Auxiliary material for
Assessment of the validity of Stokes and Reynolds equations for fluid flow through a roughwalled fracture with flow imaging
Seung Hyun Lee and Kang-Kun Lee
(School of Earth and Environmental Sciences, Seoul National University, Seoul, Republic of
Korea)
In Wook Yeo
(Department of Earth and Environmental Sciences, Chonnam National University, Gwangju,
Republic of Korea)
Geophysical Research Letters, 2014
Introduction
These data sets include the snap shots of velocity vectors measured using micro PIV
technique as figure, the complete data of magnitude of inertial and viscous forces as table,
and video files for visualizing micro-particle movements from Re of 0.029 to 17.2 and video
files. Velocity vectors for all sub-regions (a to h) using micro PIV technique at Re of 0.014,
0.029 and 0.086, which were used for an order-of-magnitude analysis in this paper, were
represented as figure file “fs01.pdf”. The complete data of inertial forces and viscous forces
in equations (2) and (3) in the paper were provided as “ts01.docx”. Also, average velocities
( u x , u z ) for all sub-regions (a to h) are provide as “ts02.docx”. Videos showing the
development of eddy structure with increasing Re were given as “ms01.avi, ms02.avi,
ms03.avi and ms04.avi.”
1. fs01.pdf (Figure S1) Velocity vectors measured by microPIV technique for all sub-regions
a to h at Re 0.014, 0.029 and 0.086. The letters of a to h in the figures represent the
relevant sub-regions (i.e., a for sub-region a), and the velocity vectors around the upper
and bottom walls of sub-region e are shown in separate images. The horizontal scale of
each sub-region is 0.4 mm and the y axis is on the same scale.
2. ts01.docx (Table S1) Magnitudes of inertial forces and viscous forces terms in equations
(2) and (3). The complete data of the magnitudes and overestimation at sub regions
presented in Figure 3 in the paper.
2.1 Column “Reynolds number”, dimensionless.
2.2 Column “terms in equation (2)”, kg/m2·s2, magnitude of viscous forces and inertial forces
in equation (2) in the paper.
2.3 Column “terms in equation (3)”, kg/m2·s2, magnitude of viscous forces and inertial forces
in equation (3) in the paper.
3. ts02.docx (Table S2) Average measured velocities ( u x , u z ) at each sub-region
3.1 Column “Reynolds number”, dimensionless
3.2 Column “ u x ”, m/s, average velocity in the x-direction
3.3 Column “ u z ”, m/s, average local velocity in the z-direction
4. ms01.avi (Video S1) Micro-particle movements at Re = 0.029 near the top wall of the
sub-region e. velocity vectors in the paper acquired from these continuous snap shots.
5. ms02.avi (Video S2) Micro-particle movements at Re = 2.87 near the top wall of the subregion e. no eddy observed.
6. ms03.avi (Video S3) Micro-particle movements at Re = 8.6 near the top wall of the subregion e. generation of the eddy observed.
7. ms04.avi (Video S4) Micro-particle movements at Re = 17.2 near the top wall of the subregion e. enlargement of the eddy observed.