116 | | It is good to see that the spectra agree quite well at resolved wave lengths and that with each additional level of data, you extend the spectra to higher wave numbers. Also the rise at the end of the spectra (as well as the smaller one to the left) coincide with the maximum resolvable wavelength which coincides with the cell size of the next coarser grid. Regions that have gradients but are not resolved to the finest level will have a stair-step signal, where each step has 2 points (or 4, or 8 points). This will lead to power with wavelengths corresponding to the nyquist frequency, or twice, four times, etc... On the first frame - the only place where there are gradients that are not completely refined - are at the edges of the colliding flow - where there is a good amount of shear. This is verified below where the initial spike at the nyquist frequency is dominated by solenoidal terms and not compressive terms. |
| 116 | It is good to see that the spectra agree quite well at resolved wave lengths and that with each additional level of data, you extend the spectra to higher wave numbers. Also the rise at the end of the spectra (as well as the smaller one to the left) coincide with the maximum resolvable wavelength which coincides with the cell size of the next coarser grid. Regions that have gradients but are not resolved to the finest level will have a stair-step signal, where each step has 2 points (or 4, or 8 points). This will lead to power with wavelengths corresponding to the nyquist frequency, or twice, four times, etc... On the first frame - the only place where there are gradients that are not completely refined - are at the edges of the colliding flow (circled below) - where there is a good amount of shear. This is verified below where the initial spike at the nyquist frequency is dominated by solenoidal terms and not compressive terms. |
124 | | Below were taken from a region 80x80x20 with a radial cosine window (ellipsoid) |
125 | | so it includes shear with ambient... Also the fact that the box is not cubic - leads to different wavenumbers (normalized to the longest mode 80 pc). While the ky and kz wavenumbers go like 1, 2, 3, 4... the kx wave numbers go like 4, 8, 12, 16, and so on... This means that if we sample radial bins with a width of 1, we will have over sampling the kx modes - which leads to the sawtooth pattern that was not seen above. |
| 124 | The following were taken from a region 80x80x20 with a radial cosine window (ellipsoid) |
| 125 | so it includes shear with ambient... Also the fact that the box is not cubic - leads to different wavenumbers (normalized to the longest mode 80 pc). While the ky and kz wavenumbers go like 1, 2, 3, 4... the kx wave numbers go like 4, 8, 12, 16, and so on... This means that if we sample radial bins with a width of 1, we will have over sampling the kx modes - which leads to the sawtooth pattern that was not seen above. This can be corrected if we switch to a 40x40x40 window. |