sandbox/MCVacher/unstable_2D_jet.c
Unstable 2D Jet.
Schlichting’s 2D jet (see here) is unstable after Re \approx 30 if you allow the left-right symmetry to be broken.
It seems that it is a Kelvin-Helmotz instability created by the shear on the sides of the jet that is the physical mechanism behind it. Starting from a fluid at rest, this shear instability can be created by the initial bulb of the jet when issuing the nozzle. Here you can admire the beautiful vortices it creates…
//test schlichting
#include "grid/multigrid.h"
#include "navier-stokes/centered.h"
#include "tracer.h"
#include "navier-stokes/perfs.h"
scalar s[];
scalar * tracers = {s};
double U0;
double R_d;
double Re;
FILE * fpmax; //
face vector muv[];
int main() {
Re=40;
R_d=0.005;
L0=1;
U0=1;
TOLERANCE = 1e-3 [*];
u.n[bottom] = dirichlet (U0*(x > -R_d && x <R_d));
u.t[bottom] = dirichlet(0.);
u.n[top] = u.n[] > 0. ? neumann(0) : dirichlet(0);
p[top] = dirichlet(0.);
s[bottom] = dirichlet (U0*(x > -R_d && x <R_d));
u.n[left] = neumann(0);
p[left] = dirichlet(0);
u.n[right] = neumann(0);
p[right] = dirichlet(0);
N=256;
origin (-L0/2, 0);
init_grid(N);
char param_dim[80];
sprintf (param_dim, "param_dim.txt");
FILE * fparam = fopen(param_dim, "w");
fprintf (fparam, "%g %g %g %d\n",L0,R_d,U0,N);
fclose (fparam);
mu=muv;
fpmax = fopen("log.dat", "w");
run();
}
event properties (i++)
{
foreach_face()
muv.x[] = fm.x[]*U0*R_d/Re;
}
event logfile (i++) {
fprintf (stderr, "%d %g\n", i, t);
fprintf (fpmax, "%d %g\n", i, t);
}
event profile (t = end) {
char name[80];
sprintf (name, "res_end.txt");
FILE * fpres = fopen(name, "w");
foreach()
fprintf (fpres, "%g %g %g %g %g %g", x, y, u.x[], u.y[], p[],s[]);
fclose(fpres);
printf ("-----END-----\n");
}
event ppm_output (t = 0; t += 0.05; t <= 50) {
char name2[80];
sprintf (name2, "uY.mp4");
output_ppm (u.y, file = name2, n = 512, min = -U0, max = +U0, linear = true);
// optionally tracer
char name3[80];
sprintf (name3, "s.mp4");
output_ppm (s, file = name3, n = 512, min = 0., max = U0, linear = true);
}Passive tracer
Vertical velocity
