The Fluid Dynamics of Intrusions

We consider intrusions generated by a constant source in a linearly stratified ambient layer at the level of neutral buoyancy. Our analysis focuses on 2D and 3D numerical simulations of the Navier-Stokes equations under the Boussinesq approximation. For sufficiently wide sources, the intrusion profiles exhibit a universal form across parameter space with a remarkably clear self-similar collapse, although they do not match the solutions of existing shallow-water models. The robustness across the parameter space suggests that the dominant effects controlling the flow may be more readily identified in this geometry, providing valuable insights for improving reduced-order models.

In contrast, for narrower, jet-like sources a prominent vortex ring is produced, followed by a profile that displays symmetry breaking and significant entrainment. However, the long-term behaviour is universal for sufficiently large ambient heights. Additionally, we observe the generation of non-linear internal waves travelling ahead of the intrusions and alongside them, which correlate with large-amplitude surface oscillations at the interface. We conduct a stability analysis to understand how these wave modes are generated and how they interact with one another. This analysis will enhance our understanding of the nature of the waves and the importance of stratification on the intrusion profiles. This will help us understand the nature of the waves and the importance of stratification on the intrusion profiles.