Liu et al. (2026) Optimality-Based Active Region Model (ARM) for Fingering Flow in the Vadose Zone: Recent Theoretical Progress

⚠️ Warning: This summary was generated from the abstract only, as the full text was not available.

Identification

• Journal: Water
• Year: 2026
• Date: 2026-03-08
• Authors: Hui-Hai Liu, Yingjun Liu, Shuo Zhang
• DOI: 10.3390/w18050641

Research Groups

Not explicitly available from the provided text.

Short Summary

This paper presents the latest theoretical developments of the optimality-based active region model (ARM), a macroscopic framework designed to accurately describe gravitational fingering flow in the vadose zone, by providing an updated mathematical derivation and extending it to a dual-flow field model for enhanced rigor and realism.

Objective

• To present the latest theoretical developments of the optimality-based active region model (ARM), a macroscopic framework for describing gravitational fingering flow in the vadose zone, to make it more rigorous and realistic for field-scale applications.

Study Configuration

• Spatial Scale: Vadose zone, field-scale applications.
• Temporal Scale: Not explicitly defined, but concerns the dynamics of water flow processes.

Methodology and Data

• Models used: Optimality-based active region model (ARM), extended to a dual-flow field model.
• Data sources: Theoretical development; no external data sources (e.g., satellite, observation, reanalysis) mentioned for this specific paper.

Main Results

• An updated mathematical derivation of ARM relationships is provided using calculus of variations.
• ARM is extended to account for small water flux in the non-fingering zone, resulting in a dual-flow field model.
• ARM's hydraulic conductivity is shown to depend on both capillary pressure (or water saturation) and water flux, reflecting the unstable nature of fingering flow.

Contributions

• Provides a more rigorous and realistic macroscopic framework (ARM) for modeling gravitational fingering flow in the vadose zone.
• Introduces a novel dual-flow field model by extending ARM to incorporate non-fingering zones with small water flux.
• Offers a unique approach where hydraulic conductivity is flux-dependent, which is crucial for accurately representing unstable fingering flow unlike traditional models.

Funding

Not available from the provided text.

Citation

@article{Liu2026OptimalityBased,
  author = {Liu, Hui-Hai and Liu, Yingjun and Zhang, Shuo},
  title = {Optimality-Based Active Region Model (ARM) for Fingering Flow in the Vadose Zone: Recent Theoretical Progress},
  journal = {Water},
  year = {2026},
  doi = {10.3390/w18050641},
  url = {https://doi.org/10.3390/w18050641}
}