The analysis of the results of these simulations to find the growth rates of the KH modes is not trivial. First the velocity perpendicular to the jet axis was averaged over 1 jet radius at a particular time. A Fourier transform of the resulting data was performed and the power contained in the wavelengths of the initial perturbation were recorded. This was done at several times during the simulation and these powers were used to derive growth rates.
The averaging process described above was carried out to reduce the effect of the different distributions of amplitude of the KH modes across the jet radius. The signal at a particular wavelength from a single row of cells parallel to the jet axis will change with distance from the axis. This signal will be given by a complicated weighted mean of the modes present. The weighting associated with a particular mode is determined by the distribution of the disturbance due to that mode across the jet. Thus, for example, if we take a row of cells located very close to the edge of the jet, the signal we receive will be biased towards surface modes. If we locate the row of cells a distance of from the jet axis the signal we will receive may be modified significantly by the presence of body modes. Averaging gives a better representation of the overall growth of the instability.
It is important to note that the averaging process described above has the effect of reducing the signal from surface modes. The growth rates calculated on the basis of this averaging will be a weighted mean of the modes present at the wavelength in question, with the lower radial index modes being more heavily weighted.
Several tests were performed using this averaging technique for the growth of the KH instability in an adiabatic jet with a Mach number of 10 and density ratio of 1. The derived growth rates were within 20% of those predicted by linear analysis where only one mode was present. If more than one mode was present, the derived growth rates at a particular wavelength lay between the growth rates predicted from theory for the modes present at that wavelength, as expected.
© European Southern Observatory (ESO) 1998
Online publication: March 3, 1998