Turbulent Couette flow

    See the GOTM web site and section 12.1.1 of the GOTM manual.

    “The Couette scenario is the most basic of all GOTM scenarios. It represents a shallow (10 m deep), unstratified layer of fluid above a flat bottom that is driven by a constant surface stress in the x-direction. Earth’s rotation is ignored. This flow is often referred to as turbulent Couette flow. After the onset of the surface stress, a thin turbulent near-surface layer is generated that rapidly entrains into the non-turbulent deeper parts of the water column. The solution at the end of the simulation, when the problem has become fully stationary, is shown in the figure below.”


    set term SVG size 600,300
    set xlabel 'u (m/s)'
    set ylabel 'z (m)'
    plot [0:1][-10:0]'log' u 2:1 w l t '' lw 2
    Stationary velocity profile (script)

    Stationary velocity profile (script)

    set xlabel 'ν_t (m^2/s)'
    plot [0:0.05][-10:0]'log' u 3:1 w l t '' lw 2
    Turbulent diffusivity (script)

    Turbulent diffusivity (script)



    Lars Umlauf, Hans Burchard, and Karsten Bolding. GOTM Source Code and Test Case Documentation, version 4 edition, 2018. [ .pdf ]

    #include "grid/multigrid1D.h"
    #include "layered/hydro.h"
    #include "layered/gotm.h"
    int main()
      G = 9.81;
      N = 1;
      nl = 100;
      DT = 20;
      size (100e3);
      periodic (right);

    We use the k-\epsilon model.

      turbulence_turb_method      = turbulence_first_order;
      turbulence_tke_method       = turbulence_tke_keps;
      turbulence_len_scale_method = turbulence_generic_eq;

    The bottom roughness leng scale (of GOTM) needs to be adjusted.

      meanflow_z0s_min = 0.003;
      meanflow_h0b = 0.1;

    The surface wind stress is constant.

      const vector tau_w[] = { 1.027 };
      airsea_tau = tau_w;

    Initial conditions

    Ten metre deep, constant layer thicknesses.

    event init (i = 0)
      foreach() {
        zb[] = -10.;
          h[] = 10./nl;


    24 hours is enough to reach a stationary profile. The turbulent diffusivity \nu_t computed by GOTM is accessed through the C interface of the corresponding Fortran field.

    event profiles (t = 24*3600)
      foreach() {
        double z = zb[];
          fprintf (stderr, "%g %g %g\n", z + h[]/2., u.x[],
    	       (turbulence_num.a[point.l] + turbulence_num.a[point.l + 1])/2.),
          z += h[];
      fprintf (stderr, "\n");