Power spectra and time-averaging

Spectrum calculation (afid_spectra)

The module afid_spectra is used to compute and store power spectra from the simulation fields. Since the computation of two-dimensional Fourier transforms involves the expensive operation of transposing the global 3-D arrays, spectra are not calculated by default. This option is activated by including a file spectra.in in the simulation directory that specifies the time from which spectra should be calculated.

Fourier transforms are performed in the y and z directions in CalcFourierCoef to produce the discretized equivalent of the three-dimensional array

\[ \hat{f}(x,k_y, k_z) = \iint f(x,y,z) e^{-i (k_y y + k_z z)} \,\mathrm{d}y \,\mathrm{d}z \]

Currently, the power spectra \(\Phi_{ff}=|\hat{f}|^2\) of the three velocity components vx, vy, vz and temperature temp are computed and stored along with the co-spectrum \(\Phi_{u\theta}=\hat{S}^* \hat{u}\) of the wall-normal concentration flux. Each spectrum is computed at each time step and integrated in time to provide a final time-averaged three-dimensional spectrum that is written to outputdir by WriteSpectra.

Time-averaged fields (afid_averaging)

A similar procedure is followed by the module afid_averaging to provide three-dimensional fields of time-averaged variables. The same input file spectra.in is needed to activate this operation, and the averaging occurs from the time specified in the input file. The subroutine UpdateTemporalAverages integrates the four basic variables in time at each time step to construct the temporal averages. The time-averaged fields are eventually written to outputdir/fields/xx_mean.h5.