

All integrable Hamiltonian systems are alike, while each nonintegrable one is nonintegrable in its own way
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+
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.
