Selection Rules for the Nonlinear Interaction of Internal Gravity Waves

Two intersecting beams of internal gravity waves will generically create two wave packets by nonlinear interaction. The frequency of one packet will be the sum and that of the other packet will be the difference of the frequencies of the intersecting beams. In principle, each packet should form an "X" pattern, or "St. Andrew's cross" consisting of four beams outgoing from the point of intersection. Here we derive selection rules and show that most of the expected nonlinear beams are forbidden. These rules can also be applied to the reflection of a beam from a boundary.