nx=32
ny=32
nz=32
mx=nx+6
my=ny+6
mz=nz+6
dx=2*!pi/nx
dy=2*!pi/ny
dz=2*!pi/nz
x=dx*(findgen(mx)-mx/2+1.5)
y=dy*(findgen(my)-my/2+1.5)
z=dz*(findgen(mz)-mz/2+1.5)
l1=2 & l2=l1+nx-1
m1=2 & m2=l1+ny-1
n1=2 & n2=l1+nz-1
;------------------------------------------------------------------------------
;
;  coordinates
;
xx = spread(x, [1,2], [my,mz])
yy = spread(y, [0,2], [mx,mz])
zz = spread(z, [0,1], [mx,my])
uu=fltarr(mx,my,mz,3)
;
;  ring parameters
;
d=1.2 & rr0=1.5 & xx0=.5*rr0 & yy0=0. & file='uu.dat'
d=0.7 & rr0=1.5 & xx0=.5*rr0 & yy0=0. & file='uu.dat' ;(imp_rring32a-c)
d=0.5 & rr0=1.5 & xx0=.5*rr0 & yy0=0. & file='uu.dat' ;(imp_sring32a-c)
d=0.5 & rr0=1.0 & xx0=.5*rr0 & yy0=0. & file='uu.dat' ;(imp_tring32a-c)
;
;  1st ring in xY-plane shifted to the right
;  The Y-direction is in the yz-plane.
;
degree=!pi/180.
alpha=45*degree
c=cos(alpha) & s=sin(alpha)
xxx=xx-xx0
yyy=+yy*c+zz*s
zzz=-yy*s+zz*c
rr=sqrt(xxx^2+yyy^2)
phi=atan(yyy,xxx)
aphi=bump(((rr-rr0)^2+zzz^2)/d^2)
uu(*,*,*,0)=+aphi*sin(phi)
uu(*,*,*,1)=-aphi*cos(phi)*c
uu(*,*,*,2)=-aphi*cos(phi)*s
;
;  2nd ring in xz-plane shifted to the left
;  The Y-direction is in the yz-plane by another angle.
;
alpha=-45*degree
c=cos(alpha) & s=sin(alpha)
xxx=xx+xx0
yyy=+yy*c+zz*s
zzz=-yy*s+zz*c
rr=sqrt(xxx^2+yyy^2)
phi=atan(yyy,xxx)
aphi=bump(((rr-rr0)^2+zzz^2)/d^2)
uu(*,*,*,0)=uu(*,*,*,0)+aphi*sin(phi)
uu(*,*,*,1)=uu(*,*,*,1)-aphi*cos(phi)*c
uu(*,*,*,2)=uu(*,*,*,2)-aphi*cos(phi)*s
;
spawn,'date',t3 & print,t3
;
uuu=uu(l1:l2,m1:m2,n1:n2,*)
umax=sqrt(max(dot2(uu)))
uuu=uuu/umax
;openw,1,'data/proc0/uu.dat',/f77
;writeu,1,uuu
;close,1
stop
;
;  kinetic helicity
;
oo=curl(uu)
ooo=oo(l1:l2,m1:m2,n1:n2,*)
print,'<ooo.uuu>=',mean(dot(ooo,uuu))
;
END