## The long-term circulation driven by density currents in a two-layer stratified basin.(English)Zbl 1106.76340

Summary: Experimentation and theory are used to study the long-term dynamics of a two-dimensional density current flowing into a two-layer stratified basin. When the initial Richardson number, $$Ri_{\rho}^{in}$$, characterizing the ratio of the background stratification to the buoyancy flux of the density current, is less than the critical value of $$Ri_{\rho}^{*}= 21-27$$, it is found that the density current penetrates the stratified interface. This result is ostensibly independent of slope for angles between $$30^{\circ}$$ and $$90^{\circ}$$. If the current does not initially penetrate the interface, then it slowly increases the density of the top layer until the interfacial density difference is reduced sufficiently to drive penetration. The time scale for this to occur, $$t_{p}= (Ri^{in}_{\rho} - Ri_{\rho}^{*}) L/B^{1/3}$$, is explicitly a function of the buoyancy flux $$B$$ and the length of the basin $$L$$. The initial Richardson number, $$Ri^{in}_{\rho}$$, is a function of depth, the initial reduced gravity of the interface and a weak function of slope angle. In the absence of initial penetration for very steep slopes of $$75^{\circ}$$ and $$90^{\circ}$$, we observe that penetrative convection at the interface leads to significant local entrainment. In consequence, the top layer thickens and the interfacial entrainment rate increases as the fifth power of the interfacial Froude number. In contrast, such a process is not observed at comparable interfacial Froude numbers on lower slopes of $$30^{\circ}$$, $$45^{\circ}$$ and $$60^{\circ}$$, thereby demonstrating the important role of impact angle on penetrative convection. We attribute the increased interfacial entrainment by the steep density currents as the result of the transition from an undular bore to a turbulent hydraulic jump at the point where the density current intrudes. We discuss the applicability of the observed circulation to the stability of the Arctic halocline where we find $$0.56\lesssim t_{p}\lesssim1.2$$ years for a range of contemporary oceanographic conditions.

### MSC:

 76B70 Stratification effects in inviscid fluids 76-05 Experimental work for problems pertaining to fluid mechanics

### Keywords:

Richardson number,; interfacial Froude number
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