Water Resources of the United States
Visualizing the SUTRA dispersion model in 3DBackgroundThe SUTRA dispersion model in three dimensions (3D) is a generalization of the original twodimensional (2D) model. The 2D and 3D SUTRA dispersion models are described in detail in Section 2.5 of the SUTRA documentation. This page supplements the formal documentation by providing interactive visualizations of the 3D dispersion model. A VRML browser is required to view the visualizations interactively. In the 3D SUTRA dispersion model, the longitudinal and transverse dispersivities, a_{L}, a_{T1}, and a_{T2}, can depend on the direction of groundwater flow, i.e., the dispersion model can be anisotropic. SUTRA computes the value of the longitudinal dispersivity, a_{L}, from the radius of an ellipsoid measured along the flow direction. Thus, a_{L} is greatest when flow is along the longest axis of the ellipsoid. The transverse dispersivities, a_{T1} and a_{T2}, are computed from radii of a second ellipsoid. These transverse radii are measured along two directions that are perpendicular to the flow direction and to each other. The user controls the behavior of the 3D dispersion model by setting SUTRA input parameters that determine the dimensions and orientation of the two ellipsoids in space:
3D visualizationsThe visualizations below are best viewed interactively, which will allow you to rotate, zoom, and pan the image. This requires a VRML browser. The way in which SUTRA computes the longitudinal dispersivity, a_{L}, as a function of flow direction is illustrated in the figure below, which corresponds to Figure 2.4b in the SUTRA documentation:
Figure. How SUTRA calculates the longitudinal dispersivity, a_{L}, as a function of flow direction. Here, v is the flow (velocity) vector; x_{max}, x_{mid}, and x_{min} are coordinates aligned with the max, mid, and min directions, respectively; and a_{L} is the squared radius measured along the flow direction. The principal radii of the ellipsoid (not labeled) have squared lengths of a_{Lmax}, a_{Lmid}, and a_{Lmin}, and are aligned with the max, mid, and min directions, respectively. Note that a_{L}=a_{Lmax} for flow in the max direction, a_{L}=a_{Lmid} for flow in the mid direction, and a_{L}=a_{Lmin} for flow in the min direction. The way in which SUTRA computes the transverse dispersivities, a_{T1} and a_{T2}, as a functions of flow direction is illustrated in the figure below, which corresponds to Figure 2.4c in the SUTRA documentation:
Figure. How SUTRA computes the transverse dispersivities, a_{T1} and a_{T2}, as a functions of flow direction. Here, v is the flow (velocity) vector and x_{max}, x_{mid}, and x_{min} are coordinates aligned with the max, mid, and min directions, respectively. The principal radii of the ellipsoid (not labeled) have squared lengths of a_{Lmax}, a_{Lmid}, and a_{Lmin}, and are aligned with the max, mid, and min directions, respectively; and a_{T1} and a_{T2} are squared radii measured in two directions perpendicular to the flow direction. These two directions, which are the transverse dispersion directions, correspond to the principal axes of the ellipse (called the slicing ellipse) formed by the intersection of the ellipsoid with the plane that passes through the origin and is perpendicular to the flow direction. Note that when groundwater flow is in one of the three principal permeability directions (max, mid, or min), a_{T1} and a_{T2} take on the values associated with the other two directions. Thus, the transverse dispersivities are a_{Tmid} and a_{Tmin} for flow in the max direction; a_{Tmax} and a_{Tmin} for flow in the mid direction; a_{Tmax} and a_{Tmid} for flow in the min direction.

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