LOCATION OF 2 1 RESONANCES IN COMPLEX DISPERSION RELATIONSHIPS/

If a system can support two (or more) waves where the frequency and wa venumber of one are twice those of the other, then the waves resonate. In non-conservative systems this can enhance the energy transfer betw een the wave and its medium, and leads to types of nonlinear interacti on not found for non-resonant waves. In this paper a method is present ed for locating resonant conditions. The method is particularly well s uited to cases where there are several branches of the dispersion rela tionship and when the dispersion relation is computationally expensive to calculate, e.g. shear layers at high Reynolds numbers. It has also been tested on capillary-gravity waves where it is shown to give accu rate results not only for the 2:1 resonance but also n:1 resonances wh ere n can become quite large.