Vertically integrated flows, discharge potential, and the Dupuit-Forchheimer approximation

Area of Science:

• Hydrology
• Fluid Dynamics
• Geosciences

Background:

• The Dupuit-Forchheimer approximation is a common simplification in regional flow modeling.
• Accurate representation of vertically integrated flows is crucial for understanding groundwater dynamics.
• Discharge potential offers a potential alternative for simplifying flow model formulations.

Purpose of the Study:

• To review and synthesize observations on discharge potential and vertically integrated flows.
• To evaluate the utility of discharge potential in regional flow modeling.
• To determine if using discharge potential simplifies model formulation without compromising accuracy.

Main Methods:

• Literature review of existing research on discharge potential and flow modeling.
• Analysis of the Dupuit-Forchheimer approximation in the context of discharge potential.
• Theoretical examination of boundary conditions and their relation to discharge potential.

Main Results:

• Discharge potential can be effectively used to formulate regional flow models.
• Boundary conditions expressed via discharge potential simplify model setup.
• The Dupuit-Forchheimer approximation is implicitly handled when using discharge potential.

Conclusions:

• Formulating regional flow models using discharge potential streamlines the process.
• This approach ensures accurate discharge calculations throughout the model domain.
• No additional simplifying assumptions are needed when discharge potential is correctly applied.