flow through a coarse grating

G I Taylor, E G Richardson and G K Batchelor used gratings in wind-tunnels in much of their early experimental work on turbulence.

Here a coarse two-dimensional grating in a pipe is modeled with Gerris (initial simulation file grating.gfs). The output of the simulation at 2 seconds was converted to GMT grd files

gfs2xyz2D -s U frame-2.0.gfs | \
  xyz2grd -Gu.grd -R-0.5/1.5/-0.5/0.5 \
          -F -I256+/128+

producing u.grd and v.grd.

The arrows layer was produced with

vfplot -v -w8i -m5/5/-0.4 -s1e-4 -i500/5 \
       -P0.1m -f100 -l0/1in --cache 256 \
       --decimate-late --decimate-contact 0.9 \
       --aspect 3.0 --glyph triangle \
       -o vfplot.eps u.grd v.grd

and combined with a background of vorticity:

CPT="vort.cpt"
GRD="vort.grd"
CIR="grating.dat"
WAL="wall.dat"
VFP="vfplot.eps"

EPS="grating.eps"

RNG="-R-0.5/1.5/-0.5/0.5"
DIM="8i/4i"
PRJ="-JX$DIM"
COM="+defaults $PRJ $RNG"
GRY="150"
PAT="-G$GRY"
PEN="-W0.07c"
FAT="-W0.6c/$GRY"

GRF="vort-fine.grd"
grdsample $GRD -G$GRF $RNG -N1024/512 -Q

psxy     $WAL $COM -L -M\# $FAT      -K
grdimage $GRF $COM -C$CPT            -K -O
psxy     $WAL $COM -L -M\# $PEN      -K -O
psxy     $CIR $COM -L -M\# $PAT $PEN -K -O
psimage  $VFP -W$DIM                    -O

rm $GRF

where the file vort.grd is produced with another gfs2xyz2D call.

Download the plot as pdf.

grating plot
Flow through a grating