The effects of propagation of a short internal gravity wave through an inertia wave on internal wave stability is analyzed and parameterized. The interactions are specifically between a short wave packet and a large inertia wave packet. The short wave packet is a wave bounded with a Gaussian envelope with high frequencies and scales in the hundreds of meters horizontally and tens of meters vertically. The inertia wave packet is also an enveloped wave but with frequencies close to the rotation of the earth and scales in the thousands of meters in the horizontal and hundreds of meters in the vertical. The wave-wave interactions are modeled using ray theory and 2d non-linear numerical models. Ray tracing is used because it is less computationally expensive, however it fails at regions of strong refraction also known as caustics. To measure stability the steepness is calculated from the 2d non-linear methods and it is compared with estimates found in the linear theory. It is determined that the estimates of the short wave steepness from linear theory are qualitatively comparable. A quantifiable comparison, although more difficult, resulted in adjustment factors to the ray tracing results. It is also found that for the particular cases modeled, convective instabilities are predominant and the influence of the shear exerted by the large inertia wave is insignificant. Instability time scales are included in the stability analysis and estimates of overturning and wave-breaking are developed for different wave-wave interactions. From the stability analysis it is found that in general the faster the short wave propagates the more likely it is to conform to both of the conditions required for wave breaking (i.e presence of instabilities and instability time scales longer than the timescale of the short wave).



College and Department

Ira A. Fulton College of Engineering and Technology; Mechanical Engineering



Date Submitted


Document Type





Internal gravity waves instability, oceanic energy dissipation, stratified fluids, Leonardo Latorre, Julie Vanderhoff