.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/nonhydro/convection_and_closures.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note :ref:`Go to the end ` to download the full example code. .. rst-class:: sphx-glr-example-title .. _sphx_glr_auto_examples_nonhydro_convection_and_closures.py: Convection and Closures ======================= Testing different momentum closures in a 2D convection problem. In this example, I test different closures for the momentum equations. The model setup is a 2D stratified fluid with a buoyancy perturbation in the middle of the domain. Thies buoyancy perturbation leads to static instability and convection. When no closure is used, a lot of energy is accumulated at the grid scale, leading to a very noisy solution: without any closure ------------------- .. video:: videos/convection_and_closures_no_closure.mp4 The most straightforward closure is by including harmonic diffusion with turbulent viscosities and diffusivities. The following video shows the solution when using :py:class:`HarmonicDiffusion ` with a coefficient of :math:`10^{-4}`: harmonic diffusion ------------------ .. video:: videos/convection_and_closures_harmonic_diffusion.mp4 The solution is much smoother, but there is also an unrealistic amount of energy dissipation. To minimize the effect of the closure on the larger scales, one can use a biharmonic diffusion closure instead of a harmonic one. The following video shows the solution when using :py:class:`BiharmonicDiffusion ` with a coefficient of :math:`10^{-6}`: biharmonic diffusion -------------------- .. video:: videos/convection_and_closures_biharmonic_diffusion.mp4 Finally, there is also the Smagorinsky-Lilly closure implemented in the model, this is a dynamic closure that adjusts the turbulent viscosities and diffusivities based on the resolved scales. The following video shows the solution when using :py:class:`SmagorinskyLilly `: smagorinsky-lilly ----------------- .. video:: videos/convection_and_closures_Smagorinsky-Lilly.mp4 .. note:: The diffusion coefficients are not fine-tuned. The purpose of this example is to show how different closures can be used in the model and how they affect the solution. .. GENERATED FROM PYTHON SOURCE LINES 51-152 .. code-block:: Python import fridom.nonhydro as nh import fridom.framework as fr import numpy as np # ---------------------------------------------------------------- # Settings # ---------------------------------------------------------------- make_video = True fps = 30 make_netcdf = False exp_name = "convection_and_closures" run_length = np.timedelta64(1, 'h') thumbnail = f"figures/{exp_name}.png" class Plotter(nh.modules.animation.ModelPlotter): def create_figure(): import matplotlib.pyplot as plt return plt.figure(figsize=(6, 4.5), dpi=32*12, tight_layout=True) def prepare_arguments(mz: nh.ModelState) -> dict: return {"b": mz.z.b.xr, "t": mz.clock.time} def update_figure(fig, b, t) -> None: import cmocean ax = fig.add_subplot(111) b.plot(ax=ax, cmap=cmocean.cm.dense_r, extend='both', vmax=3e-4, vmin=-3e-4) ax.set_aspect('equal') ax.set_title(f"t = {nh.utils.humanize_number(t, 'seconds')}", fontsize=16) def test_closure(closure: fr.modules.Module): grid = nh.grid.cartesian.Grid( N=(512, 1, 512), L=(100, 1, 100), periodic_bounds=(True, True, False)) mset = nh.ModelSettings(grid=grid, f0=0, N2=2.5e-5) mset.time_stepper.dt = np.timedelta64(1, 's') fname = exp_name + "_" + closure.name # add a video writer if make_video: mset.diagnostics.add_module(nh.modules.animation.VideoWriter( Plotter, model_time_per_second=np.timedelta64(4, "m"), filename=f"{fname}", fps=fps)) # create a NetCDF writer to save the output if make_netcdf: mset.diagnostics.add_module(nh.modules.NetCDFWriter( write_trigger = nh.ClockTrigger(time_interval=np.timedelta64(10, "m")), filename=fname)) # add the closure mset.tendencies.add_module(closure) # setup all the modules mset.setup() # create an initial condition ncp = nh.config.ncp # the array backend (numpy, cupy, ...) X, Y, Z = grid.X z = nh.State(mset) z.b.arr = 1e-3 * ncp.exp(-((X-50)**2 + (Z-50)**2)/(10)**2) # create the model, set initial conditions, and run model = nh.Model(mset) model.z = z model.run(runlen=run_length) # save thumbnail from biharmonic diffusion if closure.name == "biharmonic_diffusion": import os os.makedirs("figures", exist_ok=True) fig = Plotter(model.model_state) fig.savefig(thumbnail) @fr.utils.skip_on_doc_build def main(): # test without any closure dummy_closure = fr.modules.Module() dummy_closure.name = "no_closure" test_closure(dummy_closure) # test with smagorinsky-lilly closure test_closure(nh.modules.closures.SmagorinskyLilly()) # test with harmonic diffusion coeff = 1e-4 friction = nh.modules.closures.HarmonicFriction(ah=coeff, av=coeff) mixing = nh.modules.closures.HarmonicMixing(kh=coeff, kv=coeff) test_closure(fr.modules.ModuleContainer("harmonic_diffusion", [friction, mixing])) # test with biharmonic diffusion coeff = 1e-6 friction = nh.modules.closures.BiharmonicFriction(ah=coeff, av=coeff) mixing = nh.modules.closures.BiharmonicMixing(kh=coeff, kv=coeff) test_closure(fr.modules.ModuleContainer("biharmonic_diffusion", [friction, mixing])) if __name__ == "__main__": main() .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 1.062 seconds) .. _sphx_glr_download_auto_examples_nonhydro_convection_and_closures.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: convection_and_closures.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: convection_and_closures.zip `