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Title: 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:
 [1]; ORCiD logo [2];  [1]
  1. Princeton Univ., NJ (United States)
  2. 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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Cited by: 32 works
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The effects of fluid transport on the creation of a dense cluster of activated fractures in a porous medium
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Dispersive entrainment into gravity currents in porous media
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