The analysis is extended to more depth ranges and we compute
MPTRCMPTRC in 100 m bins. The depth of the bin with the highest tracer mass gives ZPTRCZPTRC which is plotted against ΔPEΔPE in Fig. 14. The correlation between ΔPEΔPE and ZPTRCZPTRC (black bullets) shows very little scatter and indicates a functional relationship Y-27632 ic50 between the potential energy gain and the depth of penetration. With increasing potential energy in the system the plume is capable of first breaching the 200 m then the 500 m density interface in the ambient water. The abrupt transition from arrested ( ZPTRC≈500m) to piercing ( ZPTRC≈1500m) can be explained by the lack of stratification in the bottom layer. In most experiments where the plume breaches the AW-NSDW interface it also continues to the bottom of the slope after flowing through a homogenous layer of NSDW. Using the buoyancy flux of a density current, a concept similar to the flux of potential energy, Wells and Nadarajah (2009) reported a functional dependence between the intrusion depth
Z selleck chemical of a density current and the geostrophic buoyancy flux Bgeo=g′VNofhBgeo=g′VNofh (where h is the initial height of the flow from a line source), the entrainment ratio E and the ambient buoyancy frequency N as Z∼E-13Bgeo13/N. However, their results are not readily applicable to our model which has non-linear ambient stratification with sharp density interfaces causing N to ever vary during the plume’s descent. Neither is E constant during our experiments. In Fig. 14 we also
plot the plume height hFhF (red stars) against the potential energy gain ΔPEΔPE. It shows high hFhF in runs with low ΔPEΔPE (those runs where the plume is arrested in the Atlantic Layer), and a low hFhF in high-ΔPEΔPE runs when the plume spends little time transiting the AW and flows straight through to the NSDW layer. The slow but steady rise in PE in Fig. 12 may suggest that any addition, however slow, of dense water (and thus potential energy) could eventually lead to the piercing regime if the initial SFOW density is greater than the density of the bottom layer (which is the case in our setup for S > 34.85). Under this assumption the ΔPEΔPE-axis in Fig. 14 can be taken as a proxy for time. As time progresses (and ΔPEΔPE increases) the entrainment ratio E reduces (i.e. hFhF shrinks) as the plume moves from the Atlantic Layer into the deep NSDW layer. When a certain threshold is passed, the plume has modified the ambient water sufficiently such that subsequent overflow waters pass through the AW relatively unimpeded (with less dilution) and penetrate into the deep waters. There is a caveat though, which works against the plume’s piercing ability.