velocity
========
This is a module designed to process a 2D/3D+1 velocity field with focus on turbulence research. 

Basic features:
- energy, enstrophy, vorticity fields
- energy spectra
- n-th order structure functions
- two-point velocity autocorrelations
- dissipation rate estimation
- length scales: integral scales, Taylor micro scales, Kolmogorov scales
- Reynolds numbers: turbulent Re, Taylor Re

Features to be added in sight:
- probabilistic moments (skewness, kurtosis, ...) 
- triple-point velocity autocorrelations


Philosophy: 
Prepare a velocity field array "udata". 
Then, pass it to a method in this module to obtain any quantities related to turbulence.
It should require a single line to obtain the desired quantity from a velocity field
unless intermediate steps to obtain the quantity are computationally expensive. 
The primary example is an autocorrelation function which is used for various quantities like Taylor microscale. 


udata = (ux, uy, uz) or (ux, uy)
each ui has a shape (height, width, (depth), duration)

If ui-s are individually given, make udata like 
udata = np.stack((ux, uy))

Overview
--------

.. currentmodule:: ilpm.velocity

.. autosummary:: 
    get_duidxj_tensor
    decompose_duidxj
    reynolds_decomposition
    div
    curl
    curl_2d
    get_energy
    get_enstrophy
    get_time_avg_energy
    get_time_avg_enstrophy
    get_spatial_avg_energy
    get_spatial_avg_enstrophy
    get_turbulence_intensity_local
    fft_nd
    get_energy_spectrum_nd
    get_energy_spectrum
    get_1d_energy_spectrum
    get_dissipation_spectrum
    get_rescaled_energy_spectrum
    get_1d_rescaled_energy_spectrum
    get_rescaled_dissipation_spectrum
    scale_energy_spectrum
    get_large_scale_vel_field
    get_epsilon_using_sij
    get_epsilon_iso
    get_epsilon_using_diss_spectrum
    get_epsilon_using_struc_func
    compute_spatial_autocorr
    compute_spatial_autocorr3d
    get_two_point_vel_corr_iso
    get_autocorr_functions
    get_autocorr_functions_int_list
    get_autocorrelation_tensor_iso
    get_structure_function_long
    get_structure_function
    scale_raw_structure_funciton_long
    remove_nans_for_array_pair
    get_taylor_microscales
    get_taylor_microscales_iso
    get_integral_scales
    get_integral_scales_using_rij
    get_integral_scales_iso_spec
    get_integral_scale_large_eddy
    get_integral_velocity_scale
    get_integral_scales_all
    get_taylor_microscales_all
    get_kolmogorov_scales_all
    get_turbulence_re
    get_taylor_re
    rankine_vortex_2d
    rankine_vortex_line_3d
    get_sample_turb_field_3d
    get_rescaled_energy_spectrum_saddoughi
    get_energy_spectra_jhtd
    get_rescaled_energy_spectra_jhtd
    get_rescaled_structure_function_saddoughi
    get_window_radial
    compute_signal_loss_due_to_windowing
    get_hamming_window_radial
    clean_udata_cheap
    get_mask_for_unphysical
    fill_unphysical_with_sth
    clean_udata
    fix_udata_shape
    get_hamming_window_radial
    get_equally_spaced_grid
    get_equally_spaced_kgrid
    kolmogorov_53
    kolmogorov_53_uni
    compute_kolmogorov_lengthscale_simple
    get_characteristic_velocity
    klonecker_delta
    cart2pol
    cart2sph
    natural_sort

Classes and Functions
---------------------
   
.. automodule:: ilpm.velocity
    :members: 
    :show-inheritance: