Turbulence

3D_energy_spectra_demo

This Python script, calculates 3D energy spectra. For this purpose, velocity component $(u, v, w)$ should be available in a structured grid in a volume. Here, an artificial isotropic and homogeneous velocity field is created for demo. fftn, which calculates discrete Fourier coefficients in n-dimension, is used to obtain the energy spectra. By this point, the energy spectra is a function of $\vec{K}$. Using this relation
$E(k) = \oint \frac{1}{2} E_{ii}(\vec{K}) dS(k) $,
the spectra can be defined as a function of scalar wave numer $k$. Scalar k equals to $(K_{i}^2)^{1/2}$, ans $S(k)$ represent the surface area of an sphere of radius $k$.
Parameters:
L = domain width
dim = sampling resolution

3D_Energy_Spectra_DNS

In this script, the DNS results of isotropic turbulence in a triply-periodic cube [Cardesa et al., Science 2017] is used. A snapshot is loaded which provide the fft coeffecients of $u$,$v$, and $w$. The snapshots are accessible at http://hal.dmt.upm.es/raw_database/Isotropic/Re315ForcedTimeRes/snapshots/
The code used to read data is provided by the DNS developers (#Alberto Vela-Martin, 2017).