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Title: Influence of heterogeneity on second-kind self-similar 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 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] ;  [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:
OSTI Identifier:
1200619
Report Number(s):
LA-UR-13-29555
Journal ID: ISSN 0022-1120
Grant/Contract Number:
AC52-06NA25396
Type:
Accepted Manuscript
Journal Name:
Journal of Fluid Mechanics
Additional Journal Information:
Journal Volume: 747; Journal Issue: 1; Journal ID: ISSN 0022-1120
Research Org:
Los Alamos National Laboratory (LANL)
Sponsoring Org:
USDOE
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