Internal gravity waves are abundant in stably-stratified fluids as our inertial waves in rotating flows. Rotating, stratified fluids have internal-inertial gravity waves. These waves are important in transporting momentum and energy. These waves appear spontaneously in astrophysical accretion disks and protoplanetary disks. A subset of this class of waves form critical layers. In the dissipationless limit, the velocity and/or density in these layers is singular. Although these waves have been studied for almost 100 years, there are gaps in our knowledge. When two columnated beams of inertial and/or gravity waves intersect they produce harmonic beams with one harmonic having a temporal frequency equal to the sum of the incoming beams and the other equal to their difference. A compact disturbance in a rotating and/or stratified flow will produce four beams of waves, or a St Andrews cross, emanating from the source. The angles of the beams depend upon the temporal frequency of the disturbance. It had been assumed that when two incoming beams collide, their intersection, which contains two temporal frequencies, would produce two St Andrews crosses for a total of 8 out-going beams. Numerical simulations and recent laboratory experiments show that no more than 3 outgoing beams are ever created at the intersection of two incoming beams. Our work provides analytic selection rules that successfully predict how many outgoing beams are produced by the collision of two incoming beams and also correctly predicts their frequencies and directions.

**Relevant Research:**

(2009) Selection Rules for the Nonlinear Interaction of Internal Gravity Waves, Physical Review Letters 102(12), p. 124502, APS, pdf, doi:10.1103/PhysRevLett.102.124502

(2006) A 3D spectral anelastic hydrodynamic code for shearing, stratified flows, Journal of Computational Physics 219(1), p. 21-46, pdf, doi:10.1016/j.jcp.2006.03.015

(2005) Three‐dimensional Vortices in Stratified Protoplanetary Disks, The Astrophysical Journal 623(2), p. 1157-1170, pdf, doi:10.1086/428639

*Abstracts*

(2010) Dust Settling in Protoplanetary Disks and the Onset of Kelvin-Helmholtz Instability, APS Division of Fluid Dynamics Meeting Abstracts 63, p. CV-009, pdf

(2010) Selection Rules for Internal Gravity Waves and Inertial Waves, APS Division of Fluid Dynamics Meeting Abstracts 63, p. CZ-004, pdf

(2008) A New Branch of Internal Inertial-Gravity Waves in Rotating Flows: Interactions, Selection Rules, Refraction and Roll-Up into Vortices, APS Division of Fluid Dynamics Meeting Abstracts 61, p. GH-008, pdf

(2007) Generation of Vortices from Internal Gravity Waves, APS Division of Fluid Dynamics Meeting Abstracts 60, p. NL-002, pdf