Influence of heterogeneity on secondkind selfsimilar solutions for viscous gravity currents
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 powerlaw function of the streamwise coordinate; (b) a heterogeneous porous medium whose permeability and porosity have powerlaw variations. We demonstrate that two types of selfsimilar behaviours emerge as a result of horizontal heterogeneity: (a) a firstkind selfsimilar solution is found using dimensional analysis (scaling) for viscous gravity currents that propagate away from the origin (a point of zero permeability); (b) a secondkind selfsimilar solution is found using a phaseplane analysis for viscous gravity currents that propagate toward the origin. These theoretical predictions, obtained using the ideas of selfsimilar 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]};
^{[2]}
;
^{[1]}
 Princeton Univ., NJ (United States)
 Princeton Univ., NJ (United States); Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Publication Date:
 Report Number(s):
 LAUR1329555
Journal ID: ISSN 00221120
 Grant/Contract Number:
 AC5206NA25396
 Type:
 Accepted Manuscript
 Journal Name:
 Journal of Fluid Mechanics
 Additional Journal Information:
 Journal Volume: 747; Journal Issue: 1; Journal ID: ISSN 00221120
 Research Org:
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Sponsoring Org:
 USDOE
 Country of Publication:
 United States
 Language:
 English
 Subject:
 42 ENGINEERING; 97 MATHEMATICS AND COMPUTING; Mathematics; Gravity currents, HeleShaw flows, Porous media; gravity currents; HeleShaw flows; porous media
 OSTI Identifier:
 1200619
Zheng, Zhong, Christov, Ivan C., and Stone, Howard A.. Influence of heterogeneity on secondkind selfsimilar solutions for viscous gravity currents. United States: N. p.,
Web. doi:10.1017/jfm.2014.148.
Zheng, Zhong, Christov, Ivan C., & Stone, Howard A.. Influence of heterogeneity on secondkind selfsimilar solutions for viscous gravity currents. United States. doi:10.1017/jfm.2014.148.
Zheng, Zhong, Christov, Ivan C., and Stone, Howard A.. 2014.
"Influence of heterogeneity on secondkind selfsimilar solutions for viscous gravity currents". United States.
doi:10.1017/jfm.2014.148. https://www.osti.gov/servlets/purl/1200619.
@article{osti_1200619,
title = {Influence of heterogeneity on secondkind selfsimilar 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 powerlaw function of the streamwise coordinate; (b) a heterogeneous porous medium whose permeability and porosity have powerlaw variations. We demonstrate that two types of selfsimilar behaviours emerge as a result of horizontal heterogeneity: (a) a firstkind selfsimilar solution is found using dimensional analysis (scaling) for viscous gravity currents that propagate away from the origin (a point of zero permeability); (b) a secondkind selfsimilar solution is found using a phaseplane analysis for viscous gravity currents that propagate toward the origin. These theoretical predictions, obtained using the ideas of selfsimilar 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},
journal = {Journal of Fluid Mechanics},
number = 1,
volume = 747,
place = {United States},
year = {2014},
month = {5}
}