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import matplotlib.pyplot as plt
import numpy as np
from matplotlib import cm
import matplotlib.patches as patches
from math import degrees
from util import compute_kf_kb_ko_keta_kd, customize, save_fig
plt.rcParams["text.usetex"] = True
fig, axes = plt.subplots(
ncols=2, nrows=1, figsize=(10, 1.2 * 3 * 4.5 / 4), constrained_layout=True
# Standard Navier-Stokes
sim = get_sim("L", proj=False)
mean_values = sim.output.get_mean_values(tmin="t_last-2", customize=customize)
R2 = mean_values["R2"]
Uh2 = mean_values["Uh2"]
epsK = mean_values["epsK"]
Fh = mean_values["Fh"]
proj = sim.params.projection
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]
# 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
KH, KZ = np.meshgrid(kh, kz)
EA = data["A"]
EKhd = data["Khd"]
EKz = data["Kz"]
EKhr = data["Khr"]
Epolo = EKhd + EKz
Etoro = EKhr
E = Epolo + Etoro + EA
Ee = 2 * np.minimum(Epolo, EA)
Ed = (Epolo - EA) / (Epolo + EA)
E[E == 0] = 1e-15
levels = np.linspace(0, 1, 51, endpoint=True)
K = np.sqrt(KH**2 + KZ**2)
K[K == 0] = 1e-15
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data = sim.output.spect_energy_budg.load_mean(tmin=tmin)
kh = data["kh"]
kz = data["kz"]
delta_kh = kh[1]
delta_kz = kz[1]
KH, KZ = np.meshgrid(kh, kz)
DA = data["diss_A"]
TA = data["transfer_A"]
TK = data["transfer_Kh"] + data["transfer_Kz"]
K2A = data["conv_K2A"]
DKh = data["diss_Kh"]
DKz = data["diss_Kz"]
DK = DKh + DKz
D = DA + DK
T = TA + TK
levels = np.linspace(-2 / 3, 2 / 3, 51, endpoint=True)
cs0 = ax0.contourf(
KH,
KZ,
K2A / (D + np.abs(TA) + np.abs(TK) + np.abs(K2A)),
cmap=cm.seismic,
levels=levels,
)
th = np.linspace(0, np.pi / 2, 50)
for ax in [ax0]:
# 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",
for ax in [ax0]:
# Chi_nu = 1 (Kolmogorov scale)
ax.plot(keta * np.sin(th), keta * np.cos(th), linestyle="dotted", color="g")
ax.set_xlim([kh[1], 0.8 * max(kh)])
ax.set_ylim([kz[1], 0.8 * max(kh)])
ax.set_xscale("log")
ax.set_yscale("log")
ax.set_xlabel(r"$k_h$", fontsize=20)
ax.set_xticks(
[1e1, 1e2, 1e3, kb, ko],
[r"$10^1$", r"$10^2$", r"$10^3$", r"$k_{\rm b}$", r"$k_{\rm O}$"],
fontsize=14,
ax.set_ylabel(r"$k_z$", fontsize=20)
ax.set_yticks(
[1e1, 1e2, 1e3, kb, ko],
[r"$10^1$", r"$10^2$", r"$10^3$", r"$k_{\rm b}$", r"$k_{\rm O}$"],
fontsize=14,
)
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# Without vortical modes
sim = get_sim("L", proj=True)
mean_values = sim.output.get_mean_values(tmin="t_last-2", customize=customize)
R2 = mean_values["R2"]
Uh2 = mean_values["Uh2"]
epsK = mean_values["epsK"]
Fh = mean_values["Fh"]
proj = sim.params.projection
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]
# 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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KH, KZ = np.meshgrid(kh, kz)
EA = data["A"]
EKhd = data["Khd"]
EKz = data["Kz"]
EKhr = data["Khr"]
Epolo = EKhd + EKz
Etoro = EKhr
E = Epolo + Etoro + EA
Ee = 2 * np.minimum(Epolo, EA)
Ed = (Epolo - EA) / (Epolo + EA)
E[E == 0] = 1e-15
levels = np.linspace(0, 1, 51, endpoint=True)
K = np.sqrt(KH**2 + KZ**2)
K[K == 0] = 1e-15
data = sim.output.spect_energy_budg.load_mean(tmin=tmin)
kh = data["kh"]
kz = data["kz"]
delta_kh = kh[1]
delta_kz = kz[1]
KH, KZ = np.meshgrid(kh, kz)
DA = data["diss_A"]
TA = data["transfer_A"]
TK = data["transfer_Kh"] + data["transfer_Kz"]
K2A = data["conv_K2A"]
DKh = data["diss_Kh"]
DKz = data["diss_Kz"]
DK = DKh + DKz
D = DA + DK
T = TA + TK
levels = np.linspace(-2 / 3, 2 / 3, 51, endpoint=True)
cs1 = ax1.contourf(
KH,
KZ,
K2A / (D + np.abs(TA) + np.abs(TK) + np.abs(K2A)),
cmap=cm.seismic,
levels=levels,
th = np.linspace(0, np.pi / 2, 50)
for ax in [ax1]:
# 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",
)
for ax in [ax1]:
# Chi_nu = 1 (Kolmogorov scale)
ax.plot(keta * np.sin(th), keta * np.cos(th), linestyle="dotted", color="g")
ax.set_xlim([kh[1], 0.8 * max(kh)])
ax.set_ylim([kz[1], 0.8 * max(kh)])
ax.set_xscale("log")
ax.set_yscale("log")
ax.set_xlabel(r"$k_h$", fontsize=20)
ax.set_xticks(
[1e1, 1e2, 1e3, kb, ko],
[r"$10^1$", r"$10^2$", r"$10^3$", r"$k_{\rm b}$", r"$k_{\rm O}$"],
fontsize=14,
)
ax.set_ylabel(r"$k_z$", fontsize=20)
ax.set_yticks(
[1e1, 1e2, 1e3, kb, ko],
[r"$10^1$", r"$10^2$", r"$10^3$", r"$k_{\rm b}$", r"$k_{\rm O}$"],
fontsize=14,
)
for ax in [ax1]:
ax.set_ylabel(None)
ax.set_yticks([])
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)
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for ax in [ax0, ax1]:
# 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,
)
fig.subplots_adjust(right=0.85)
cbar_ax = fig.add_axes([0.88, 0.17, 0.02, 0.65])
cbar = fig.colorbar(cs1, cax=cbar_ax)
cbar.set_ticks([-2 / 3, -1 / 3, 0.0, 1 / 3, 2 / 3])
cbar.set_ticklabels(
[r"$-2/3$", r"$-1/3$", r"$0$", r"$1/3$", r"$2/3$"], fontsize=14
)
cbar.set_label(r"$\tilde{\mathcal{B}}$", fontsize=20)