# Fig. 6: Flapping frequency map — f_flap/f_turb vs f_nat/f_turb
# Main result of the paper: two regimes separated at f_nat/f_turb ~ 1.
#   Horizontal branch (f_nat/f_turb << 1): f_flap ~ f_turb (fiber follows flow)
#   Ascending branch  (f_nat/f_turb >> 1): f_flap ~ f_nat  (fiber oscillates naturally)
# f_turb = 0.5 Ub/H for all cases at Re=5600; same f_turb used for Re=10000 scaling.
# Error bars: variation in f_flap when halving the time history.
# 
# Each series contributes 3 columns: fnat_over_fturb, fflap_over_fturb, yerr
# Series descriptions:
#   case1_std: h/H=0.5, rho_s/rho_f=1.08, Re=5600
#   case1_HR: h/H=0.5, rho_s/rho_f=1.08, Re=5600, high-res grid
#   case2_std: h/H=0.5, rho_s/rho_f=1.8, Re=5600
#   case2_HR: h/H=0.5, rho_s/rho_f=1.8, Re=5600, high-res grid
#   case3_std: h/H=0.25, rho_s/rho_f=1.08, Re=5600
#   case3_HRe: h/H=0.25, rho_s/rho_f=1.08, Re=10000
#   case4_std: h/H=0.125, rho_s/rho_f=1.08, Re=5600
# 
# Reference lines (not columns — defined by 2 endpoints each):
#   Ascending branch  (dash-dot): fnat/fturb in [1.00e+00, 2.00e+02], fflap/fturb = fnat/fturb
#   Horizontal branch (dashed):   fnat/fturb in [5.00e-03, 1.00e+00], fflap/fturb = 1.0
# 
# Rows beyond a series length are filled with NaN.
# 
# fnat_over_fturb_case1_std	fflap_over_fturb_case1_std	yerr_case1_std	fnat_over_fturb_case1_HR	fflap_over_fturb_case1_HR	yerr_case1_HR	fnat_over_fturb_case2_std	fflap_over_fturb_case2_std	yerr_case2_std	fnat_over_fturb_case2_HR	fflap_over_fturb_case2_HR	yerr_case2_HR	fnat_over_fturb_case3_std	fflap_over_fturb_case3_std	yerr_case3_std	fnat_over_fturb_case3_HRe	fflap_over_fturb_case3_HRe	yerr_case3_HRe	fnat_over_fturb_case4_std	fflap_over_fturb_case4_std	yerr_case4_std
3.843502e+00	3.600000e+00	6.666667e-02	6.956252e+01	8.160000e+01	0.000000e+00	2.980081e+00	2.653333e+00	4.000000e-02	1.234909e+01	1.400000e+01	8.000000e-01	4.861689e+01	5.746667e+01	4.800000e-01	1.076473e+01	8.240000e+00	0.000000e+00	6.149604e+00	4.506667e+00	1.733333e-01
1.215422e+00	1.826667e+00	1.333333e-01	2.199760e+01	2.540000e+01	1.800000e+00	9.423845e-01	1.453333e+00	4.000000e-02	nan	nan	nan	1.537401e+01	1.982667e+01	3.200000e-01	3.404105e+00	4.040000e+00	0.000000e+00	1.944675e+00	2.626667e+00	8.133333e-01
3.843502e-01	8.400000e-01	3.333333e-01	nan	nan	nan	2.980081e-01	1.400000e+00	1.466667e-01	nan	nan	nan	4.861689e+00	4.613333e+00	1.866667e-01	1.076473e+00	1.560000e+00	0.000000e+00	6.149604e-01	1.146667e+00	2.666667e-02
1.215422e-01	9.333333e-01	0.000000e+00	nan	nan	nan	9.423845e-02	1.306667e+00	3.733333e-01	nan	nan	nan	1.537401e+00	1.826667e+00	8.000000e-02	3.404105e-01	1.040000e+00	4.400000e-01	1.944675e-01	1.120000e+00	2.800000e-01
3.843502e-02	9.600000e-01	1.333333e-01	nan	nan	nan	2.980081e-02	1.266667e+00	4.533333e-01	nan	nan	nan	4.861689e-01	1.200000e+00	6.666667e-02	1.076473e-01	9.600000e-01	0.000000e+00	nan	nan	nan
1.215422e-02	7.600000e-01	3.200000e-01	nan	nan	nan	9.423845e-03	8.400000e-01	2.533333e-01	nan	nan	nan	1.537401e-01	1.066667e+00	0.000000e+00	nan	nan	nan	nan	nan	nan
nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	nan	4.861689e-02	1.080000e+00	2.266667e-01	nan	nan	nan	nan	nan	nan