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Critical Reynolds Number for the Occurrence of Nonlinear Flow in a Rough-walled Rock Fracture
암반단열에서 비선형유동이 발생하는 임계 레이놀즈수
Econ. Environ. Geol. 2019 Aug;52(4):291-7
Published online August 31, 2019;
Copyright © 2019 the Korean society of economic and environmental gelology.

Dahye Kim and In Wook Yeo*
김다혜 · 여인욱*

Department of Geological and Environmental Sciences, Chonnam National University, Gwangju 61186, Korea
전남대학교 지구환경과학부
Received July 29, 2019; Revised August 27, 2019; Accepted August 27, 2019.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License ( which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
Fluid flow through rock fractures has been quantified using equations such as Stokes equations, Reynolds equation (or local cubic law), cubic law, etc. derived from the Navier-Stokes equations under the assumption that linear flow prevails. Therefore, these simplified equations are limited to linear flow regime, and cause errors in nonlinear flow regime. In this study, causal mechanism of nonlinear flow and critical Reynolds number were presented by carrying out fluid flow modeling with both the Navier-Stokes equations and the Stokes equations for a three-dimensional rough-walled rock fracture. This study showed that flow regimes changed from linear to nonlinear at the Reynolds number greater than 10. This is because the inertial forces, proportional to the square of the fluid velocity, increased enough to overwhelm the viscous forces. This tendency was also shown for the unmated (slightly sheared) rock fracture. It was found that nonlinear flow was caused by the rapid increase in the inertial forces with increasing fluid velocity, not by the growing eddies that have been ascribed to nonlinear flow.
Keywords : rock fracture, nonlinear flow, critical Reynolds number, Navier-Stokes equations, Stokes equations


August 2019, 52 (4)