). These equations, which are also known as the Saint-Venant equations, are obtained by averaging the full 3D Reynold’s averaged Navier-Stokes equations (WILSON et al., 2002) and express conservation of mass and momentum (BRESCH, 2009).
The general form of the continuity equation and momentum equations along the x-axis and y-axis in 2D
The approach proposed by VAN DE WIEL (2003) considers plants as flexible elements and, therefore, incorporates mechanical aspects in the analysis. In his work, VAN DE WIEL (2003) refers to the study carried out by RAHMEYER et al. (1999), in which mechanical and resistance properties of different plant species were tested. RAHMEYER et al. (1999) stablished a relationship between the force required to bend the plant to an angle of 45 degrees in terms of the plant’s modulus of elasticity (E) and its moment of Inertia. VAN DE WIEL (2003) suggests that this relationship can be generalized to: F_α= 6EI/H^2 (sinα )^2 (10)
By definition, the force Fα applied to the vegetation equals the drag force FD applied by the flow. The …show more content…
(2011) discusses the improvements made to Van de Wiel’s vegetation roughness model. Two adjustments have been conducted in order to account for the contribution of leaves and branches to drag force. First, the streamlining factor (bv) is incorporated in the determination of a new calculated stem diameter (dveg). Second, a method for the determination of plant density (δ) is also presented. Plant density is another factor considered for the determination of dveg.
Calculated stem diameter …show more content…
A methodology for its determination is presented in BLAMAUER et al. (2011).
4.2 Two-Dimensional (2D) Hydrodynamic Modeling
This section provides an overview of the theoretical fundamentals of the 2D hydrodynamic modeling. It is divided into four subsections dealing, first, with the governing equations of 2D-Modeling. Secondly, the methods used for spatial discretization are briefly discussed. Afterwards, the different types of grid structures used in numerical modeling are described. Then, to conclude on the fundamentals of 2D hydrodynamic modeling, the approaches available for the temporal discretization are briefly explained. 4.2.1 Governing Equations
Two-dimensional Hydrodynamic models are governed by the 2D shallow water equations (NÉELZ and PENDER, 2009). These equations, which are also known as the Saint-Venant equations, are obtained by averaging the full 3D Reynold’s averaged Navier-Stokes equations (WILSON et al., 2002) and express conservation of mass and momentum (BRESCH, 2009).
The general form of the continuity equation and momentum equations along the x-axis and y-axis in 2D