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Extra resources for A note on the existence of H-bubbles via perturbation methods
At the lateral boundaries non-reflecting boundary conditions were used. 1. 3 the eigenfunctions are shown for the two cases, where ˆ· denotes the complex eigenfunction for the respective variable. Normalization was achieved such that max(|ˆ u1 |) = 1. For the tests the box size was chosen so that it exactly contained one wavelength of the instability mode. The modal energy of this mode was computed as E(1, 0) = u1 (nκ,1 = 1, nκ,3 = 0) u∗1 (nκ,1 = 1, nκ,3 = 0) . 11) Here, u1 (nκ,1 , nκ,3 ) denotes the spatial Fourier transform of the downi )Bi ) and ·∗ denotes stream velocity (wavenumbers κ1 , κ3 , nκ,i = (κ2π the complex conjugate.
Again we plot mean the flow data in the jet center-planes (x2 = 0 and x3 = 0) at 9 different equidistant downstream stations, where the inflow plane corresponds to the first graph shown. 61L2/2. Due to the mean flow symmetry it is sufficient to plot the profiles only on the positive x2 − and x3 − semi-axes. 5 the mean profiles of the density and the downstream and cross-stream velocity components are shown. The density profiles of the two simulations match rather well. The velocity profiles of the LES capture the main characteristics of the DNS data quite well.
In the lateral directions at the second point of the computational boundary, condition 4 is discarded and the coefficients are determined using K = 3 with also a one-sided four-point stencil. In boundary-normal direction at the boundary grid points no filtering is applied at all boundaries. 5 was the subject of investigation. Unless specified otherwise, reference quantities are the jet center velocity udj , the dimension Ld2 /2, the density ρdj and the temperature Tjd . The index ·j denotes jet center quantities.