Influence of heterogeneity on second-kind self-similar solutions for viscous gravity currents
Abstract
We report experimental, theoretical and numerical results on the effects of horizontal heterogeneities on the propagation of viscous gravity currents. We use two geometries to highlight these effects: (a) a horizontal channel (or crack) whose gap thickness varies as a power-law function of the streamwise coordinate; (b) a heterogeneous porous medium whose permeability and porosity have power-law variations. We demonstrate that two types of self-similar behaviours emerge as a result of horizontal heterogeneity: (a) a first-kind self-similar solution is found using dimensional analysis (scaling) for viscous gravity currents that propagate away from the origin (a point of zero permeability); (b) a second-kind self-similar solution is found using a phase-plane analysis for viscous gravity currents that propagate toward the origin. These theoretical predictions, obtained using the ideas of self-similar intermediate asymptotics, are compared with experimental results and numerical solutions of the governing partial differential equation developed under the lubrication approximation. All three results are found to be in good agreement.
- Authors:
-
- Princeton Univ., NJ (United States)
- Princeton Univ., NJ (United States); Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Publication Date:
- Research Org.:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1200619
- Report Number(s):
- LA-UR-13-29555
Journal ID: ISSN 0022-1120
- Grant/Contract Number:
- AC52-06NA25396
- Resource Type:
- Journal Article: Accepted Manuscript
- Journal Name:
- Journal of Fluid Mechanics
- Additional Journal Information:
- Journal Volume: 747; Journal Issue: 1; Journal ID: ISSN 0022-1120
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 42 ENGINEERING; 97 MATHEMATICS AND COMPUTING; Mathematics; Gravity currents, Hele-Shaw flows, Porous media; gravity currents; Hele-Shaw flows; porous media
Citation Formats
Zheng, Zhong, Christov, Ivan C., and Stone, Howard A. Influence of heterogeneity on second-kind self-similar solutions for viscous gravity currents. United States: N. p., 2014.
Web. doi:10.1017/jfm.2014.148.
Zheng, Zhong, Christov, Ivan C., & Stone, Howard A. Influence of heterogeneity on second-kind self-similar solutions for viscous gravity currents. United States. https://doi.org/10.1017/jfm.2014.148
Zheng, Zhong, Christov, Ivan C., and Stone, Howard A. 2014.
"Influence of heterogeneity on second-kind self-similar solutions for viscous gravity currents". United States. https://doi.org/10.1017/jfm.2014.148. https://www.osti.gov/servlets/purl/1200619.
@article{osti_1200619,
title = {Influence of heterogeneity on second-kind self-similar solutions for viscous gravity currents},
author = {Zheng, Zhong and Christov, Ivan C. and Stone, Howard A.},
abstractNote = {We report experimental, theoretical and numerical results on the effects of horizontal heterogeneities on the propagation of viscous gravity currents. We use two geometries to highlight these effects: (a) a horizontal channel (or crack) whose gap thickness varies as a power-law function of the streamwise coordinate; (b) a heterogeneous porous medium whose permeability and porosity have power-law variations. We demonstrate that two types of self-similar behaviours emerge as a result of horizontal heterogeneity: (a) a first-kind self-similar solution is found using dimensional analysis (scaling) for viscous gravity currents that propagate away from the origin (a point of zero permeability); (b) a second-kind self-similar solution is found using a phase-plane analysis for viscous gravity currents that propagate toward the origin. These theoretical predictions, obtained using the ideas of self-similar intermediate asymptotics, are compared with experimental results and numerical solutions of the governing partial differential equation developed under the lubrication approximation. All three results are found to be in good agreement.},
doi = {10.1017/jfm.2014.148},
url = {https://www.osti.gov/biblio/1200619},
journal = {Journal of Fluid Mechanics},
issn = {0022-1120},
number = 1,
volume = 747,
place = {United States},
year = {Thu May 01 00:00:00 EDT 2014},
month = {Thu May 01 00:00:00 EDT 2014}
}
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