We present direct numerical simulations of planar intrusions from a constant source into a linearly stratified ambient fluid for Reynolds numbers between 200 and 5000, inlet widths W 2. 2 Q/N and ambient layer thicknesses Hₐ between W and 20 Q/N, where Q is the supply rate (area per unit time) and N is the buoyancy frequency. Across this broad parameter space, the intrusions form a universal self-similar shape with a constant thickness of approximately 2. 2 Q/N at the source tapering towards a tip that propagates at a constant speed of approximately 0. 7 NQ. This broad-scale structure does not change regardless of whether the intrusions are subcritical or supercritical relative to internal waves. The perturbations to the ambient resulting from the intrusive flow appear as a near-universal uplift/depression of isopycnals immediately above/below the intrusion, upstream blocking ahead of the intrusion and, for subcritical intrusions, columnar disturbances. A moderate-amplitude wave train is also formed on the surface of subcritical intrusions. This appears at approximately the mid-length of the intrusion, with the waves propagating towards the tip. We also compare our results with the solution of the Mei shallow-water model. The comparison is poor and we rederive the model, carefully examining the underlying assumptions against the simulation data. The only assumption that is violated is that the ambient density is unperturbed. We present extensions to the model allowing for a density perturbation based on (i) simple data fits and (ii) a solution to the Dubreil-Jacotin–Long equation for shallow ambients. These significantly improve the predictive ability of the model for this geometry.
Vu et al. (Mon,) studied this question.