/
plot_processing.py
executable file
·636 lines (539 loc) · 21.7 KB
/
plot_processing.py
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#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Tue Feb 2 17:07:04 2021
@author: samvirthandi
"""
# locating latex installation
import os
import numpy as np
import matplotlib.pyplot as plt
from highspeed_fft import (model_growth_rate, velocity_calculator,
weber_velocity, file_id)
from scipy.special import i0, i1
from scipy.signal import savgol_filter
os.environ['PATH'] = os.environ['PATH'] + ':/Library/TeX/texbin'
def rayleigh():
"""
Produces rayleigh dispersion relation
Returns
-------
None.
"""
k = np.linspace(0, 1000, 10000)
sigma = 0.07
a = 1e-3
rho = 1000
w_squared = ((sigma*k)/(rho*a**2))*(1-k**2*a**2)*(i1(k*a)/i0(k*a))
normaliser = np.sqrt(sigma/rho*a**3)
normal_w = w_squared**0.5/normaliser
sqrt_w = np.sqrt(w_squared)
fig, ax = plt.subplots()
ax.plot(k*a, normal_w)
ax.set_xlim(0, 1.2)
wavelength = 2*np.pi/k
u_g = weber_velocity(5.22, 1551)
u_l = velocity_calculator(1551)
u_avg = (u_l+u_g)/2
u_arbitrary = (u_l+u_g)/2 - 2.5
freq = u_avg/wavelength
fig1, ax1 = plt.subplots()
ax1.plot(freq, sqrt_w)
print(u_arbitrary)
print(u_g)
print(u_l)
print(u_avg)
def moro_re_calc(Re):
"""
Function to calculate velocity for Morozumi's data
Parameters
----------
Re : int
Reynolds number
Returns
-------
u : float
velocity.
"""
# viscosity
mu = 8.9e-4
# density
rho = 1000
# diameter
d = 4/1000
# reynolds number standard equation
u = Re*mu/(rho*d)
return u
def rayleigh_moro():
k = np.linspace(0, 1000, 10000)
sigma = 0.07
a = 2e-3
rho = 1000
w_squared = ((sigma*k)/(rho*a**2))*(1-k**2*a**2)*(i1(k*a)/i0(k*a))
normaliser = np.sqrt(sigma/rho*a**3)
normal_w = w_squared**0.5/normaliser
sqrt_w = np.sqrt(w_squared)
fig, ax = plt.subplots()
ax.plot(k*a, normal_w)
ax.set_xlim(0, 1.2)
wavelength = 2*np.pi/k
u_l = moro_re_calc(2940)
freq = u_l/wavelength
fig1, ax1 = plt.subplots()
ax1.plot(freq, sqrt_w)
ax1.set_xlabel('Frequencies (Hz)')
ax1.set_ylabel('Growth rate (1/s)')
ax1.set_title('Rayleigh with Morozumi parameters')
def plotting_generic(file1, file2, file3, file4):
"""
Main plotting function
"""
freqs, _, morozumi_time, _, _, _, _ = np.loadtxt(file1, delimiter=',',
unpack=True)
freqs, _, constant_vel, _, _, _, _ = np.loadtxt(file2, delimiter=',',
unpack=True)
freqs, _, avg_vel, _, _, _, _ = np.loadtxt(file3, delimiter=',',
unpack=True)
freqs, _, aero_vel, _, _, _, _ = np.loadtxt(file4, delimiter=',',
unpack=True)
k = np.linspace(0, 1000, 10000)
sigma = 0.07
a = 1e-3
rho = 1000
w_squared = ((sigma*k)/(rho*a**2))*(1-k**2*a**2)*(i1(k*a)/i0(k*a))
sqrt_w = np.sqrt(w_squared)
wavelength = 2*np.pi/k
u_g = weber_velocity(5.22, 1551)
u_l = velocity_calculator(1551)
u_avg = (u_l+u_g)/2 - 2.5
freq_ra = u_avg/wavelength
print(u_avg)
print(u_l)
print(u_g)
fig, ax = plt.subplots()
ax.plot(freqs, morozumi_time, label='Morozumi time')
ax.plot(freqs, constant_vel, label='constant velocity')
ax.plot(freqs, avg_vel, label='averaged velocity')
ax.plot(freq_ra, sqrt_w, label='Rayleigh theoretical')
ax.set_xlim(0, 1250)
ax.set_ylim(0, 600)
ax.set_title('Unfiltered data')
ax.set_xlabel('Frequencies (Hz)')
ax.set_ylabel('Growth rate (1/s)')
ax.legend()
savgol_moro = savgol_filter(morozumi_time, 1001, 2)
savgol_const = savgol_filter(constant_vel, 1001, 2)
savgol_avg = savgol_filter(avg_vel, 1001, 2)
fig1, ax1 = plt.subplots()
ax1.plot(freqs, savgol_moro, label='Morozumi time')
ax1.plot(freqs, savgol_const, label='Constant velocity')
ax1.plot(freqs, savgol_avg, label='Averaged velocity')
ax1.plot(freq_ra, sqrt_w, label='Rayleigh theoretical')
ax1.set_xlim(0, 700)
ax1.set_ylim(0, 600)
ax1.set_title('Savgol filtering (window size = 1001) data')
ax1.set_xlabel('Frequencies (Hz)')
ax1.set_ylabel('Growth rate (1/s)')
ax1.legend()
def plotting_ra(file1):
"""
Main plotting function
"""
freqs, _, rayleigh_1300, _, _, _, _ = np.loadtxt(file1, delimiter=',',
unpack=True)
k = np.linspace(0, 1000, 10000)
sigma = 0.07
a = 1e-3
rho = 1000
w_squared = ((sigma*k)/(rho*a**2))*(1-k**2*a**2)*(i1(k*a)/i0(k*a))
sqrt_w = np.sqrt(w_squared)
wavelength = 2*np.pi/k
u_l = velocity_calculator(1551)
freq_ra = u_l/wavelength
fig, ax = plt.subplots()
ax.plot(freqs, rayleigh_1300, label='Experimental Rayleigh')
ax.plot(freq_ra, sqrt_w, label='Theoretical Rayleigh')
ax.set_xlim(0, 1250)
ax.set_ylim(0, 100)
ax.set_title('Unfiltered data')
ax.set_xlabel('Frequencies (Hz)')
ax.set_ylabel('Growth rate (1/s)')
ax.legend()
savgol_ra = savgol_filter(rayleigh_1300, 1001, 2)
fig1, ax1 = plt.subplots()
ax1.plot(freqs, savgol_ra, label='Experimental Rayleigh')
ax1.plot(freq_ra, sqrt_w, label='Theoretical Rayleigh')
ax1.set_xlim(0, 500)
ax1.set_ylim(0, 100)
ax1.set_title('Savgol filtering (window size = 1001) data')
ax1.set_xlabel('Frequencies (Hz)')
ax1.set_ylabel('Growth rate (1/s)')
ax1.legend()
peak_freq = freqs[np.where(savgol_ra == np.max(savgol_ra))]
print(peak_freq)
return peak_freq
def plotting_moro(file1):
"""
Main plotting function
"""
freqs, _, morozumi, _, _, _, _ = np.loadtxt(file1, delimiter=',',
unpack=True)
fig, ax = plt.subplots()
ax.plot(freqs, morozumi, label='Morozumi replica Re=2940, We=5.22')
ax.set_xlim(0, 1250)
ax.set_ylim(0, 100)
ax.set_title('Unfiltered data')
ax.set_xlabel('Frequencies (Hz)')
ax.set_ylabel('Growth rate (1/s)')
ax.legend()
savgol_ra = savgol_filter(morozumi, 101, 2)
fig1, ax1 = plt.subplots()
ax1.plot(freqs, savgol_ra, label='Morozumi replica Re=2940, We=5.22')
ax1.set_xlim(0, 500)
ax1.set_ylim(0, 100)
ax1.set_title('Savgol filtering (window size = 11) data')
ax1.set_xlabel('Frequencies (Hz)')
ax1.set_ylabel('Growth rate (1/s)')
ax1.legend()
def arai_velocity(Re):
g = 9.81
z_pixels = np.array([50, 100, 150, 250, 350, 450, 550, 650, 750, 800])
v = velocity_calculator(Re)
print(v)
z = z_pixels*0.02/1000
z_star = 2*g*z/(v**2)
wave_vel = v*(1+z_star)**0.5
avg = np.mean(wave_vel)
return avg
def plotting_arai(file1):
"""
Main plotting function
"""
freqs, _, control, _, _, _, _ = np.loadtxt(file1, delimiter=',',
unpack=True)
k = np.linspace(0, 3000, 10000)
sigma = 0.07
a = (2e-3)/2
rho = 1000
w_squared = ((sigma*k)/(rho*a**2))*(1-k**2*a**2)*(i1(k*a)/i0(k*a))
sqrt_w = np.sqrt(w_squared)
v = arai_velocity(1551)
wavelength = v/freqs
wavenumber = 2*np.pi/wavelength
savgol_control = savgol_filter(control, 1001, 2)
fig, ax = plt.subplots()
ax.plot(k*a, sqrt_w, label='Rayleigh')
ax.plot(wavenumber*a, savgol_control,
label='Experimental (average velocity)')
ax.set_xlim(0, 7)
ax.set_ylim(0, 100)
ax.legend()
ax.set_xlabel('ka', fontsize=16)
ax.set_ylabel('$\\omega$', fontsize=16)
def plotting_measured_wavelength(file1, file2, file3, file4):
"""
Main plotting function
"""
freqs, _, control, _, _, _, _ = np.loadtxt(file1, delimiter=',',
unpack=True)
freqs, _, control_2, _, _, _, _ = np.loadtxt(file2, delimiter=',',
unpack=True)
freqs, _, control_3, _, _, _, _ = np.loadtxt(file3, delimiter=',',
unpack=True)
freqs, _, control_4, _, _, _, _ = np.loadtxt(file4, delimiter=',',
unpack=True)
k = np.linspace(0, 7000, 10000000)
sigma = 0.07
a = 1e-3
rho = 1000
w_squared = ((sigma*k)/(rho*a**2))*(1-k**2*a**2)*(i1(k*a)/i0(k*a))
sqrt_w = np.sqrt(w_squared)
v = 1.2668032087199999
wavelength = v/freqs
wavenumber = 2*np.pi/wavelength
savgol_control = savgol_filter(control, 101, 2)
savgol_control_3 = savgol_filter(control_3, 101, 2)
fig, ax = plt.subplots()
ax.plot(k*a, sqrt_w, label='Rayleigh', color='black', linestyle='solid')
ax.plot(wavenumber*a, savgol_control, label='Morozumi and Fukai model')
ax.plot(wavenumber*a, savgol_control_3, label='Arai and Amagai model')
ax.set_xlim(0, 3.5)
ax.set_ylim(0, 100)
ax.legend()
ax.set_xlabel('ka', fontsize=16)
ax.set_ylabel('$\\omega$ (1/s)', fontsize=16)
ax.grid()
fig.set_size_inches(6, 4)
fig.savefig(fname='time_models.pgf', bbox_inches='tight')
def plotting_2file(file1, file2):
# load the two files
freqs, _, file1_axi, _, _, file1_as, _ = np.loadtxt(file1, delimiter=',',
unpack=True)
freqs, _, file2_axi, _, _, file2_as, _ = np.loadtxt(file2, delimiter=',',
unpack=True)
file1_axi_savgol = savgol_filter(file1_axi, 1001, 2)
file2_axi_savgol = savgol_filter(file2_axi, 1001, 2)
fig, ax = plt.subplots()
ax.plot(freqs, file1_axi, label='file1')
ax.plot(freqs, file2_axi, label='file2')
ax.set_title('Standard data')
ax.legend()
ax.set_xlim(0, 10000)
ax.set_ylim(0, 250)
fig1, ax1 = plt.subplots()
ax1.plot(freqs, file1_axi_savgol, label='file1')
ax1.plot(freqs, file2_axi_savgol, label='file2')
ax1.set_title('Savgol')
ax1.legend()
ax1.set_xlim(0, 1000)
ax1.set_ylim(0, 140)
fig2, ax2 = plt.subplots()
file1_as_savgol = savgol_filter(file1_as, 101, 2)
file2_as_savgol = savgol_filter(file2_as, 101, 2)
ax2.plot(freqs, file1_as_savgol, label='file1')
ax2.plot(freqs, file2_as_savgol, label='file2')
ax2.legend()
ax2.set_xlim(0, 15000)
ax2.set_ylim(0, 300)
def plotting_3file(file1, file2, file3):
# load the two files
freqs, _, file1_axi, _, _, _, _ = np.loadtxt(file1, delimiter=',',
unpack=True)
freqs, _, file2_axi, _, _, _, _ = np.loadtxt(file2, delimiter=',',
unpack=True)
freqs, _, file3_axi, _, _, _, _ = np.loadtxt(file3, delimiter=',',
unpack=True)
file1_axi_savgol = savgol_filter(file1_axi, 1001, 2)
file2_axi_savgol = savgol_filter(file2_axi, 1001, 2)
file3_axi_savgol = savgol_filter(file3_axi, 1001, 2)
fig, ax = plt.subplots()
ax.plot(freqs, file1_axi_savgol, label='file1')
ax.plot(freqs, file2_axi_savgol, label='file2')
ax.plot(freqs, file3_axi_savgol, label='file3')
ax.set_xlabel('$f$ (Hz)', fontsize=16)
ax.set_ylabel('$\\omega$ (1/s)', fontsize=16)
ax.grid()
ax.tick_params(axis='both', labelsize=12)
ax.legend()
ax.set_xlim(0, 4000)
ax.set_ylim(0, 140)
def plotting_4file(file1, file2, file3, file4):
"""
Main plotting function
"""
freqs1, _, file1_axi, _, _, file1_as, _ = np.loadtxt(file1, delimiter=',',
unpack=True)
freqs2, _, file2_axi, _, _, file2_as, _ = np.loadtxt(file2, delimiter=',',
unpack=True)
freqs3, _, file3_axi, _, _, file3_as, _ = np.loadtxt(file3, delimiter=',',
unpack=True)
freqs4, _, file4_axi, _, _, file4_as, _ = np.loadtxt(file4, delimiter=',',
unpack=True)
casename, Re, We = file_id(file1)
fig, ax = plt.subplots()
ax.plot(freqs1, file1_axi, label='$RR_G=1.5$')
ax.plot(freqs2, file2_axi, label='$RR_G=3.9$')
ax.plot(freqs3, file3_axi, label='$RR_G=6.3$')
ax.plot(freqs4, file4_axi, label='$RR_G=8.7$')
ax.set_xlim(0, 1250)
ax.set_ylim(0, 400)
ax.set_title('Unfiltered data')
ax.set_xlabel('Frequencies (Hz)')
ax.set_ylabel('Growth rate (1/s)')
ax.legend()
savgol_file1_axi = savgol_filter(file1_axi, 701, 2)
savgol_file2_axi = savgol_filter(file2_axi, 701, 2)
savgol_file3_axi = savgol_filter(file3_axi, 701, 2)
savgol_file4_axi = savgol_filter(file4_axi, 701, 2)
savgol_file1_as = savgol_filter(file1_as, 801, 2)
savgol_file2_as = savgol_filter(file2_as, 801, 2)
savgol_file3_as = savgol_filter(file3_as, 801, 2)
savgol_file4_as = savgol_filter(file4_as, 801, 2)
fig1, ax1 = plt.subplots()
ax1.plot(freqs1, savgol_file1_axi,
label='$RR_G=1.5$')
ax1.plot(freqs2, savgol_file2_axi,
label='$RR_G=3.9$')
ax1.plot(freqs3, savgol_file3_axi,
label='$RR_G=6.3$')
ax1.plot(freqs4, savgol_file4_axi,
label='$RR_G=8.7$')
ax1.set_xlim(0, 4000)
ax1.set_ylim(0, 180)
ax1.set_xlabel('$f$ (Hz)', fontsize=16)
ax1.set_ylabel('$\\omega$ (1/s)', fontsize=16)
ax1.grid()
ax1.tick_params(axis='both', labelsize=12)
ax1.legend()
We_underscored = We.split('.')[0] + '_' + We.split('.')[1]
fig1filename = str(Re) + '_' + str(We_underscored) + '_' + 'axi.pgf'
print(fig1filename)
fig1.set_size_inches(6, 4)
fig1.savefig(fname=fig1filename, bbox_inches='tight')
# ASYMMETRIC PLOTS
fig2, ax2 = plt.subplots()
ax2.plot(freqs1, savgol_file1_as, label='$RR_G=1.5$')
ax2.plot(freqs2, savgol_file2_as, label='$RR_G=3.9$')
ax2.plot(freqs3, savgol_file3_as, label='$RR_G=6.3$')
ax2.plot(freqs4, savgol_file4_as, label='$RR_G=8.7$')
ax2.set_xlim(0, 4000)
ax2.set_ylim(0, 180)
ax2.set_xlabel('$f$ (Hz)', fontsize=16)
ax2.set_ylabel('$\\omega$ (1/s)', fontsize=16)
ax2.grid()
ax2.tick_params(axis='both', labelsize=12)
ax2.legend()
fig2filename = str(Re) + '_' + str(We_underscored) + '_' + 'as.pgf'
print(fig2filename)
fig2.set_size_inches(6, 4)
fig2.savefig(fname=fig2filename, bbox_inches='tight')
def plotting_1file(file1):
# load the file
freqs, _, file1_axi, _, _, file1_as, _ = np.loadtxt(file1, delimiter=',',
unpack=True)
file1_axi_savgol = savgol_filter(file1_axi, 11, 2)
file1_axi_savgol_101 = savgol_filter(file1_axi, 101, 2)
file1_axi_savgol_1001 = savgol_filter(file1_axi, 1001, 2)
fig, ax = plt.subplots()
ax.plot(freqs, file1_axi, color='black')
ax.set_xlim(0, 1000)
ax.set_ylim(0, 90)
ax.set_xlabel('$f$ (Hz)', fontsize=16)
ax.set_ylabel('$\\omega$ (1/s)', fontsize=16)
ax.tick_params(axis='both', labelsize=12)
fig.set_size_inches(6, 4)
fig.savefig(fname='unfiltered_example.pgf', bbox_inches='tight')
fig1, ax1 = plt.subplots()
ax1.plot(freqs, file1_axi_savgol, color='black')
ax1.set_xlim(0, 1000)
ax1.set_ylim(0, 90)
ax1.set_xlabel('$f$ (Hz)', fontsize=16)
ax1.set_ylabel('$\\omega$ (1/s)', fontsize=16)
ax1.tick_params(axis='both', labelsize=12)
fig1.set_size_inches(6, 4)
fig1.savefig(fname='savgol_11_example.pgf', bbox_inches='tight')
fig2, ax2 = plt.subplots()
ax2.plot(freqs, file1_axi_savgol_101, color='black')
ax2.set_xlim(0, 1000)
ax2.set_ylim(0, 90)
ax2.set_xlabel('$f$ (Hz)', fontsize=16)
ax2.set_ylabel('$\\omega$ (1/s)', fontsize=16)
ax2.tick_params(axis='both', labelsize=12)
fig2.set_size_inches(6, 4)
fig2.savefig(fname='savgol_101_example.pgf', bbox_inches='tight')
fig3, ax3 = plt.subplots()
ax3.plot(freqs, file1_axi_savgol_1001, color='black')
ax3.set_xlim(0, 1000)
ax3.set_ylim(0, 90)
ax3.set_xlabel('$f$ (Hz)', fontsize=16)
ax3.set_ylabel('$\\omega$ (1/s)', fontsize=16)
ax3.tick_params(axis='both', labelsize=12)
fig3.set_size_inches(6, 4)
fig3.savefig(fname='savgol_1001_example.pgf', bbox_inches='tight')
print(len(freqs))
print(len(file1_axi_savgol_1001))
def example_curve_fit(filename):
(freqs, diameter_a0, diameter_growth_rates, diameter_errs, centroid_a0,
centroid_growth_rates, centroid_errs) = np.loadtxt(filename,
delimiter=',',
unpack=True)
modelling_ts = np.linspace(0, 0.02, 1000)
modelling_amps = model_growth_rate(modelling_ts, diameter_a0[600],
diameter_growth_rates[600])
fig, ax = plt.subplots()
ax.plot(modelling_ts, modelling_amps)
ax.set_xlabel('$\\frac{a}{a}$')
def morozumi_comparison(morozumi_axi_5_22, morozumi_as_5_22,
morozumi_axi_22_9, morozumi_as_22_9,
morozumi_axi_52_7, morozumi_as_52_7,
experimental_file_5_22, experimental_file_22_9):
# loading the 5.22 experimental file
(freqs_5_22, _, exp_5_22_axi, _, _,
exp_5_22_as, _) = np.loadtxt(experimental_file_5_22,
delimiter=',', unpack=True)
# loading the 22.9 experimental file
(freqs_22_9, _, exp_22_9_axi, _, _,
exp_22_9_as, _) = np.loadtxt(experimental_file_22_9,
delimiter=',', unpack=True)
# loading the morozumi axisymmetric 5.22 data file
(morozumi_axi_5_22_freqs,
moro_axi_5_22_growth_rates) = np.loadtxt(morozumi_axi_5_22,
delimiter=',', unpack=True)
# loading the morozumi asymmteric 5.22 data file
(morozumi_as_5_22_freqs,
moro_as_5_22_growth_rates) = np.loadtxt(morozumi_as_5_22,
delimiter=',', unpack=True)
# loading the morozumi axisymmetric 22.9 data file
(morozumi_axi_22_9_freqs,
moro_axi_22_9_growth_rates) = np.loadtxt(morozumi_axi_22_9,
delimiter=',', unpack=True)
# loading the morozumi asymmteric 22.9 data file
(morozumi_as_22_9_freqs,
moro_as_22_9_growth_rates) = np.loadtxt(morozumi_as_22_9,
delimiter=',', unpack=True)
# loading the morozumi axisymmetric 52.7 data file
(morozumi_axi_52_7_freqs,
moro_axi_52_7_growth_rates) = np.loadtxt(morozumi_axi_52_7,
delimiter=',', unpack=True)
# loading the morozumi asymmteric 52.7 data file
(morozumi_as_52_7_freqs,
moro_as_52_7_growth_rates) = np.loadtxt(morozumi_as_52_7,
delimiter=',', unpack=True)
# performing savgol filtering on both the axisymmetric and asymmetric 5.22
# experimental files
savgol_axi_5_22 = savgol_filter(exp_5_22_axi, 101, 2)
savgol_as_5_22 = savgol_filter(exp_5_22_as, 101, 2)
# performing savgol filtering on both the axisymmetric and asymmetric 22.9
# experimental files
savgol_axi_22_9 = savgol_filter(exp_22_9_axi, 101, 2)
savgol_as_22_9 = savgol_filter(exp_22_9_as, 101, 2)
# setting up the plots
fig, ax = plt.subplots()
ax.plot(freqs_5_22, savgol_axi_5_22,
label='Experimental data $\\mathrm{We}_\\mathrm{g}=5.22$',
color='black', linewidth=1)
ax.plot(freqs_22_9, savgol_axi_22_9,
label='Experimental data $\\mathrm{We}_\\mathrm{g}=22.9$',
color='black', linestyle='dotted', linewidth=1)
ax.plot(morozumi_axi_5_22_freqs, moro_axi_5_22_growth_rates,
label='Morozumi and Fukai $\\mathrm{We}_\\mathrm{g}=5.22$',
marker='o', markevery=10, markersize=7, color='black')
ax.plot(morozumi_axi_22_9_freqs, moro_axi_22_9_growth_rates,
label='Morozumi and Fukai $\\mathrm{We}_\\mathrm{g}=22.9$',
marker='s', markevery=10, markersize=7, color='black')
ax.plot(morozumi_axi_52_7_freqs, moro_axi_52_7_growth_rates,
label='Morozumi and Fukai $\\mathrm{We}_\\mathrm{g}=52.7$',
marker='^', markevery=10, markersize=7, color='black')
ax.set_xlim(0, 1000)
ax.set_ylim(-20, 220)
ax.legend(fontsize=8)
ax.set_xlabel('$f$ (Hz)', fontsize=14)
ax.set_ylabel('$\\omega$ (1/s)', fontsize=14)
ax.tick_params(axis='both', labelsize=12)
fig.set_size_inches(6, 6)
fig.savefig(fname='morozumi_axi_comparison.pgf', bbox_inches='tight')
fig1, ax1 = plt.subplots()
ax1.plot(freqs_5_22, savgol_as_5_22,
label='Experimental data $\\mathrm{We}_\\mathrm{g}=5.22$',
color='black', linewidth=1)
ax1.plot(freqs_22_9, savgol_as_22_9,
label='Experimental data $\\mathrm{We}_\\mathrm{g}=22.9$',
color='black', linestyle='dotted', linewidth=1)
ax1.plot(morozumi_as_5_22_freqs, moro_as_5_22_growth_rates,
label='Morozumi and Fukai $\\mathrm{We}_\\mathrm{g}=5.22$',
marker='o', markevery=10, markersize=7, color='black')
ax1.plot(morozumi_as_22_9_freqs, moro_as_22_9_growth_rates,
label='Morozumi and Fukai $\\mathrm{We}_\\mathrm{g}=22.9$',
marker='s', markevery=10, markersize=7, color='black')
ax1.plot(morozumi_as_52_7_freqs, moro_as_52_7_growth_rates,
label='Morozumi and Fukai $\\mathrm{We}_\\mathrm{g}=52.7$',
marker='^', markevery=10, markersize=7, color='black')
ax1.legend()
ax1.set_xlim(0, 800)
ax1.set_ylim(0, 200)
ax1.legend(fontsize=8)
ax1.set_xlabel('$f$ (Hz)', fontsize=16)
ax1.set_ylabel('$\\omega$ (1/s)', fontsize=16)
ax1.tick_params(axis='both', labelsize=12)
fig1.set_size_inches(6, 6)
fig1.savefig(fname='morozumi_as_comparison.pgf', bbox_inches='tight')