Rapid Distortion Power Spectra

drdmannturb.spectra_fitting.power_spectra_rdt.PowerSpectraRDT()

Classical rapid distortion spectra, which is the solution to

\[\frac{\bar{D} \mathrm{~d} Z_j(\boldsymbol{k}, t)}{\bar{D} t}=\frac{\partial U_{\ell}}{\partial x_k}\left(2 \frac{k_j k_{\ell}}{k^2}-\delta_{j \ell}\right) \mathrm{d} Z_k(\boldsymbol{k}, t)\]

given by

\[\mathrm{d} \mathbf{Z}(\boldsymbol{k}(t), t)=\boldsymbol{D}_\tau(\boldsymbol{k}) \mathrm{d} \mathbf{Z}\left(\boldsymbol{k}_0, 0\right).\]

Refer to the original DRD paper, Section III, subsection B for a full expansion.

Parameters:

• k (torch.Tensor) – Wave vector domain.

• beta (torch.Tensor) – Evaluated eddy lifetime function.

• E0 (torch.Tensor) – Evaluated and non-dimensionalized von Karman energy spectrum.

Returns:

tuple[Tensor, Tensor, Tensor, Tensor, Tensor, Tensor] – 6-tuple of the components of the velocity-spectrum tensor in the order: \(\Phi_{11}, \Phi_{22}, \Phi_{33}, \Phi_{13}, \Phi_{12}, \Phi_{23}\).