Two-dimensional internal gravity wave beam instability

The instability of propagating internal gravity waves is of long-standing interest in geophysical fluid dynamics since breaking gravity waves exchange energy and momentum with the large-scale flow and hence support the large-scale circulation. In this study a low-order gravity wave beam model is used to delineate the linear stability of wave beams and also to study subcritical non-modal transient instability. Assuming that the dissipation of the linearly unstable beam equilibrates with the small-scale turbulence, the model explains the constancy with the height of the amplitude of the wave beam, so that oblique wave beams can reach significant altitudes without disintegrating due to the instability that arises [1]. We further study the robustness of the transient growth when the initial condition for optimal growth is randomly perturbed [2]. It is concluded that for full randomization, in particular, shallow wave beams can show subcritical growth when entering a turbulent background field. Such growing and eventually breaking wave beams might add turbulence to existing background turbulence that originates from other sources of instability.

[1] Kurgansky and Harlander (2021) Two-dimensional internal gravity wave beam instability. Part I: Linear theory, submitted.

[2] Harlander and Kurgansky (2021) Two-dimensional internal gravity wave beam instability. Part II: Subcritical instability, submitted.