Two‐dimensional shallow flow equations for partially dry areas

Abstract

Abstract. A new set of two-dimensional shallow flow equations is developed in order to deal with partially wet and very irregular domains. The bottom irregularities, which in many practical cases strongly affect the dynamics and the continuity, are accounted for statistically. Assuming hydrostatic approximation, the three-dimensional Reynolds equations are suitably averaged over a representative elementary area and then integrated over the depth. The resulting subgrid model for ground irregularities is tested by resolving two sample problems. The first concerns the wetting and drying of tidal flats; the second deals with overland flow on an irregular plane surface. Numerical simulations show that the proposed equations are a useful tool for modelers who have to cope with partially dry domains.

Flood inundation modeling in urbanized areas: A mesh-independent porosity approach with anisotropic friction

“…A N U S C R I P T 4 [31]; in their Dual Integral Porosity (DIP), the distinction between storage and conveyance porosities is better formalized, and simple closure relations are introduced to link them together. As a result, only the storage porosity appears in the continuity equation, in agreement with previous findings [32].…”

Flood inundation modeling in urbanized areas: A mesh-independent porosity approach with anisotropic friction

“…A N U S C R I P T 4 [31]; in their Dual Integral Porosity (DIP), the distinction between storage and conveyance porosities is better formalized, and simple closure relations are introduced to link them together. As a result, only the storage porosity appears in the continuity equation, in agreement with previous findings [32].…”

On the drainage density of tidal networks

“…It appears that, in general, the divides do not coincide with the lines equidistant from channel axes, and that they migrate during the tidal cycle thus inducing a time variability of the watersheds. This behavior is clearly shown in Figure 5, which shows the temporal evolution of watershed areas of the tidal subbasins specified in Figure 4, and is consistent with observations and with results from a finite element model [ Defina , 2000] (which is appropriately described below). The deviations from the values obtained by assuming an instantaneous propagation of the tidal wave in the channel network, represented by straight horizontal lines, do not follow any particular trend, their extent depending on the subbasin considered.…”

Dual integral porosity shallow water model for urban flood modelling

“…It is interesting to notice that only the storage porosity φ Ω appears in the continuity equation (in contrast with the original IP model). This makes the new continuity equation consistent with that derived by Dena [9]. Table 1 summarizes the various available formulations for u and f , the corresponding Jacobian matrices A and their eigenvalues λ in the one-dimensional case.…”

Flood inundation modeling in urbanized areas: A mesh-independent porosity approach with anisotropic friction

“…A N U S C R I P T 4 [31]; in their Dual Integral Porosity (DIP), the distinction between storage and conveyance porosities is better formalized, and simple closure relations are introduced to link them together. As a result, only the storage porosity appears in the continuity equation, in agreement with previous findings [32].…”

On the drainage density of tidal networks

“…It appears that, in general, the divides do not coincide with the lines equidistant from channel axes, and that they migrate during the tidal cycle thus inducing a time variability of the watersheds. This behavior is clearly shown in Figure 5, which shows the temporal evolution of watershed areas of the tidal subbasins specified in Figure 4, and is consistent with observations and with results from a finite element model [ Defina , 2000] (which is appropriately described below). The deviations from the values obtained by assuming an instantaneous propagation of the tidal wave in the channel network, represented by straight horizontal lines, do not follow any particular trend, their extent depending on the subbasin considered.…”

Dual integral porosity shallow water model for urban flood modelling

“…It is interesting to notice that only the storage porosity φ Ω appears in the continuity equation (in contrast with the original IP model). This makes the new continuity equation consistent with that derived by Dena [9]. Table 1 summarizes the various available formulations for u and f , the corresponding Jacobian matrices A and their eigenvalues λ in the one-dimensional case.…”

Flood inundation modeling in urbanized areas: A mesh-independent porosity approach with anisotropic friction

“…A N U S C R I P T 4 [31]; in their Dual Integral Porosity (DIP), the distinction between storage and conveyance porosities is better formalized, and simple closure relations are introduced to link them together. As a result, only the storage porosity appears in the continuity equation, in agreement with previous findings [32].…”

On the drainage density of tidal networks

“…It appears that, in general, the divides do not coincide with the lines equidistant from channel axes, and that they migrate during the tidal cycle thus inducing a time variability of the watersheds. This behavior is clearly shown in Figure 5, which shows the temporal evolution of watershed areas of the tidal subbasins specified in Figure 4, and is consistent with observations and with results from a finite element model [ Defina , 2000] (which is appropriately described below). The deviations from the values obtained by assuming an instantaneous propagation of the tidal wave in the channel network, represented by straight horizontal lines, do not follow any particular trend, their extent depending on the subbasin considered.…”

Dual integral porosity shallow water model for urban flood modelling

“…It is interesting to notice that only the storage porosity φ Ω appears in the continuity equation (in contrast with the original IP model). This makes the new continuity equation consistent with that derived by Dena [9]. Table 1 summarizes the various available formulations for u and f , the corresponding Jacobian matrices A and their eigenvalues λ in the one-dimensional case.…”