Competition Is the Underlying Mechanism Controlling Viscous Fingering and Wormhole Growth
Abstract Viscous fingering and wormhole growth are complex nonlinear unstable phenomena. We view both as the result of competition for water in which the capacity of an instability to grow depends on its ability to carry water. We derive empirical solutions to quantify the finger/wormhole flow rate...
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| Format: | Article |
| Language: | English |
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Wiley
2020-02-01
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| Series: | Geophysical Research Letters |
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| Online Access: | https://doi.org/10.1029/2019GL084795 |
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| author | Yoar Cabeza Juan J. Hidalgo Jesus Carrera |
| author_facet | Yoar Cabeza Juan J. Hidalgo Jesus Carrera |
| author_sort | Yoar Cabeza |
| collection | DOAJ |
| description | Abstract Viscous fingering and wormhole growth are complex nonlinear unstable phenomena. We view both as the result of competition for water in which the capacity of an instability to grow depends on its ability to carry water. We derive empirical solutions to quantify the finger/wormhole flow rate in single‐, two‐, and multiple‐finger systems. We use these solutions to show that fingering and wormhole patterns are a deterministic result of competition. For wormhole growth, controlled by dissolution, we solve reactive transport analytically within each wormhole to compute dissolution at the wormhole walls and tip. The generated patterns (both for viscous fingering and wormhole growth under moderate Damköhler number values) follow a power law decay of the number of fingers/wormholes with depth with an exponent of −1 consistent with field observations. |
| format | Article |
| id | doaj-art-52b95e8a25eb45b28c93a0a35b94b1d0 |
| institution | OA Journals |
| issn | 0094-8276 1944-8007 |
| language | English |
| publishDate | 2020-02-01 |
| publisher | Wiley |
| record_format | Article |
| series | Geophysical Research Letters |
| spelling | doaj-art-52b95e8a25eb45b28c93a0a35b94b1d02025-08-20T01:50:15ZengWileyGeophysical Research Letters0094-82761944-80072020-02-01473n/an/a10.1029/2019GL084795Competition Is the Underlying Mechanism Controlling Viscous Fingering and Wormhole GrowthYoar Cabeza0Juan J. Hidalgo1Jesus Carrera2Institute of Environmental Assessment and Water (IDAEA) Spanish National Research Council (CSIC) Barcelona SpainInstitute of Environmental Assessment and Water (IDAEA) Spanish National Research Council (CSIC) Barcelona SpainInstitute of Environmental Assessment and Water (IDAEA) Spanish National Research Council (CSIC) Barcelona SpainAbstract Viscous fingering and wormhole growth are complex nonlinear unstable phenomena. We view both as the result of competition for water in which the capacity of an instability to grow depends on its ability to carry water. We derive empirical solutions to quantify the finger/wormhole flow rate in single‐, two‐, and multiple‐finger systems. We use these solutions to show that fingering and wormhole patterns are a deterministic result of competition. For wormhole growth, controlled by dissolution, we solve reactive transport analytically within each wormhole to compute dissolution at the wormhole walls and tip. The generated patterns (both for viscous fingering and wormhole growth under moderate Damköhler number values) follow a power law decay of the number of fingers/wormholes with depth with an exponent of −1 consistent with field observations.https://doi.org/10.1029/2019GL084795wormholesviscous fingerscompetitionhydrologykarst |
| spellingShingle | Yoar Cabeza Juan J. Hidalgo Jesus Carrera Competition Is the Underlying Mechanism Controlling Viscous Fingering and Wormhole Growth Geophysical Research Letters wormholes viscous fingers competition hydrology karst |
| title | Competition Is the Underlying Mechanism Controlling Viscous Fingering and Wormhole Growth |
| title_full | Competition Is the Underlying Mechanism Controlling Viscous Fingering and Wormhole Growth |
| title_fullStr | Competition Is the Underlying Mechanism Controlling Viscous Fingering and Wormhole Growth |
| title_full_unstemmed | Competition Is the Underlying Mechanism Controlling Viscous Fingering and Wormhole Growth |
| title_short | Competition Is the Underlying Mechanism Controlling Viscous Fingering and Wormhole Growth |
| title_sort | competition is the underlying mechanism controlling viscous fingering and wormhole growth |
| topic | wormholes viscous fingers competition hydrology karst |
| url | https://doi.org/10.1029/2019GL084795 |
| work_keys_str_mv | AT yoarcabeza competitionistheunderlyingmechanismcontrollingviscousfingeringandwormholegrowth AT juanjhidalgo competitionistheunderlyingmechanismcontrollingviscousfingeringandwormholegrowth AT jesuscarrera competitionistheunderlyingmechanismcontrollingviscousfingeringandwormholegrowth |