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import numpy as np
from math import degrees
from util import compute_kf_kb_ko_keta_kd, save_fig
from util_simuls_regimes import get_sim
cm = matplotlib.cm.get_cmap("inferno", 100)
# Latex
plt.rcParams["text.latex.preamble"] = r"\usepackage{bm}"
def plot_spectra(sim, ax, key="Ee"):
p_oper = sim.params.oper
kmax = p_oper.coef_dealiasing * p_oper.nx * np.pi / p_oper.Lx
t_start, t_last = sim.output.print_stdout.get_times_start_last()
tmin = t_last - 2.0
kf, kb, ko, keta, kd = compute_kf_kb_ko_keta_kd(sim, tmin)
data = sim.output.spectra.load_kzkh_mean(
tmin, key_to_load=["A", "Khd", "Kz", "Khr"]
)
kh = data["kh_spectra"]
kz = data["kz"]
delta_kh = kh[1]
delta_kz = kz[1]
if key == "EA":
spectrum = data["A"]
elif key == "Epolo":
EKhd = data["Khd"]
EKz = data["Kz"]
spectrum = EKhd + EKz
elif key == "Ee":
EA = data["A"]
EKhd = data["Khd"]
EKz = data["Kz"]
Epolo = EKhd + EKz
spectrum = 2 * np.minimum(EA, Epolo)
elif key == "Ed":
EA = data["A"]
EKhd = data["Khd"]
EKz = data["Kz"]
Epolo = EKhd + EKz
spectrum = EA + Epolo - 2 * np.minimum(EA, Epolo)
elif key == "Etoro":
spectrum = data["Khr"]
else:
print(f"Don't know key: {key} \n")
exit
cs = ax.pcolormesh(
kh,
kz,
np.log10(spectrum),
cmap=cm,
vmin=-9.0,
vmax=-1.0,
shading="nearest",
# Forcing
kf_min = sim.params.forcing.nkmin_forcing * delta_kz
kf_max = sim.params.forcing.nkmax_forcing * delta_kz
angle = sim.params.forcing.tcrandom_anisotropic.angle
delta_angle = sim.params.forcing.tcrandom_anisotropic.delta_angle
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# Forcing
ax.add_patch(
patches.Arc(
xy=(0, 0),
width=2 * kf_max,
height=2 * kf_max,
angle=0,
theta1=90.0 - degrees(angle) - 0.5 * degrees(delta_angle),
theta2=90.0 - degrees(angle) + 0.5 * degrees(delta_angle),
linestyle="-",
color="orange",
linewidth=1,
)
)
ax.add_patch(
patches.Arc(
xy=(0, 0),
width=2 * kf_min,
height=2 * kf_min,
angle=0,
theta1=90.0 - degrees(angle) - 0.5 * degrees(delta_angle),
theta2=90.0 - degrees(angle) + 0.5 * degrees(delta_angle),
linestyle="-",
color="orange",
linewidth=1,
)
)
ax.plot(
[
kf_min * np.sin(angle - 0.5 * delta_angle),
kf_max * np.sin(angle - 0.5 * delta_angle),
],
[
kf_min * np.cos(angle - 0.5 * delta_angle),
kf_max * np.cos(angle - 0.5 * delta_angle),
],
linestyle="-",
color="orange",
linewidth=1,
)
ax.plot(
[
kf_min * np.sin(angle + 0.5 * delta_angle),
kf_max * np.sin(angle + 0.5 * delta_angle),
],
[
kf_min * np.cos(angle + 0.5 * delta_angle),
kf_max * np.cos(angle + 0.5 * delta_angle),
],
linestyle="-",
color="orange",
linewidth=1,
)
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# kb
ax.plot(kb * np.sin(th), kb * np.cos(th), color="cyan", linestyle="dashed")
# Chi_L = 1/3, 3
a = 1 / 3
xa = np.linspace(kh[1], a**1.5 * ko, 50, endpoint=True)
ax.plot(
xa,
xa * np.sqrt((a**1.5 * ko / xa) ** 0.8 - 1),
linestyle="dotted",
color="cyan",
)
a = 3
xa = np.linspace(kh[1], a**1.5 * ko, 50, endpoint=True)
ax.plot(
xa,
xa * np.sqrt((a**1.5 * ko / xa) ** 0.8 - 1),
linestyle="dotted",
color="cyan",
)
# Chi_d = 1
a = 1.0
xa = np.linspace(kh[1], kd, 50, endpoint=True)
ax.plot(
xa,
xa * np.sqrt((kd / xa) ** (4 / 3) - 1),
linestyle="dotted",
color="magenta",
)
# Chi_nu = 1 (Kolmogorov scale)
ax.plot(keta * np.sin(th), keta * np.cos(th), linestyle="dotted", color="g")
ax.set_xticks(
[1e1, kb, 1e2, ko, 1e3],
[r"$10^1$", r"$k_{\rm b}$", r"$10^2$", r"$k_{\rm O}$", r"$10^3$"],
fontsize=14,
)
ax.set_yticks(
[1e1, kb, 1e2, ko, 1e3],
[r"$10^1$", r"$k_{\rm b}$", r"$10^2$", r"$k_{\rm O}$", r"$10^3$"],
fontsize=14,
)
ax.set_xlim([delta_kh, kmax])
ax.set_ylim([delta_kz, kmax])
ax.set_xscale("log")
ax.set_yscale("log")
# ax.grid(True)
return cs
fig, axes = plt.subplots(
ncols=2, nrows=3, figsize=(10, 3 * 3 * 4.5 / 4), constrained_layout=True
)
ax0 = axes[0, 0]
ax1 = axes[0, 1]
ax2 = axes[1, 0]
ax3 = axes[1, 1]
ax4 = axes[2, 0]
ax5 = axes[2, 1]
axs = [ax0, ax1, ax2, ax3, ax4, ax5]
sim = get_sim(letter)
cs0 = plot_spectra(sim, ax0, key="Etoro")
cs2 = plot_spectra(sim, ax2, key="Epolo")
cs4 = plot_spectra(sim, ax4, key="EA")
sim = get_sim(letter, proj=True)
cs1 = plot_spectra(sim, ax1, key="Etoro")
cs3 = plot_spectra(sim, ax3, key="Epolo")
cs5 = plot_spectra(sim, ax5, key="EA")
for ax in [ax0, ax2, ax4]:
ax.set_ylabel(r"$k_z$", fontsize=20)
for ax in [ax4, ax5]:
ax.set_xlabel(r"$k_h$", fontsize=20)
for ax in [ax0, ax1, ax2, ax3]:
ax.set_xticklabels([])
for ax in [ax1, ax3, ax5]:
ax.set_yticklabels([])
ax0.set_title(r"Standard Navier-Stokes" + "\n" + r"$\rm (a)$", fontsize=20)
ax1.set_title(r"Without vortical modes" + "\n" + r"$\rm (b)$", fontsize=20)
ax2.set_title(r"$\rm (c)$", fontsize=20)
ax3.set_title(r"$\rm (d)$", fontsize=20)
ax4.set_title(r"$\rm (e)$", fontsize=20)
ax5.set_title(r"$\rm (f)$", fontsize=20)
# Add annotations for the lines and forcing region
ax1.text(
4.5,
1.5e1,
r"Forcing",
color="orange",
rotation=0.7 * 180 / np.pi,
fontsize=10,
)
ax1.text(1e1, 1.5e1, r"$\chi_{\mathbf{k}} < 1/3$", color="cyan", fontsize=14)
ax1.text(1e2, 1.5e2, r"$\chi_{\mathbf{k}} < 3$", color="cyan", fontsize=14)
ax1.text(7e1, 5e1, r"$\gamma_{\mathbf{k}} < 1$", color="m", fontsize=14)
fig.tight_layout()
fig.subplots_adjust(right=0.85)
cbar_ax0 = fig.add_axes([0.88, 0.675, 0.02, 0.25])
cbar0 = fig.colorbar(cs0, cax=cbar_ax0, cmap=cm, orientation="vertical")
cbar0.set_label(r"$\log_{10} E_{\rm toro}$", fontsize=20)
cbar_ax2 = fig.add_axes([0.88, 0.3725, 0.02, 0.25])
cbar2 = fig.colorbar(cs2, cax=cbar_ax2, cmap=cm, orientation="vertical")
cbar2.set_label(r"$\log_{10} E_{\rm polo}$", fontsize=20)
cbar_ax4 = fig.add_axes([0.88, 0.07, 0.02, 0.25])
cbar4 = fig.colorbar(cs4, cax=cbar_ax4, cmap=cm, orientation="vertical")
cbar4.set_label(r"$\log_{10} E_{\rm pot}$", fontsize=20)
for cbar in [cbar0, cbar2, cbar4]:
cbar.set_ticks([-9, -7, -5, -3, -1])
cbar.set_ticklabels(
[r"$-9$", r"$-7$", r"$-5$", r"$-3$", r"$-1$"], fontsize=14
)
save_fig(fig, "figure8.png")