Resonant Three-Wave Interactions and an Application to Solar G Mode Oscillations

Abstract

We present here some initial results of a long-term investigation of resonant three-wave interactions in the solar interior, which indicate that these nonlinear interactions take place in the sun and are, in fact, responsible for the observed g mode spectrum. Resonant three-wave interactions, as the name implies, involve the coupled interaction of three waves which satisfy the resonant condition where ω 0 , and ω 1 are the frequencies of the three waves. Two of the waves, mode 0 and 1 for example, couple together to produce a third beat wave which has a frequency equal to the frequency difference of the first two waves. This wave is normally very weak. If its frequency happens to equal the frequency of an oscillation mode of the sun, the wave can be pumped by resonance to very large amplitudes. In the sun, resonant interactions would take place if three natural oscillation modes of the sun satisfy the resonance condition.