moist_bubble.c

A rising moist bubble
- Output and Results
- Reference

A rising moist bubble

A moist bubble is placed in the atmosphere and rises because water vapor is lighter than air. It reaches condensation levels soon to form a cloud. The setup is inspired by Grabowski and Clark (1991) and the setup of B van Stratum.

#include "grid/octree.h"
#include "navier-stokes/centered.h"
#include "thermo.h"
#include "bwatch.h"

int maxlevel = 8;

int main(int argc, char * argv[]) {
  if (argc > 1)
    maxlevel = atoi (argv[1]);
  const face vector K[] = {0.1, 0.1, 0.1};
  mu = K;
  L0 = 3600;
  X0 = Z0 = -L0/2;
  periodic (left);
#if (dimension == 3)
  periodic (front);
#endif
  N = 64;
  run();
}

#define RADIUS (sqrt(sq(x) + sq(y - 800.) + sq (z)))
event init (t = 0) {
  T_ref = 283.;
  P0 = 1e5;
  double dlnthetadz = 1.0e-5;
  refine (RADIUS < 350. && level < maxlevel);
  foreach() 
    thl[] = exp(log(283.) + dlnthetadz*y) + 0.05*noise();

q_t may be initialized via the relative humidity (using the QSAT macro). However it requires an iterative method to find the corresponding hydrostatic pressure profile. The procedure is started after we have taken a first guess.

  scalar p_temp[];
  int j = 0, j_max = 10;
  set_pres (guess = true);
  do {
    foreach() {
      double r = RADIUS;
      if (r < 200)
	qt[] = QSAT;
      else if (r < 300) 
	qt[] = QSAT * (0.2 + 0.8 * sq(cos(pi*(r - 200.)/200.)));
      else 
	qt[] = QSAT * 0.2;
    }
    set_pres ();
    j++;
  } while (change (pres, p_temp) > .01 && j < j_max);
  if (j == j_max)
    fprintf (stderr,
	     "Static Pressure not found with %d iterations\n", j);
  system ("wget https://previews.123rf.com/images/naypong/naypong1707/naypong170700178/81549848-top-view-of-natural-green-grass-texture-aerial-view-of-park.jpg");
  system ("convert 81549848-top-view-of-natural-green-grass-texture-aerial-view-of-park.jpg -resize 400x400! grass.jpg");
}

#include "diffusion.h"
event tracer_diffusion (i++) {
  for (scalar s in tracers)
    diffusion (s, dt, mu);
}

event logger (i += 5) 
  fprintf(stdout, "%g %d\n", t, i);

event adapt (i++) 
  adapt_wavelet ((scalar*){qt, u},
		 (double[]){0.0005, 0.1, 0.1, 0.1}, maxlevel, 5);

event stop (t = 1000);

Output and Results

We output a movie.

event movie (t += 5) {
  scalar qc[];
  foreach() 
    qc[] = QC;
  boundary ({qc});
  static FILE * fp = popen ("ppm2mp4 cloud.mp4", "w");

  default_lights();
  lights[1].dir.y *= 2;
  normalize (&lights[2].dir);
  watch (fov = 2500, O = {5000, 3000, 2000},
	 poi = {0, 1000, 0});
  image ("grass.jpg", n = {0,1,0}, alpha = 1);
  volume (qc, sc = 0.02, cols = true, shading = 1, min = -1, max = 1);
  store (fp);
  plain();
}

Reference

Grabowski, Wojciech W., and Terry L. Clark. “Cloud–environment interface instability: Rising thermal calculations in two spatial dimensions.” Journal of the Atmospheric Sciences 48.4 (1991): 527-546.